This document summarizes research on generating micron- and nanosize liquid droplets using surface acoustic waves (SAWs). SAWs produce localized acoustic and electric Maxwell pressures near the contact line between a liquid drop and solid substrate. These pressures generate two sequences of self-similar hemispherical satellite droplets at different scales. The acoustic pressure dominates when the film thickness exceeds one-quarter the SAW wavelength and affects the mother drop shape and stability. The Maxwell pressure of nanodrops exceeds ten atmospheres and is sensitive to contact angle. Scaling theories are presented to explain how acoustic and Maxwell pressures govern droplet sizes.
Voyager 2 plasma observations of the heliopauseFelipe Hime
The document describes observations from the Voyager 2 spacecraft of plasma properties at and near the heliopause (HP), which separates the solar wind from the very local interstellar medium (VLISM). Key findings include:
1) Voyager 2 observed a plasma boundary region starting 1.5 au before the HP, where the plasma slowed down, heated up, and doubled in density compared to typical heliosheath plasma.
2) Just inside the HP, a thinner boundary layer was observed over 0.06 au where the radial speed decreased and density and magnetic field increased.
3) In the VLISM beyond the HP, plasma currents were variable and implied temperatures of 30,000-50
This document discusses fluid-induced vibration (FIV) in heat exchangers. It covers topics like vortex shedding, synchronization, critical velocity, fluid-elastic instability, and vibration damage patterns. The key points are:
- Vortex shedding from cylindrical structures can cause fluid excitation forces at the shedding frequency, and fluid-structure coupling forces if that frequency matches structural natural frequencies.
- There is a critical cross-flow velocity at which fluid-elastic instability occurs, causing rapid increases in vibration amplitude.
- Vibration damage in heat exchangers can include tube collisions, baffle damage, tube sheet effects, and acoustic resonance failures.
A high performance model for rainfall effect on radio signalsAlexander Decker
The document presents a mathematical model for calculating radio signal attenuation due to rain. The model is based on using spheroid rain drops over a broad frequency range of 3GHz, 5GHz and 10GHz. Numerical simulations were conducted using MATLAB. The results showed that attenuation (path loss) due to rainfall was 75.46% greater than free space attenuation. Additionally, the received power for the rainfall model was 24.61% less than the free space model. The model provides a more accurate calculation of radio signal attenuation compared to existing models that do not account for factors like rainfall.
Infrared radiation associated with vapor-liquid phase transition of water is investigated
using a suspension of cloud droplets and mid-infrared (IR) (3–5 lm) radiation absorption
measurements. Recent measurements and Monte Carlo (MC) modeling performed at
60 C and 1 atm resulted in an interfacial radiative phase-transition probability of
5108 and a corresponding surface absorption efficiency of 3–4%, depending on
wavelength. In this paper, the measurements and modeling have been extended to 75 C
in order to examine the effect of temperature on water’s liquid-vapor phase-change radiation.
It was found that the temperature dependence of the previously proposed phasechange
absorption theoretical framework by itself was insufficient to account for
observed changes in radiation absorption without a change in cloud droplet number density.
Therefore, the results suggest a strong temperature dependence of cloud condensation
nuclei (CCN) concentration, i.e., CCN increasing approximately a factor of two from
60 C to 75C at near saturation conditions. The new radiative phase-transition probability
is decreased slightly to 3108. Theoretical results were also calculated at 50 C
in an effort to understand behavior at conditions closer to atmospheric. The results suggest
that accounting for multiple interface interactions within a single droplet at wavelengths
in atmospheric windows (where anomalous IR radiation is often reported) will be
important. Modeling also suggests that phase-change radiation will be most important at
wavelengths of low volumetric absorption, i.e., atmospheric windows such as 3–5 lm and
8–10 lm, and for water droplets smaller than stable cloud droplet sizes (<20 lm diameter),
where surface effects become relatively more important. This could include unactivated,
hygroscopic aerosol particles (not CCN) that have absorbed water and are
undergoing dynamic evaporation and condensation. This mechanism may be partly responsible
for water vapor’s IR continuum absorption in these atmospheric windows.
This document summarizes a numerical study of turbulent flow downstream from a linear heat source placed inside the cylinder wake. The study used computational fluid dynamics (CFD) to model the flow and heat transfer at varying Reynolds numbers. The k-ε realizable turbulence model was applied. Results showed that instabilities in the wake zone increase with Reynolds number, forming a von Karman vortex street that influences the thermal field and diffusion process. Comparisons of numerical results to experimental data were satisfactory. The study provides insight into how wake structures impact heat transport and scalar diffusion in turbulent flows.
Early kick detection and nonlinear behavior of drilling mu…Frank-Michael Jäger
The following test measurements serve the quantification of resolution and achievable sensitivity of parameters of sound velocity and sound absorption in wellbore fluids. More precisely, these studies refer to tools and methods to identify the flow of liquids or gases, preferably hydrocarbons in the well bore in real time during the drilling. The aim is a way to show with the highly sensitive and robust tools for use in the deep ocean can be realized.
Pulsar emission amplified and resolved by plasma lensing in an eclipsing binarySérgio Sacani
Radio pulsars scintillate because their emission travels through the
ionized interstellar medium along multiple paths, which interfere
with each other. It has long been realized that, independent of their
nature, the regions responsible for the scintillation could be used
as ‘interstellar lenses’ to localize pulsar emission regions1,2
. Most
such lenses, however, resolve emission components only marginally,
limiting results to statistical inferences and detections of small
positional shifts3–5
. As lenses situated close to their source offer
better resolution, it should be easier to resolve emission regions of
pulsars located in high-density environments such as supernova
remnants6
or binaries in which the pulsar’s companion has an
ionized outflow. Here we report observations of extreme plasma
lensing in the ‘black widow’ pulsar, B1957+20, near the phase in its
9.2-hour orbit at which its emission is eclipsed by its companion’s
outflow7–9
. During the lensing events, the observed radio flux is
enhanced by factors of up to 70–80 at specific frequencies. The
strongest events clearly resolve the emission regions: they affect the
narrow main pulse and parts of the wider interpulse differently. We
show that the events arise naturally from density fluctuations in
the outer regions of the outflow, and we infer a resolution of our
lenses that is comparable to the pulsar’s radius, about 10 kilometres.
Furthermore, the distinct frequency structures imparted by the
lensing are reminiscent of what is observed for the repeating fast
radio burst FRB 121102, providing observational support for the
idea that this source is observed through, and thus at times strongly
magnified by, plasma lenses10
This document summarizes key concepts about wave deformation, including refraction, diffraction, and breaking. It discusses how wave refraction causes wave crests to bend toward depth contours as waves propagate into shallower water. Diffraction causes wave energy to spread laterally around barriers. Wave breaking occurs when the wave steepness exceeds certain thresholds and depends on beach slope. It classifies breakers as spilling, plunging, or surging based on wave and slope characteristics. Refraction diagrams and formulas are presented to analyze wave behavior near coastal structures.
Voyager 2 plasma observations of the heliopauseFelipe Hime
The document describes observations from the Voyager 2 spacecraft of plasma properties at and near the heliopause (HP), which separates the solar wind from the very local interstellar medium (VLISM). Key findings include:
1) Voyager 2 observed a plasma boundary region starting 1.5 au before the HP, where the plasma slowed down, heated up, and doubled in density compared to typical heliosheath plasma.
2) Just inside the HP, a thinner boundary layer was observed over 0.06 au where the radial speed decreased and density and magnetic field increased.
3) In the VLISM beyond the HP, plasma currents were variable and implied temperatures of 30,000-50
This document discusses fluid-induced vibration (FIV) in heat exchangers. It covers topics like vortex shedding, synchronization, critical velocity, fluid-elastic instability, and vibration damage patterns. The key points are:
- Vortex shedding from cylindrical structures can cause fluid excitation forces at the shedding frequency, and fluid-structure coupling forces if that frequency matches structural natural frequencies.
- There is a critical cross-flow velocity at which fluid-elastic instability occurs, causing rapid increases in vibration amplitude.
- Vibration damage in heat exchangers can include tube collisions, baffle damage, tube sheet effects, and acoustic resonance failures.
A high performance model for rainfall effect on radio signalsAlexander Decker
The document presents a mathematical model for calculating radio signal attenuation due to rain. The model is based on using spheroid rain drops over a broad frequency range of 3GHz, 5GHz and 10GHz. Numerical simulations were conducted using MATLAB. The results showed that attenuation (path loss) due to rainfall was 75.46% greater than free space attenuation. Additionally, the received power for the rainfall model was 24.61% less than the free space model. The model provides a more accurate calculation of radio signal attenuation compared to existing models that do not account for factors like rainfall.
Infrared radiation associated with vapor-liquid phase transition of water is investigated
using a suspension of cloud droplets and mid-infrared (IR) (3–5 lm) radiation absorption
measurements. Recent measurements and Monte Carlo (MC) modeling performed at
60 C and 1 atm resulted in an interfacial radiative phase-transition probability of
5108 and a corresponding surface absorption efficiency of 3–4%, depending on
wavelength. In this paper, the measurements and modeling have been extended to 75 C
in order to examine the effect of temperature on water’s liquid-vapor phase-change radiation.
It was found that the temperature dependence of the previously proposed phasechange
absorption theoretical framework by itself was insufficient to account for
observed changes in radiation absorption without a change in cloud droplet number density.
Therefore, the results suggest a strong temperature dependence of cloud condensation
nuclei (CCN) concentration, i.e., CCN increasing approximately a factor of two from
60 C to 75C at near saturation conditions. The new radiative phase-transition probability
is decreased slightly to 3108. Theoretical results were also calculated at 50 C
in an effort to understand behavior at conditions closer to atmospheric. The results suggest
that accounting for multiple interface interactions within a single droplet at wavelengths
in atmospheric windows (where anomalous IR radiation is often reported) will be
important. Modeling also suggests that phase-change radiation will be most important at
wavelengths of low volumetric absorption, i.e., atmospheric windows such as 3–5 lm and
8–10 lm, and for water droplets smaller than stable cloud droplet sizes (<20 lm diameter),
where surface effects become relatively more important. This could include unactivated,
hygroscopic aerosol particles (not CCN) that have absorbed water and are
undergoing dynamic evaporation and condensation. This mechanism may be partly responsible
for water vapor’s IR continuum absorption in these atmospheric windows.
This document summarizes a numerical study of turbulent flow downstream from a linear heat source placed inside the cylinder wake. The study used computational fluid dynamics (CFD) to model the flow and heat transfer at varying Reynolds numbers. The k-ε realizable turbulence model was applied. Results showed that instabilities in the wake zone increase with Reynolds number, forming a von Karman vortex street that influences the thermal field and diffusion process. Comparisons of numerical results to experimental data were satisfactory. The study provides insight into how wake structures impact heat transport and scalar diffusion in turbulent flows.
Early kick detection and nonlinear behavior of drilling mu…Frank-Michael Jäger
The following test measurements serve the quantification of resolution and achievable sensitivity of parameters of sound velocity and sound absorption in wellbore fluids. More precisely, these studies refer to tools and methods to identify the flow of liquids or gases, preferably hydrocarbons in the well bore in real time during the drilling. The aim is a way to show with the highly sensitive and robust tools for use in the deep ocean can be realized.
Pulsar emission amplified and resolved by plasma lensing in an eclipsing binarySérgio Sacani
Radio pulsars scintillate because their emission travels through the
ionized interstellar medium along multiple paths, which interfere
with each other. It has long been realized that, independent of their
nature, the regions responsible for the scintillation could be used
as ‘interstellar lenses’ to localize pulsar emission regions1,2
. Most
such lenses, however, resolve emission components only marginally,
limiting results to statistical inferences and detections of small
positional shifts3–5
. As lenses situated close to their source offer
better resolution, it should be easier to resolve emission regions of
pulsars located in high-density environments such as supernova
remnants6
or binaries in which the pulsar’s companion has an
ionized outflow. Here we report observations of extreme plasma
lensing in the ‘black widow’ pulsar, B1957+20, near the phase in its
9.2-hour orbit at which its emission is eclipsed by its companion’s
outflow7–9
. During the lensing events, the observed radio flux is
enhanced by factors of up to 70–80 at specific frequencies. The
strongest events clearly resolve the emission regions: they affect the
narrow main pulse and parts of the wider interpulse differently. We
show that the events arise naturally from density fluctuations in
the outer regions of the outflow, and we infer a resolution of our
lenses that is comparable to the pulsar’s radius, about 10 kilometres.
Furthermore, the distinct frequency structures imparted by the
lensing are reminiscent of what is observed for the repeating fast
radio burst FRB 121102, providing observational support for the
idea that this source is observed through, and thus at times strongly
magnified by, plasma lenses10
This document summarizes key concepts about wave deformation, including refraction, diffraction, and breaking. It discusses how wave refraction causes wave crests to bend toward depth contours as waves propagate into shallower water. Diffraction causes wave energy to spread laterally around barriers. Wave breaking occurs when the wave steepness exceeds certain thresholds and depends on beach slope. It classifies breakers as spilling, plunging, or surging based on wave and slope characteristics. Refraction diagrams and formulas are presented to analyze wave behavior near coastal structures.
This document summarizes direct numerical simulations (DNS) of multiphase flows performed by Grétar Tryggvason and colleagues. It discusses DNS of bubbly flows in vertical channels, including the effects of bubble deformability and size on turbulent upflow. Machine learning methods are applied to DNS data to derive closure relationships for modeling averaged multiphase flows. More complex gas-liquid flows involving many bubbles of different sizes in turbulent channel flow are also examined.
This document provides an overview of geophysical data analysis and seismic wave theory. It defines key terms like body waves, surface waves, reflection, refraction, and diffraction. Body waves include compressional P-waves and shear S-waves, while surface waves are Rayleigh and Love waves. Reflection, refraction, and diffraction occur when seismic waves encounter interfaces between layers with different velocities. Multiples and ghosts are examples of phenomena that can complicate seismic data analysis if not properly handled. The document aims to give theoretical background knowledge needed to understand seismic data.
Austin Journal of Hydrology is an open access, peer reviewed, scholarly journal dedicated to publish articles in all areas of Hydrology.
The aim of the journal is to provide a platform for engineers, scientists and academicians all over the world to endorse, discuss and share various new issues and developments in diverse areas of hydrology.
Austin Journal of Hydrology accepts original research articles, review articles, case reports, commentaries, clinical images and rapid communication on all the aspects of Hydrology.
Herschel observations of water in comets found diversity in their D/H ratios. The Jupiter family comet 103P/Hartley 2 had a surprisingly low D/H ratio, similar to Earth's oceans and lower than typical Oort cloud comets. However, the long period comet C/2009 P1 had a higher D/H ratio, inconsistent with Earth's value. This suggests comet water did not originate from a single reservoir and that radial mixing occurred in the early solar system, contributing to the diversity of D/H ratios seen today. Further measurements are needed to better understand the origin and evolution of water in the solar system.
This document discusses different types of waves including transverse waves, longitudinal waves, and electromagnetic waves. It defines key wave properties such as amplitude, wavelength, frequency, speed, and period. It provides examples of calculating wavelength, frequency, and speed using the wave equations. The document also covers the electromagnetic spectrum and properties of different regions including gamma rays, x-rays, ultraviolet, visible light, infrared, microwaves, and radio waves.
This document discusses fluid flow in pipes under pressure. It presents equations to describe laminar and turbulent flow. For laminar flow, the Hagen-Poiseuille equation gives the relationship between pressure drop and flow rate. For turbulent flow, the velocity profile consists of a thin viscous sublayer near the wall and a fully turbulent center zone. Equations are derived to describe velocity profiles in both the sublayer and center zone based on viscosity and turbulence effects. Pipes are classified as smooth or rough depending on roughness size compared to the sublayer thickness.
The document describes a study that investigated the depth-wise profiles of velocity and turbulence parameters in the proximity of a mid-channel bar using experimental and computational fluid dynamics (CFD) modeling methods. Velocity measurements were taken at various depths and locations near the mid-channel bar using an acoustic Doppler velocimeter (ADV). The study found changes in the velocity and turbulence profiles due to interactions between the fluid flow and the mid-channel bar. CFD modeling with the Reynolds stress model was also used to validate the experimental results.
On the Analysis of the Laminar to Turbulent Flow Patterns in the Treatment of...Waqas Tariq
This document analyzes the transition from laminar to turbulent flow for 13 patients receiving oxygen treatment. It finds that for 12 out of the 13 patients, the critical radius for the onset of turbulent flow is much smaller when breathing a helium-oxygen mixture (HeOx) compared to regular air. For all patients breathing air, the critical radius is larger than the patient's throat or endotracheal tube radius, indicating turbulent flow, whereas HeOx results in laminar flow for most patients. The document concludes that HeOx is superior to air for treating patients with breathing difficulties as it promotes easier laminar flow.
1.5 interference - Interferens Fizik SPMCikgu Fizik
1. The document discusses the principles of interference and superposition of waves. It describes how two waves can interfere constructively or destructively depending on whether their crests and troughs coincide or cancel each other out.
2. Experiments are described to investigate the interference patterns of water waves. It is shown that the distance between nodes increases with increasing wavelength and decreasing separation between the two sources.
3. Young's double-slit experiment is explained as demonstrating the interference of light waves. Light passing through two slits acts as two coherent sources, producing an interference pattern of bright and dark fringes on a screen.
1) Local head losses occur in pipes due to changes in cross-sectional area, flow direction, or devices in the pipe. They are called minor losses and can usually be neglected for long pipe systems.
2) The document derives equations for calculating loss coefficients and head losses due to abrupt enlargements and contractions in pipes based on impuls-momentum and Bernoulli equations. It provides example loss coefficient values from experiments.
3) It discusses applying the same methods to model head losses in pipe junctions and conduits with multiple reservoirs.
This document discusses surface runoff, stream flow, hydrographs, and unit hydrographs. It begins by defining surface runoff and stream flow, explaining that surface runoff occurs when precipitation is unable to infiltrate the ground and flows overland into streams, rivers, and other bodies of water. It then discusses measuring stream flow through various methods like current meters and weirs to determine discharge. The document introduces the concept of hydrographs, which plot discharge over time, and unit hydrographs, which represent the hydrograph resulting from 1 unit of excess precipitation. It provides examples of using unit hydrographs and the S-curve method to develop hydrographs of different durations.
1.1 Gelombang - SPM - Fizik -Tingkatan 5Cikgu Fizik
1. Waves transfer energy from one place to another without transferring matter. Examples of waves include water waves, sound waves, and light waves.
2. There are two main types of waves - transverse waves, where the vibration is perpendicular to the direction of travel, and longitudinal waves, where the vibration is parallel.
3. Key wave properties include amplitude (height of the wave), wavelength (distance between two points of the same phase), period (time for one full oscillation), and frequency (number of oscillations per second). The speed of a wave can be calculated from its wavelength and frequency.
This document summarizes a study that used computational fluid dynamics (CFD) to simulate flow patterns around six types of triangular porous weirs with various upstream and downstream slopes. The study examined flow depth, discharge through the porous media, and velocity fields. Key findings include:
- Weirs with steeper upstream slopes produced lower upstream water levels and higher ratios of flow passing through the weir.
- The weir with a 30° downstream slope produced the highest upstream head and lowest discharge coefficient.
- Flow through the porous weirs reduced upstream water levels and vortex areas compared to solid weirs.
This document discusses turbulent fluid flow. It defines turbulence as an irregular flow with random variations in time and space that can be expressed statistically. Turbulence occurs above a critical Reynolds number when the kinetic energy of the flow is enough to sustain random fluctuations against viscous damping. Characteristics of turbulent flow include fluctuating velocities and pressures, and more uniform velocity distributions compared to laminar flow. Turbulence can be generated by solid walls or shear between layers, and can be categorized as homogeneous, isotropic, or anisotropic. Transition from laminar to turbulent flow is also discussed.
This document discusses the development and structure of axisymmetric turbulent jets. It begins by describing how turbulent jets form from an initial laminar shear layer at the nozzle exit, through the creation of ring vortices and pairing of adjacent vortices, eventually developing into a fully turbulent flow many diameters downstream. It then outlines different visualization techniques used to study turbulent jet structures over time, from early hot-wire measurements to modern particle image velocimetry and direct numerical simulation. Finally, it describes in detail the different regions of a turbulent jet - the potential core, transition zone, and fully developed region - and the coherent structures that form within the jet, including shear layers, ring vortices, and streamwise vortices.
Oscillations and waves can be described by key parameters including amplitude, period, and frequency. Amplitude refers to the maximum displacement from equilibrium, period is the time for one full oscillation, and frequency is the number of oscillations per second. Common examples of oscillations include a pendulum, mass on a spring, and ocean tides. For an object to undergo simple harmonic motion, it must experience a restoring force proportional to and directed towards its displacement from equilibrium.
The current study examines the generation and propagation of a Third order solitary water wave along
the channel. Surface displacement and wave profi le prediction challenges are interesting subjects in the
fi eld of marine engineering and many researchers have tried to investigate these parameters. To study the
wave propagation problem, here, fi rstly the meshless Incompressible Smoothed Particle Hydrodynamics
(ISPH) numerical method is described. Secondly,
The document describes seismic interpretation workflows, including conventional and unconventional techniques. Conventional techniques involve horizon interpretations, fault picking, and tying seismic data to well logs to understand subsurface geology. Unconventional techniques analyze seismic attribute variations like amplitudes to identify hydrocarbon indicators. The workflow includes generating synthetics from well logs, interpreting horizons on seismic sections, identifying structures like faults and gas chimneys, and determining direct hydrocarbon indicators.
This document discusses fluid kinematics, which is the branch of fluid mechanics that deals with the geometry and motion of fluids without considering forces. It defines key concepts like acceleration fields, Lagrangian and Eulerian methods of describing motion, types of flow such as laminar vs turbulent and steady vs unsteady, streamlines vs pathlines vs streaklines, circulation and vorticity, and analytical tools like the stream function and velocity potential function. Flow nets are introduced as a way to graphically study two-dimensional irrotational flows using a grid of intersecting streamlines and equipotential lines.
This document discusses fluid kinematics, which is the branch of fluid mechanics that deals with the geometry of motion of fluids without considering forces or energies. It describes Lagrangian and Eulerian methods for describing fluid motion, defines types of flow such as laminar, turbulent, steady, and unsteady. It also discusses concepts like acceleration fields, circulation, vorticity, streamlines, pathlines, streaklines, stream functions, and velocity potential functions. Flow nets, which use a grid of streamlines and equipotential lines, are introduced as a way to study two-dimensional irrotational flows.
This document summarizes direct numerical simulations (DNS) of multiphase flows performed by Grétar Tryggvason and colleagues. It discusses DNS of bubbly flows in vertical channels, including the effects of bubble deformability and size on turbulent upflow. Machine learning methods are applied to DNS data to derive closure relationships for modeling averaged multiphase flows. More complex gas-liquid flows involving many bubbles of different sizes in turbulent channel flow are also examined.
This document provides an overview of geophysical data analysis and seismic wave theory. It defines key terms like body waves, surface waves, reflection, refraction, and diffraction. Body waves include compressional P-waves and shear S-waves, while surface waves are Rayleigh and Love waves. Reflection, refraction, and diffraction occur when seismic waves encounter interfaces between layers with different velocities. Multiples and ghosts are examples of phenomena that can complicate seismic data analysis if not properly handled. The document aims to give theoretical background knowledge needed to understand seismic data.
Austin Journal of Hydrology is an open access, peer reviewed, scholarly journal dedicated to publish articles in all areas of Hydrology.
The aim of the journal is to provide a platform for engineers, scientists and academicians all over the world to endorse, discuss and share various new issues and developments in diverse areas of hydrology.
Austin Journal of Hydrology accepts original research articles, review articles, case reports, commentaries, clinical images and rapid communication on all the aspects of Hydrology.
Herschel observations of water in comets found diversity in their D/H ratios. The Jupiter family comet 103P/Hartley 2 had a surprisingly low D/H ratio, similar to Earth's oceans and lower than typical Oort cloud comets. However, the long period comet C/2009 P1 had a higher D/H ratio, inconsistent with Earth's value. This suggests comet water did not originate from a single reservoir and that radial mixing occurred in the early solar system, contributing to the diversity of D/H ratios seen today. Further measurements are needed to better understand the origin and evolution of water in the solar system.
This document discusses different types of waves including transverse waves, longitudinal waves, and electromagnetic waves. It defines key wave properties such as amplitude, wavelength, frequency, speed, and period. It provides examples of calculating wavelength, frequency, and speed using the wave equations. The document also covers the electromagnetic spectrum and properties of different regions including gamma rays, x-rays, ultraviolet, visible light, infrared, microwaves, and radio waves.
This document discusses fluid flow in pipes under pressure. It presents equations to describe laminar and turbulent flow. For laminar flow, the Hagen-Poiseuille equation gives the relationship between pressure drop and flow rate. For turbulent flow, the velocity profile consists of a thin viscous sublayer near the wall and a fully turbulent center zone. Equations are derived to describe velocity profiles in both the sublayer and center zone based on viscosity and turbulence effects. Pipes are classified as smooth or rough depending on roughness size compared to the sublayer thickness.
The document describes a study that investigated the depth-wise profiles of velocity and turbulence parameters in the proximity of a mid-channel bar using experimental and computational fluid dynamics (CFD) modeling methods. Velocity measurements were taken at various depths and locations near the mid-channel bar using an acoustic Doppler velocimeter (ADV). The study found changes in the velocity and turbulence profiles due to interactions between the fluid flow and the mid-channel bar. CFD modeling with the Reynolds stress model was also used to validate the experimental results.
On the Analysis of the Laminar to Turbulent Flow Patterns in the Treatment of...Waqas Tariq
This document analyzes the transition from laminar to turbulent flow for 13 patients receiving oxygen treatment. It finds that for 12 out of the 13 patients, the critical radius for the onset of turbulent flow is much smaller when breathing a helium-oxygen mixture (HeOx) compared to regular air. For all patients breathing air, the critical radius is larger than the patient's throat or endotracheal tube radius, indicating turbulent flow, whereas HeOx results in laminar flow for most patients. The document concludes that HeOx is superior to air for treating patients with breathing difficulties as it promotes easier laminar flow.
1.5 interference - Interferens Fizik SPMCikgu Fizik
1. The document discusses the principles of interference and superposition of waves. It describes how two waves can interfere constructively or destructively depending on whether their crests and troughs coincide or cancel each other out.
2. Experiments are described to investigate the interference patterns of water waves. It is shown that the distance between nodes increases with increasing wavelength and decreasing separation between the two sources.
3. Young's double-slit experiment is explained as demonstrating the interference of light waves. Light passing through two slits acts as two coherent sources, producing an interference pattern of bright and dark fringes on a screen.
1) Local head losses occur in pipes due to changes in cross-sectional area, flow direction, or devices in the pipe. They are called minor losses and can usually be neglected for long pipe systems.
2) The document derives equations for calculating loss coefficients and head losses due to abrupt enlargements and contractions in pipes based on impuls-momentum and Bernoulli equations. It provides example loss coefficient values from experiments.
3) It discusses applying the same methods to model head losses in pipe junctions and conduits with multiple reservoirs.
This document discusses surface runoff, stream flow, hydrographs, and unit hydrographs. It begins by defining surface runoff and stream flow, explaining that surface runoff occurs when precipitation is unable to infiltrate the ground and flows overland into streams, rivers, and other bodies of water. It then discusses measuring stream flow through various methods like current meters and weirs to determine discharge. The document introduces the concept of hydrographs, which plot discharge over time, and unit hydrographs, which represent the hydrograph resulting from 1 unit of excess precipitation. It provides examples of using unit hydrographs and the S-curve method to develop hydrographs of different durations.
1.1 Gelombang - SPM - Fizik -Tingkatan 5Cikgu Fizik
1. Waves transfer energy from one place to another without transferring matter. Examples of waves include water waves, sound waves, and light waves.
2. There are two main types of waves - transverse waves, where the vibration is perpendicular to the direction of travel, and longitudinal waves, where the vibration is parallel.
3. Key wave properties include amplitude (height of the wave), wavelength (distance between two points of the same phase), period (time for one full oscillation), and frequency (number of oscillations per second). The speed of a wave can be calculated from its wavelength and frequency.
This document summarizes a study that used computational fluid dynamics (CFD) to simulate flow patterns around six types of triangular porous weirs with various upstream and downstream slopes. The study examined flow depth, discharge through the porous media, and velocity fields. Key findings include:
- Weirs with steeper upstream slopes produced lower upstream water levels and higher ratios of flow passing through the weir.
- The weir with a 30° downstream slope produced the highest upstream head and lowest discharge coefficient.
- Flow through the porous weirs reduced upstream water levels and vortex areas compared to solid weirs.
This document discusses turbulent fluid flow. It defines turbulence as an irregular flow with random variations in time and space that can be expressed statistically. Turbulence occurs above a critical Reynolds number when the kinetic energy of the flow is enough to sustain random fluctuations against viscous damping. Characteristics of turbulent flow include fluctuating velocities and pressures, and more uniform velocity distributions compared to laminar flow. Turbulence can be generated by solid walls or shear between layers, and can be categorized as homogeneous, isotropic, or anisotropic. Transition from laminar to turbulent flow is also discussed.
This document discusses the development and structure of axisymmetric turbulent jets. It begins by describing how turbulent jets form from an initial laminar shear layer at the nozzle exit, through the creation of ring vortices and pairing of adjacent vortices, eventually developing into a fully turbulent flow many diameters downstream. It then outlines different visualization techniques used to study turbulent jet structures over time, from early hot-wire measurements to modern particle image velocimetry and direct numerical simulation. Finally, it describes in detail the different regions of a turbulent jet - the potential core, transition zone, and fully developed region - and the coherent structures that form within the jet, including shear layers, ring vortices, and streamwise vortices.
Oscillations and waves can be described by key parameters including amplitude, period, and frequency. Amplitude refers to the maximum displacement from equilibrium, period is the time for one full oscillation, and frequency is the number of oscillations per second. Common examples of oscillations include a pendulum, mass on a spring, and ocean tides. For an object to undergo simple harmonic motion, it must experience a restoring force proportional to and directed towards its displacement from equilibrium.
The current study examines the generation and propagation of a Third order solitary water wave along
the channel. Surface displacement and wave profi le prediction challenges are interesting subjects in the
fi eld of marine engineering and many researchers have tried to investigate these parameters. To study the
wave propagation problem, here, fi rstly the meshless Incompressible Smoothed Particle Hydrodynamics
(ISPH) numerical method is described. Secondly,
The document describes seismic interpretation workflows, including conventional and unconventional techniques. Conventional techniques involve horizon interpretations, fault picking, and tying seismic data to well logs to understand subsurface geology. Unconventional techniques analyze seismic attribute variations like amplitudes to identify hydrocarbon indicators. The workflow includes generating synthetics from well logs, interpreting horizons on seismic sections, identifying structures like faults and gas chimneys, and determining direct hydrocarbon indicators.
This document discusses fluid kinematics, which is the branch of fluid mechanics that deals with the geometry and motion of fluids without considering forces. It defines key concepts like acceleration fields, Lagrangian and Eulerian methods of describing motion, types of flow such as laminar vs turbulent and steady vs unsteady, streamlines vs pathlines vs streaklines, circulation and vorticity, and analytical tools like the stream function and velocity potential function. Flow nets are introduced as a way to graphically study two-dimensional irrotational flows using a grid of intersecting streamlines and equipotential lines.
This document discusses fluid kinematics, which is the branch of fluid mechanics that deals with the geometry of motion of fluids without considering forces or energies. It describes Lagrangian and Eulerian methods for describing fluid motion, defines types of flow such as laminar, turbulent, steady, and unsteady. It also discusses concepts like acceleration fields, circulation, vorticity, streamlines, pathlines, streaklines, stream functions, and velocity potential functions. Flow nets, which use a grid of streamlines and equipotential lines, are introduced as a way to study two-dimensional irrotational flows.
Las tecnologías de la información y la comunicación (TIC) procesan, almacenan, resumen y presentan información de varias formas, principalmente informática, internet y telecomunicaciones. Han revolucionado la sociedad al facilitar la comunicación y el acceso a la información. Si bien tienen beneficios como la educación y el entretenimiento, también plantean desafíos como la pérdida de privacidad y el aislamiento si no se usan de forma equilibrada.
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This document summarizes a panel discussion on ERP outsourcing featuring representatives from Sunny Delight Beverages, Targus, and Skanska USA Building. OneNeck provided outsourcing services including application management, infrastructure support, and a 24/7 support center for each company. The customers discussed how outsourcing to OneNeck allowed them to focus on their core businesses while improving the performance of their Dynamics AX, Baan, and JD Edwards environments.
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AIM Control Group provides cargo tally and marine survey services during loading and unloading to verify exact cargo quantities and weights. It operates in Vietnam, China, Korea, and India, tallying cargo for shipowners, logistics companies, and other parties. Services include tallying quantities loaded onto ships and containers against purchase orders and packing lists, and tallying discharge quantities against bills of lading.
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Tester Motivation - the results of a 600 tester survey with Stuart ReidTEST Huddle
View the webinar here: http://testhuddle.com/forums/topic/tester-motivation-the-results-of-a-600-tester-survey/
Stuart Reid shares the results of a motivation survey of over 600 testers. The study separated out the survey respondents into six distinct testing roles: Developer/Tester, Test Analyst, Test Lead, Test Manager, Test Consultant and Head of Testing. The factors and job characteristics that affect testers in each of the roles are also taken into account and they are compared and contrasted, as are the range of activities they perform.
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Learn to to increase your team’s productivity by learning a smarter way of motivating your testers
Identify areas that will make you more motivated in your job as a tester or test manager
Learn how testers in different roles are motivated by quite different factors
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Este documento resume la historia de la vida en la Tierra. Explica cómo los fósiles nos permiten conocer la vida pasada, incluyendo los primeros organismos, cómo evolucionaron y conquistaron los continentes, y cómo algunas especies se extinguieron. También describe cómo comenzó la vida con la formación de los océanos y la aparición de los primeros seres vivos sencillos, que luego evolucionaron a formas más complejas como plantas y diferentes tipos de animales como reptiles, pterosaurios y dinosaurios.
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This document summarizes research on the interaction between surface acoustic waves (SAWs) and liquid films at a pinned contact line. Three key findings are presented:
1) The exponentially decaying acoustic pressure of SAWs sustains a conic liquid film with micron-sized modulations that grow exponentially from the tip. This creates strong wicking of liquid through filter paper.
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The Effect of High Zeta Potentials on the Flow Hydrodynamics in Parallel-Plat...CSCJournals
This paper investigates the effect of the EDL at the solid-liquid interface on the liquid flow through a micro-channel formed by two parallel plates. The complete Poisson-Boltzmann equation (without the frequently used linear approximation) was solved analytically in order to determine the EDL field near the solid-liquid interface. The momentum equation was solved analytically taking into consideration the electrical body force resulting from the EDL field. Effects of the channel size and the strength of the zeta-potential on the electrostatic potential, the streaming potential, the velocity profile, the volume flow rate, and the apparent viscosity are presented and discussed. Results of the present analysis, which are based on the complete Poisson-Boltzmann equation, are compared with a simplified analysis that used a linear approximation of the Poisson-Boltzmann equation.
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2) In turbulent plane Couette flow at low Reynolds numbers, streamwise vortices that span the entire gap between plates have been observed.
3) The document proposes a two-step Galerkin projection method to derive a low-order model that can illustrate the dynamics and generation mechanism of these streamwise vortices, in a way that is analogous to what is observed in turbulent boundary layers.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
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International Journal of Computational Engineering Research(IJCER)ijceronline
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Directional Spreading Effect on a Wave Energy ConverterElliot Song
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Characteristic equation and properties of electron waves in periodic structures
SAWNanodrops
1. Self-Similar Micron-Size and Nanosize Drops of Liquid Generated by Surface Acoustic Waves
Daniel Taller,1
David B. Go,1
and Hsueh-Chia Chang2,*
1
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA
2
Department of Chemical and Biomolecular Engineering, Center for Microfluidics & Medical Diagnostics,
University of Notre Dame, Notre Dame, Indiana 46556, USA
(Received 13 September 2012; published 27 November 2012)
A planar surface acoustic wave on a solid substrate and its radiated sound into a static liquid drop
produce time-averaged, exponentially decaying acoustic and electric Maxwell pressures near the contact
line. These localized contact-line pressures are shown to generate two sequences of hemispherical satellite
droplets at the tens of microns and submicron scales, both obeying self-similar exponential scaling but
with distinct exponents that correspond to viscous dissipation and field leakage length scales, respectively.
The acoustic pressure becomes dominant when the film thickness exceeds (1=4) of the surface acoustic
wave wavelength and it affects the shape and stability of the mother drop. The Maxwell pressure of the
nanodrops, which exceeds ten atmospheres, is sensitive to the contact angle.
DOI: 10.1103/PhysRevLett.109.224301 PACS numbers: 43.35.Pt, 68.35.Iv, 78.67.Tf
Surface acoustic waves (SAWs) are elastic compression
surface waves generated on piezoelectric crystals by alter-
nating current (ac) electric fields sustained by an interdi-
gitated electrode transducer [1–3]. Both compression and
electric traveling waves of specific wavelength can be
generated on the surface of the crystal. Like plasmonic
optical surface waves, SAWs are dispersive [4], but unlike
optical waves, they are highly nonlinear [5]. Surface acous-
tic compression waves involve nanometer high deforma-
tion on the solid and have in-phase [6] electric components.
Historically, SAW devices have found widespread use
as filters, oscillators, and transformers in the electronics
industry [2]. More recently, they have been incorporated
into microfluidic devices, where they can be used to mani-
pulate fluids on the surface of the SAW device or disperse
fluid into aerosols, with applications ranging from mass
spectrometry [6–8] to pulmonary drug delivery [9,10].
Extensive studies have been undertaken to characterize
breakup of liquid drops by SAWs [11,12] to generate jets
[13,14] and aerosols [15,16].
Microfluidic and mass spectrometry applications are
particularly intriguing, as they involve the scattering of
the surface wave into a drop or film on the substrate.
This scattering is like optical refraction, but the wedge-
shaped geometry of the drop at the scattering location
(contact line) suggests an electric hot spot similar to a
plasmonic hot spots or singular scattering near the tip of
a wedge [17,18]. Since the SAW wavelength (SAW %
132 m) is much larger than the scattering region, an
‘‘electrostatic’’ approximation is permissible for the acous-
tic wave equation to yield a quasistatic analysis of the
acoustic field near the contact line, as is commonly done
for the Maxwell wave equation for optics [6,17].
It is indeed known that the acoustic waves that scatter
into a bulk drop or a liquid film will generate high acoustic
pressure at the contact line [19]. This acoustic radiation
pressure can drive a dc streaming flow that is suspected
to be responsible for a contact line instability that pulls a
thin film of liquid away from the bulk and causes rupture
[20]. However, the time-averaged system can also remain
at equilibrium, and the acoustic pressure can be com-
pensated by capillary pressure resulting in a quasistatic
equilibrium [20].
While the scattered sound waves produce an acoustic
pressure in the bulk liquid, the traveling electric field of
the transmitted SAW on the piezoelectric substrate can
produce dielectric polarization at the solid-liquid interface
with a corresponding electric Maxwell pressure. The sin-
gular Laplace harmonics at geometric singularities [21–25]
also suggest that the electric traveling wave will gene-
rate an electric field maximum (or singularity) near the
contact line, which could be responsible for the ionization
observed in SAW mass spectrometry. It follows that the
SAW-induced Maxwell pressure can also balance the cap-
illary pressure to generate similar small satellite droplets
at the contact line or even quasistatic cones, albeit at a
shorter length scale since the Maxwell pressure is expected
to be shorter range than the acoustic pressure. This balance
of electric and capillary pressures at the contact line is
analogous to dc Taylor and ac electrospray cones, where
an electric Maxwell pressure is balanced by the capillary
pressure so that both vary toward infinity in the same
manner approaching the cone tip [22,25]. In fact, previous
experimental and numerical studies of SAWs along wedge-
shaped channels show both high acoustic and electric fields
at the tip of the wedge [26,27].
In the present Letter, we experimentally confirm the
presence of these effects for the first time and offer scaling
theories to clarify where the acoustic and Maxwell pres-
sures dominate. For the quasistatic structures to exist, it is
important that the drop does not move under the influence
of the SAW. As such, we generate pinned stationary drops
PRL 109, 224301 (2012) P H Y S I C A L R E V I E W L E T T E R S
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30 NOVEMBER 2012
0031-9007=12=109(22)=224301(5) 224301-1 Ó 2012 American Physical Society
2. by extracting small amounts ($ 0:1 L) of liquid onto
a SAW device via a paper wick such that the drop is
constrained by contact with the paper.
The SAW device for the present study was fabricated
using standard photolithographic methods on a 127.68
yx-cut lithium niobate (LiNbO3) substrate. The SAW de-
vice was fabricated with focusing electrodes as pioneered
by Wu et al. [28] and used in previous studies of SAW for
mass spectrometry and microfluidics [6,7]. A small plastic
weigh boat was used as a reservoir to supply the working
fluid, deionized (DI) water. Cleanroom paper (TX 609
TechniCloth Non Woven Wipers) was used to wick the
working fluid onto the substrate so that fluid could be
supplied continuously. For all experiments, an ac voltage
was applied to the SAW transducers via a waveform gen-
erator (Agilent 33250A) attached to an amplifier (EI
325LA) at a frequency of fSAW ¼ 29:5 MHz. Prior to
operation, the paper wick was saturated with fluid from
the reservoir and brought to the edge of the SAW device.
Upon the application of ac power, SAWs were generated and
liquid was drawn from the saturated paper onto the device
surface, and at sufficient power aerosolized. This was filmed
using a high-speed camera (Photron Fastcam SA4) with a
Navitar telescopic lens ($ 48 Â magnification) adjacent to
the SAW device. A schematic of the SAW device and place-
ment of the paper wick is shown in Fig. 1(a).
At low powers, prior to the onset of aerosolization, a
liquid film was extracted from the paper by SAWs and a
sequence of self-similar satellite droplets formed on the
substrate, as discussed above and shown in Fig. 1(a). The
substrate was either cleaned with acetone or was treated
with trichloro(1H,1H,2H,2H-perfluorooctyl)silane via evap-
oration to change the liquid contact angle. The droplets
increase in radius closer to the paper wick, which is along
the direction of SAW propagation (x coordinate), and the
sequence of droplet sizes has a strong dependence on the
contact angle [Fig. 2(b)].
We model the droplet size distribution as a train of
hemispherical droplets whose radii are controlled by the
acoustic or Maxwell pressure that decays into the liquid.
The nth hemisphere thus has radius Rn, with position Ln ¼
2
Pn
m¼1 Rm, so that the smallest droplet of radius R1 begins
at L0 ¼ 0, the next droplet begins at L1 ¼ 2R1, and so on.
Assuming that the droplet radius Rn is governed by the
applied pressure at LnÀ1, given by PSAWðLnÀ1Þ, a balance
of capillary pressure and the acoustic or Maxwell pressure
requires that 2
=Rn ¼ PSAWðLnÀ1Þ, where
is surface
tension. Hence,
Ln ¼ 4
Xn
m¼1
1
PSAWðLmÀ1Þ
: (1)
In the case that acoustic pressure is dominant, PSAW is
due to viscous dissipation of a bulk acoustic wave that
refracts off the substrate at an angle corresponding to the
Rayleigh scattering angle when the SAW enters into the
liquid. The leading-order theory for the propagation and
viscous attenuation of the sound wave produces a fluid
displacement velocity u1 with zero time average.
However, the time averaged Bernoulli dynamic pressure,
hu2
1=2i, where is the ambient equilibrium density, is
nonzero and produces a time-averaged acoustic radiation
pressure [9,19],
Pacoustic ¼
1
2
ð1 þ 2
ÞA2
!2
eÀ2ðkxxþkyyÞ
; (2)
which decays exponentially into the fluid in the same
direction of propagation as the velocity u1 with a character-
istic decay length of lR ¼ 1=2kR. The Rayleigh acoustic
decay constant kR is in the direction of the Rayleigh refrac-
tion angle R from the normal, as shown in Fig. 1(a), and
has components kx ¼ kR sinðRÞ and ky ¼ kR cosðRÞ,
where the Rayleigh angle is R ¼ sinÀ1ðVw=VRÞ using
Snell’s law for the refracted liquid sound wave velocity
Vw and the SAW Rayleigh wavevelocity VR. The parameter
! ¼ 2fSAW is the angular frequency, A is the amplitude
of the SAW, and 2
¼ cot2
ðRÞ ¼ ðVR=VwÞ2
À 1 is an
attenuation constant arising from the change in speed of
the wave from the solid to the liquid phase.
The radiation pressure (2) can sometimes drive a stream-
ing flow and is hence referred to as a streaming pressure.
However, for a thin film, it can be balanced quasistatically
FIG. 1 (color online). (a) Schematic of SAW device producing
a droplet train from a pinned liquid film (side view) with inset
showing an experimental image of the droplet train using DI
water. The acoustic waves refract into the fluid at Rayleigh angle
R. (b) Top view of surface droplets for contact angles 45 (left)
and 80
(right). Note that the Maxwell droplets decay much
more quickly in the image on the right due to the change in
contact angle.
PRL 109, 224301 (2012) P H Y S I C A L R E V I E W L E T T E R S
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224301-2
3. by an interfacial capillary pressure and a pressure field
within the film without generating a dc flow. This radiation
pressure is derived for an infinitely large drop. Our original
drop size is that of the extracted film with a thickness of
about one millimeter and is indeed much larger than the
SAW wavelength. As a simple model, we assume the
acoustic radiation pressure of the original film remains
valid as the film thins near the contact line and droplets
smaller than the SAW wavelength are formed. Since the
thin film that breaks up into droplets is slender in aspect
ratio, we also neglect the decay of the acoustic radiation
pressure in the vertical direction and use the average
acoustic pressure at a particular droplet to estimate its
capillary pressure and diameter.
Combining Eqs. (1) and (2) with these approximations,
we obtain
Lnþ1 ¼ Ln þ
8
ð1 þ 2
ÞA2
!2
e2kxLn ; (3)
such that the radius of the droplets away from the pinned
film will decrease exponentially away from the pinned film
with a characteristic decay length that is half of the
Rayleigh decay length. If we transpose Eq. (3) so that the
difference of the lengths Lnþ1 and Ln is the droplet diame-
ter D, and Ln is equivalent to position x, then the scaling
relationship for droplet size becomes lnðDÞ / x with con-
stant of proportionality 2kx. Figure 2(a) shows experimen-
tal data using DI water as the working fluid at a variety of
SAW powers and confirms this exponential relationship
with x taken to be zero where the smallest visible droplets
are seen (more details on this measurement included in the
Supplemental Material [29]). Further, when the SAW am-
plitude is scaled away, the different data sets all collapse
according to the scaling suggested in Eq. (3), as shown in
Fig. 2(b). The distance Ltransition, from where the smallest
visible droplets are seen to the transition region where
the decay rate changes, is measured experimentally. The
decay length lx
M and the drop diameter at the transition
region Dtransition are adjusted empirically but both will be
compared to predicted values from our theory for the
Maxwell drops.
Curiously, there are actually two sets of collapsed data
with two distinct exponents in Fig. 2. For the larger drop-
lets (at greater x), an acoustic decay constant kx value of
6800 mÀ1 (corresponding to lx
R ¼ 1=kx ¼ 147 m) can
be extracted and it is on the same order of magnitude,
though larger than the reported value for water of
1370 mÀ1
or lx
R ¼ 730 m [19]. We attribute this discrep-
ancy to droplets coalescing prior to measurement, which
occurs most dramatically for larger droplets, thus artifi-
cially increasing the slope. We estimate the acoustic pres-
sure by assuming an amplitude A on the order of ten
nanometers, consistent with past studies [30], and find
Pacoustic $ 102–103 Pa provides sufficient pressure to sus-
tain droplets with diameter D on the order of tens to
hundreds of microns, corresponding to the larger droplets.
Thus it is clear that the larger sequence of satellite droplets
are generated because of the acoustic pressure near the
contact line, and the sequence of these acoustic Rayleigh
drops is due to a static balance between the exponentially
decaying acoustic pressure and the local capillary pressure.
The second set of collapsed data for the sequence of
smaller droplets suggests that a different exponentially
decaying pressure with a different decay rate must be at
play closer to the original contact line. We attribute this
sequence of satellite drops to the Maxwell pressure due to
the electric field of the transmitted SAWs that remain on
the substrate. Because of the finite wavelength SAW of the
SAW, its electric field decays in the direction normal to the
surface due to field leakage both out into the gas phase and
FIG. 2 (color online). (a) Plot of lnðDÞ as a function of x for data acquired at different SAW powers along with linear curve fits.
All units are in meters and c ¼ 45 for the untreated substrate. The slopes of the linear fits are equivalent to the decay constant.
(b) The data sets collapsed on a single plot, where Dtransition is the droplet size where the transition for the two droplet families occurs
(% 11 m), Ltransition is the measured x location of the transition, and lx
M is the decay length of the Maxwell pressure. Two sets of data
(open and closed symbols) were acquired for each power setting.
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4. from the high potential region to the low potential region of
the traveling wave on the substrate [31].
A Fourier expansion of the Laplace equation for the
potential (see Ref. [31]) within and outside a horizontal
film of thickness h, driven by a harmonic surface potential
ðx; y ¼ 0Þ ¼ o cosðkxÞ by a SAW of wavelength
SAW ¼ 2=k yields a Maxwell pressure change across
the interface, averaged over one wavelength, of PM ¼
liquid2
ok2ð2 À 1ÞeX=½ðÀ1 þ eXÞ þ ð1 þ eXÞŠ2, where
is the ratio of liquid permittivity liquid to air permittivity
air and X ¼ ð4h=SAWÞ. An expression for large for
large X, PM $ liquid2
ok2
expðÀXÞ, shows that the
Maxwell pressure decays exponentially with respect to
the film thickness and that the Maxwell pressure becomes
appreciable at X $ 1, which produces a transition film
thickness of h ¼ SAW=4 or about 10.5 microns for our
SAW wavelength. This is the observed value of transition
droplet diameter Dtransition in Fig. 2(a) and is used to
collapse the data in Fig. 2(b). This transition film height,
which delineates the Maxwell drops from the Rayleigh
drops, also appears in the exponent of several exponen-
tially decaying functions in this problem. It is the decay
length of the Maxwell pressure with respect to film height
for large X. An expansion about X ¼ 1 for large , which
reveals a scaling of PM $ liquid2
ok2
exp½À0:462ðX À 1ÞŠ
with exponential factor ðe À 1Þ=ðe þ 1Þ % 0:462, is
assumed to be valid for the observed Maxwell droplets.
With a thin-film approximation, the film height of the
wedge-shaped film near the contact line is h ¼ x tanðcÞ
where x is the tangential coordinate from the contact line.
This approximation allows us to use the X $ 1 flat-film
Maxwell pressure to estimate the Maxwell pressure decay
with respect to x, PM $ liquid2
ok2 expðÀx=lx
MÞ, where
lx
M ¼ SAW
4 tanc
eþ1
eÀ1 is the Maxwell pressure decay length in
the x direction. This Maxwell decay length for c % 45 is
computed to be 22:7 m, which is roughly the value
obtained from Fig. 2(a) of 19:2 m by empirical fit.
Since the tangential decay length for the Maxwell drop-
lets is a strong function of the contact angle, we explore
this wettability dependence by pretreating the substrate
with trichloro(1H,1H,2H,2H-perfluorooctyl)silane via
evaporation. The untreated substrate produced a contact
angle of 45
while the chemical produced contact angles of
70
and 80
. As is evident in Fig. 3(a), the Rayleigh drop
distribution and the transition film thickness are unaffected
by the contact angle but the decay length of the Maxwell
droplets is indeed a strong function of the contact angle.
Inserting the scaling of tanc collapses the data for differ-
ent contact angles in Fig. 3(b). We observe that when a
nonwetting droplet with contact angle as high as c $ 120
is subjected to a SAW, its contact angle decreases to a
saturation value of approximately 85 and Maxwell nano-
droplets are still generated. In general, however, the thin
film field-leakage mechanism breaks down for nonwetting
liquids so we do not expect Maxwell drops to form for c
much greater than 90.
In addition to enhanced Maxwell stress due to field
leakage for thin films, there could also be singular harmon-
ics at contact-line wedge [21–25] that further magnifies the
electric field. By seeding the solution with nanocrystals
and imaging the residual crystallization on the substrate
after the droplets evaporated, we were able to confirm that
the rapidly decaying Maxwell pressure is strong enough to
produce sub-micron droplets with extremely large capil-
lary pressures as shown in Fig. 4 in the case of the untreated
substrate with 45
contact angle. The outer rim of depos-
ited nanocolloids corresponds to the original nanodrop
size, and we estimate the corresponding capillary pressure
to be $106 Pa. By reducing the wavelength and increasing
the amplitude of SAW to their physical limits, pressures
as high as $107 Pa, corresponding to D $ 10 nanometers,
FIG. 3 (color online). (a) Plot of lnðDÞ as a function of x for data acquired at different contact angles along with linear curve fits.
The slopes of the linear fits are equivalent to the decay constant. All units are in meters. (b) The data sets collapsed on a single plot,
where Dtransition is the droplet size where the transition for the two droplet families occurs % 11 m), Ltransition is the measured
x location of the transition, and lx
M is the decay length of the Maxwell pressure. Two sets of data (open and closed symbols) were
acquired for each contact angle.
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5. may be achieved. This large pressure (and corresponding
electric field in excess of 108
V=m) suggests that atomic
field strengths are available at the contact-line hotspot
and SAW may be able to drive new chemistry there and
may explain the high ionization efficiency of SAW mass
spectrometry [6–8].
D. T. wishes to acknowledge the Arthur J. Schmitt
Foundation for their generous funding and Ming K. Tan
for fabrication of SAW devices. In addition, D. T. would
like to acknowledge the help of the Notre Dame Integrated
Imaging Facility for assistance with scanning electron
microscope imaging.
*Author to whom correspondence should be addressed.
hchang@nd.edu
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FIG. 4 (color online). Scanning electron microscope images
of dried nano-droplet on an untreated substrate. DI water was
seeded with 20 nanometer gold spheres for visualization.
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