SlideShare a Scribd company logo
1
Fundamentals of Capillarity and
Wetting (CLL763)
2
Fundamental Forces in Nature
Typically, four fundamental forces
1. Strong force – make stable nucleus of an atom (10-5nm)
2. Weak force – β decay in the nucleus
3. Gravitational force – 𝑭 = 𝑮
𝒎𝟏𝒎𝟐
𝒓𝟐
4. Electromagnetic force – 𝑭 =
𝟏
𝟒𝝅𝜺𝟎
𝒒𝟏𝒒𝟐
𝒓𝟐
Electromagnetic force: Origin of all intermolecular forces that
determines the properties of solids, liquids, and gases, solution
behaviour, chemical reactions and the organization of biological
structures
3
van der Waals equation of state
Started with the fact that real gases does not obey ideal gas law:
PV= RT
𝑷 =
𝑹𝑻
𝑽
; 𝑽 − 𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝒗𝒐𝒍𝒖𝒎𝒆 𝒑𝒆𝒓 𝒎𝒐𝒍𝒆
van der Waals introduced two parameters ‘a’ and ‘b’ in ideal gas
law to capture the behavior of real gas.
b→ excluded volume to account for the finite size of molecules. It
accounts for the increase in pressure.
a→ signifies the attractive force that decreases pressure.
𝑷 =
𝑹𝑻
𝑽 − 𝒃
; 𝑽 − 𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝒗𝒐𝒍𝒖𝒎𝒆 𝒑𝒆𝒓 𝒎𝒐𝒍𝒆
𝑨𝒄𝒕𝒖𝒂𝒍 𝒗𝒐𝒊𝒅 𝒔𝒑𝒂𝒄𝒆
4
van der Waals equation of state
Due to the intermolecular attraction, pressure is reduced at the wall.
The amount by which the pressure is reduced is =
𝒂
𝑽𝟐
So, the final pressure due to the finite particle size and intermolecular
attraction: 𝑷 =
𝑹𝑻
𝑽−𝒃
−
𝒂
𝑽𝟐 => 𝑷 +
𝒂
𝑽𝟐 𝑽 − 𝒃 = 𝑹𝑻
It is now gradually accepted that intermolecular forces exist. But the
origin and the nature of the forces were not still clear.
Understanding of different forces at different length scales were
confusing.
5
Cataloguing Forces
Gravity– attractive
Ideal gas– repulsive
Condensed phases– attractive
molecules do not collapse; meaning some kinds of repulsive forces.
Decreasing length scale
Intermolecular forces are not of a simple nature
6
Understanding IMFs…
What about the interactions between two molecules.
For short range IMFs, n>3
𝑭(𝒓) = −
𝒅𝒘 𝒓
𝒅𝒓
; 𝒘 𝒓 − 𝒊𝒏𝒕𝒆𝒓𝒎𝒐𝒍𝒆𝒄𝒖𝒍𝒂𝒓 𝒑𝒂𝒊𝒓 𝒑𝒐𝒕𝒆𝒏𝒕𝒊𝒂𝒍
𝒘 𝒓 = −
𝑪𝒎𝟏𝒎𝟐
𝒓𝒏
; 𝑪 − 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕; 𝒎𝒂𝒕𝒆𝒓𝒊𝒂𝒍 𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕
𝒂𝒏𝒅, 𝑭 = −
𝒅𝒘 𝒓
𝒅𝒓
= −
𝒏𝑪𝒎𝟏𝒎𝟐
𝒓𝒏+𝟏
homework
7
Understanding IMFs…
vein Mie pair potential → 𝒘 𝒓 = −
𝑨
𝒓𝒏 +
𝑩
𝒓𝒎
Lennard-Jones pair potential → 𝒘 𝒓 = −
𝑨
𝒓𝟔 +
𝑩
𝒓𝟏𝟐
Attractive component;
operates at long distances
repulsive component;
operates at short distances
For interaction between two atoms: A=10-77 Jm6; B=10-134 Jm12
𝑭(𝒓) = −
𝒅𝒘 𝒓
𝒅𝒓
8
Intermolecular Forces (IMFs)
In nature, there are different types of IMFs which give rise to
macroscopic behaviour of materials
0.0 Steric repulsion (Pauli exclusion principle)
0.1 Coulombic Interaction (Charge-Charge/dipole)
1 Dipole-Dipole (Keesom or orientational interaction)
2 Dipole-Induced dipole (Debye or Inductive)
3 Induced dipole- induced dipole (London Dispersion)
}van der
Waals
9
Intermolecular Forces (IMFs)
Dipole-Dipole Dipole- Induced Dipole
Induced Dipole-
Induced Dipole
w(r)= −
𝑢1𝑢2
3 4𝜋𝜖0
2𝑘𝑇 𝑟6
u→ electric dipole moment
𝝐𝟎→dielectric permittivity of vacuum
k→ Boltzmann constant
w(r)= −
𝑢𝛼
4𝜋𝜖0
2 𝑟6
𝜶→ electric polarizability
w(r)= −
3 ℎν𝛼2
4 4𝜋𝜖0
2 𝑟6
𝝂→ ionization freq.
1
0
Surface Forces (SFs)
1 van der Waals (vdW) force between surfaces
(adhesion and cohesion)
2 Electric double layer force (EDL)
3 Steric forces
4 Capillary forces (vdW force between molecules in a meniscus)
5 Friction and lubrication forces
}DLVO
}Entropically
driven forces
1
1
Capillary bridge and adhesion
h
1
2
Capillary bridge and adhesion
θ
R
𝑹′
h/2
θ
1
3
Capillary bridge and adhesion
R1 = R and R2 = R’
𝑹’ =
ൗ
𝒉
𝟐
𝒄𝒐𝒔𝜽
𝜟𝒑 = 𝝈 (
𝟏
𝑹
−
𝒄𝒐𝒔𝜽
ൗ
𝒉
𝟐
)
Capillary pressure within the bridge:
𝜟𝒑 = 𝝈 (
𝟏
𝑹𝟏
+
𝟏
𝑹𝟐
)
1
4
Capillary bridge and adhesion
A= π R2
Force due to capillary pressure:
FC = 𝜟𝒑 𝑨
FC = π R 2 𝝈 (
𝟏
𝑹
−
𝒄𝒐𝒔𝜽
ൗ
𝒉
𝟐
)
If R >> h ; ‫׀‬ FC ‫׀‬ ~ π R 2 (
𝟐𝝈𝒄𝒐𝒔𝜽
𝒉
)
1
5
Capillary bridge and adhesion
concave cylinder convex sphere
Attractive capillary force
FC = 0
16
Drop bouncing and spreading
17
Drop bouncing and spreading
Ruiter J, et. al. Nature Physics, 11, 2015.
18
Normal force component in Young equation
𝐜𝐨𝐬 𝜽𝑬 =
𝝈𝑺𝑽
−𝝈𝑺𝑳
𝝈
Young equation
❖ In mechanical equilibrium, all forces must balance each other;
otherwise contact line will start to move along the surface.
❖ Gradual increase in σSV will gradually decrease 𝜽𝑬 and at some
point, it will reach to zero. This is called wetting transition.
❖ What happens with normal force component of σ?
19
Normal force component in Young equation

More Related Content

Similar to Lecture 3_forces and capillary bridge.pdf

9783642349904 c2
9783642349904 c29783642349904 c2
9783642349904 c2
Lotanna Ezeonu
 
Fundamental Concepts on Electromagnetic Theory
Fundamental Concepts on Electromagnetic TheoryFundamental Concepts on Electromagnetic Theory
Fundamental Concepts on Electromagnetic Theory
AL- AMIN
 
chemistry11.pptx
chemistry11.pptxchemistry11.pptx
chemistry11.pptx
Gaurav917092
 
States of matter
States of matterStates of matter
Norman John Brodeur Nuclear Physics.pdf
Norman John Brodeur Nuclear Physics.pdfNorman John Brodeur Nuclear Physics.pdf
Norman John Brodeur Nuclear Physics.pdf
Norman John Brodeur
 
Structure of atom
Structure of atom Structure of atom
Structure of atom
Dr. Tanuja Nautiyal
 
Atomic theory
Atomic theoryAtomic theory
Atomic theory
FLI
 
Riconda_Catarina.pptx
Riconda_Catarina.pptxRiconda_Catarina.pptx
Riconda_Catarina.pptx
AbdelhameDAlI7
 
FirstMatter - Copy
FirstMatter - CopyFirstMatter - Copy
FirstMatter - Copy
Doug Leadenham
 
Stabilization of emulsion via electrostatic
Stabilization of emulsion via electrostaticStabilization of emulsion via electrostatic
Stabilization of emulsion via electrostatic
Ling Ling Ng
 
Stabilization of emulsion via electrostatic
Stabilization of emulsion via electrostaticStabilization of emulsion via electrostatic
Stabilization of emulsion via electrostatic
Ling Ling Ng
 
Spin spin coupling and coupling constant
Spin spin coupling and coupling constantSpin spin coupling and coupling constant
Spin spin coupling and coupling constant
Himal Barakoti
 
Coulombs law
Coulombs law Coulombs law
Coulombs law
Qaisar Shahzad
 
Unit 1 State of matter.pptx
Unit 1 State of matter.pptxUnit 1 State of matter.pptx
Unit 1 State of matter.pptx
Shaikh Ayesha
 
PHYSICAL WORLD part 2
PHYSICAL WORLD part 2PHYSICAL WORLD part 2
PHYSICAL WORLD part 2
Priyanka Jakhar
 
electric field, (dipoles)
  electric field, (dipoles)  electric field, (dipoles)
electric field, (dipoles)
Abhinay Potlabathini
 
Unit iv (4.1. electrochemistry - I
Unit   iv (4.1. electrochemistry - IUnit   iv (4.1. electrochemistry - I
Unit iv (4.1. electrochemistry - I
ganapathimurugan1
 
atomic_nucleus.ppt
atomic_nucleus.pptatomic_nucleus.ppt
atomic_nucleus.ppt
mragarwal
 
atomic_nucleus.ppt
atomic_nucleus.pptatomic_nucleus.ppt
atomic_nucleus.ppt
Nasiruddin Mirza
 
Atomic_Nucleus.ppt for general physics 2
Atomic_Nucleus.ppt for general physics 2Atomic_Nucleus.ppt for general physics 2
Atomic_Nucleus.ppt for general physics 2
JosephMuez2
 

Similar to Lecture 3_forces and capillary bridge.pdf (20)

9783642349904 c2
9783642349904 c29783642349904 c2
9783642349904 c2
 
Fundamental Concepts on Electromagnetic Theory
Fundamental Concepts on Electromagnetic TheoryFundamental Concepts on Electromagnetic Theory
Fundamental Concepts on Electromagnetic Theory
 
chemistry11.pptx
chemistry11.pptxchemistry11.pptx
chemistry11.pptx
 
States of matter
States of matterStates of matter
States of matter
 
Norman John Brodeur Nuclear Physics.pdf
Norman John Brodeur Nuclear Physics.pdfNorman John Brodeur Nuclear Physics.pdf
Norman John Brodeur Nuclear Physics.pdf
 
Structure of atom
Structure of atom Structure of atom
Structure of atom
 
Atomic theory
Atomic theoryAtomic theory
Atomic theory
 
Riconda_Catarina.pptx
Riconda_Catarina.pptxRiconda_Catarina.pptx
Riconda_Catarina.pptx
 
FirstMatter - Copy
FirstMatter - CopyFirstMatter - Copy
FirstMatter - Copy
 
Stabilization of emulsion via electrostatic
Stabilization of emulsion via electrostaticStabilization of emulsion via electrostatic
Stabilization of emulsion via electrostatic
 
Stabilization of emulsion via electrostatic
Stabilization of emulsion via electrostaticStabilization of emulsion via electrostatic
Stabilization of emulsion via electrostatic
 
Spin spin coupling and coupling constant
Spin spin coupling and coupling constantSpin spin coupling and coupling constant
Spin spin coupling and coupling constant
 
Coulombs law
Coulombs law Coulombs law
Coulombs law
 
Unit 1 State of matter.pptx
Unit 1 State of matter.pptxUnit 1 State of matter.pptx
Unit 1 State of matter.pptx
 
PHYSICAL WORLD part 2
PHYSICAL WORLD part 2PHYSICAL WORLD part 2
PHYSICAL WORLD part 2
 
electric field, (dipoles)
  electric field, (dipoles)  electric field, (dipoles)
electric field, (dipoles)
 
Unit iv (4.1. electrochemistry - I
Unit   iv (4.1. electrochemistry - IUnit   iv (4.1. electrochemistry - I
Unit iv (4.1. electrochemistry - I
 
atomic_nucleus.ppt
atomic_nucleus.pptatomic_nucleus.ppt
atomic_nucleus.ppt
 
atomic_nucleus.ppt
atomic_nucleus.pptatomic_nucleus.ppt
atomic_nucleus.ppt
 
Atomic_Nucleus.ppt for general physics 2
Atomic_Nucleus.ppt for general physics 2Atomic_Nucleus.ppt for general physics 2
Atomic_Nucleus.ppt for general physics 2
 

Recently uploaded

Object Oriented Analysis and Design - OOAD
Object Oriented Analysis and Design - OOADObject Oriented Analysis and Design - OOAD
Object Oriented Analysis and Design - OOAD
PreethaV16
 
NATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENT
NATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENTNATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENT
NATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENT
Addu25809
 
Data Driven Maintenance | UReason Webinar
Data Driven Maintenance | UReason WebinarData Driven Maintenance | UReason Webinar
Data Driven Maintenance | UReason Webinar
UReason
 
ITSM Integration with MuleSoft.pptx
ITSM  Integration with MuleSoft.pptxITSM  Integration with MuleSoft.pptx
ITSM Integration with MuleSoft.pptx
VANDANAMOHANGOUDA
 
Applications of artificial Intelligence in Mechanical Engineering.pdf
Applications of artificial Intelligence in Mechanical Engineering.pdfApplications of artificial Intelligence in Mechanical Engineering.pdf
Applications of artificial Intelligence in Mechanical Engineering.pdf
Atif Razi
 
Generative AI Use cases applications solutions and implementation.pdf
Generative AI Use cases applications solutions and implementation.pdfGenerative AI Use cases applications solutions and implementation.pdf
Generative AI Use cases applications solutions and implementation.pdf
mahaffeycheryld
 
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
MadhavJungKarki
 
Height and depth gauge linear metrology.pdf
Height and depth gauge linear metrology.pdfHeight and depth gauge linear metrology.pdf
Height and depth gauge linear metrology.pdf
q30122000
 
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
shadow0702a
 
Transformers design and coooling methods
Transformers design and coooling methodsTransformers design and coooling methods
Transformers design and coooling methods
Roger Rozario
 
5G Radio Network Througput Problem Analysis HCIA.pdf
5G Radio Network Througput Problem Analysis HCIA.pdf5G Radio Network Througput Problem Analysis HCIA.pdf
5G Radio Network Througput Problem Analysis HCIA.pdf
AlvianRamadhani5
 
Accident detection system project report.pdf
Accident detection system project report.pdfAccident detection system project report.pdf
Accident detection system project report.pdf
Kamal Acharya
 
Zener Diode and its V-I Characteristics and Applications
Zener Diode and its V-I Characteristics and ApplicationsZener Diode and its V-I Characteristics and Applications
Zener Diode and its V-I Characteristics and Applications
Shiny Christobel
 
Call For Paper -3rd International Conference on Artificial Intelligence Advan...
Call For Paper -3rd International Conference on Artificial Intelligence Advan...Call For Paper -3rd International Conference on Artificial Intelligence Advan...
Call For Paper -3rd International Conference on Artificial Intelligence Advan...
ijseajournal
 
Supermarket Management System Project Report.pdf
Supermarket Management System Project Report.pdfSupermarket Management System Project Report.pdf
Supermarket Management System Project Report.pdf
Kamal Acharya
 
Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...
Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...
Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...
Transcat
 
Open Channel Flow: fluid flow with a free surface
Open Channel Flow: fluid flow with a free surfaceOpen Channel Flow: fluid flow with a free surface
Open Channel Flow: fluid flow with a free surface
Indrajeet sahu
 
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Sinan KOZAK
 
一比一原版(CalArts毕业证)加利福尼亚艺术学院毕业证如何办理
一比一原版(CalArts毕业证)加利福尼亚艺术学院毕业证如何办理一比一原版(CalArts毕业证)加利福尼亚艺术学院毕业证如何办理
一比一原版(CalArts毕业证)加利福尼亚艺术学院毕业证如何办理
ecqow
 
Software Engineering and Project Management - Introduction, Modeling Concepts...
Software Engineering and Project Management - Introduction, Modeling Concepts...Software Engineering and Project Management - Introduction, Modeling Concepts...
Software Engineering and Project Management - Introduction, Modeling Concepts...
Prakhyath Rai
 

Recently uploaded (20)

Object Oriented Analysis and Design - OOAD
Object Oriented Analysis and Design - OOADObject Oriented Analysis and Design - OOAD
Object Oriented Analysis and Design - OOAD
 
NATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENT
NATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENTNATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENT
NATURAL DEEP EUTECTIC SOLVENTS AS ANTI-FREEZING AGENT
 
Data Driven Maintenance | UReason Webinar
Data Driven Maintenance | UReason WebinarData Driven Maintenance | UReason Webinar
Data Driven Maintenance | UReason Webinar
 
ITSM Integration with MuleSoft.pptx
ITSM  Integration with MuleSoft.pptxITSM  Integration with MuleSoft.pptx
ITSM Integration with MuleSoft.pptx
 
Applications of artificial Intelligence in Mechanical Engineering.pdf
Applications of artificial Intelligence in Mechanical Engineering.pdfApplications of artificial Intelligence in Mechanical Engineering.pdf
Applications of artificial Intelligence in Mechanical Engineering.pdf
 
Generative AI Use cases applications solutions and implementation.pdf
Generative AI Use cases applications solutions and implementation.pdfGenerative AI Use cases applications solutions and implementation.pdf
Generative AI Use cases applications solutions and implementation.pdf
 
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
 
Height and depth gauge linear metrology.pdf
Height and depth gauge linear metrology.pdfHeight and depth gauge linear metrology.pdf
Height and depth gauge linear metrology.pdf
 
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
 
Transformers design and coooling methods
Transformers design and coooling methodsTransformers design and coooling methods
Transformers design and coooling methods
 
5G Radio Network Througput Problem Analysis HCIA.pdf
5G Radio Network Througput Problem Analysis HCIA.pdf5G Radio Network Througput Problem Analysis HCIA.pdf
5G Radio Network Througput Problem Analysis HCIA.pdf
 
Accident detection system project report.pdf
Accident detection system project report.pdfAccident detection system project report.pdf
Accident detection system project report.pdf
 
Zener Diode and its V-I Characteristics and Applications
Zener Diode and its V-I Characteristics and ApplicationsZener Diode and its V-I Characteristics and Applications
Zener Diode and its V-I Characteristics and Applications
 
Call For Paper -3rd International Conference on Artificial Intelligence Advan...
Call For Paper -3rd International Conference on Artificial Intelligence Advan...Call For Paper -3rd International Conference on Artificial Intelligence Advan...
Call For Paper -3rd International Conference on Artificial Intelligence Advan...
 
Supermarket Management System Project Report.pdf
Supermarket Management System Project Report.pdfSupermarket Management System Project Report.pdf
Supermarket Management System Project Report.pdf
 
Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...
Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...
Tools & Techniques for Commissioning and Maintaining PV Systems W-Animations ...
 
Open Channel Flow: fluid flow with a free surface
Open Channel Flow: fluid flow with a free surfaceOpen Channel Flow: fluid flow with a free surface
Open Channel Flow: fluid flow with a free surface
 
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
 
一比一原版(CalArts毕业证)加利福尼亚艺术学院毕业证如何办理
一比一原版(CalArts毕业证)加利福尼亚艺术学院毕业证如何办理一比一原版(CalArts毕业证)加利福尼亚艺术学院毕业证如何办理
一比一原版(CalArts毕业证)加利福尼亚艺术学院毕业证如何办理
 
Software Engineering and Project Management - Introduction, Modeling Concepts...
Software Engineering and Project Management - Introduction, Modeling Concepts...Software Engineering and Project Management - Introduction, Modeling Concepts...
Software Engineering and Project Management - Introduction, Modeling Concepts...
 

Lecture 3_forces and capillary bridge.pdf

  • 1. 1 Fundamentals of Capillarity and Wetting (CLL763)
  • 2. 2 Fundamental Forces in Nature Typically, four fundamental forces 1. Strong force – make stable nucleus of an atom (10-5nm) 2. Weak force – β decay in the nucleus 3. Gravitational force – 𝑭 = 𝑮 𝒎𝟏𝒎𝟐 𝒓𝟐 4. Electromagnetic force – 𝑭 = 𝟏 𝟒𝝅𝜺𝟎 𝒒𝟏𝒒𝟐 𝒓𝟐 Electromagnetic force: Origin of all intermolecular forces that determines the properties of solids, liquids, and gases, solution behaviour, chemical reactions and the organization of biological structures
  • 3. 3 van der Waals equation of state Started with the fact that real gases does not obey ideal gas law: PV= RT 𝑷 = 𝑹𝑻 𝑽 ; 𝑽 − 𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝒗𝒐𝒍𝒖𝒎𝒆 𝒑𝒆𝒓 𝒎𝒐𝒍𝒆 van der Waals introduced two parameters ‘a’ and ‘b’ in ideal gas law to capture the behavior of real gas. b→ excluded volume to account for the finite size of molecules. It accounts for the increase in pressure. a→ signifies the attractive force that decreases pressure. 𝑷 = 𝑹𝑻 𝑽 − 𝒃 ; 𝑽 − 𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝒗𝒐𝒍𝒖𝒎𝒆 𝒑𝒆𝒓 𝒎𝒐𝒍𝒆 𝑨𝒄𝒕𝒖𝒂𝒍 𝒗𝒐𝒊𝒅 𝒔𝒑𝒂𝒄𝒆
  • 4. 4 van der Waals equation of state Due to the intermolecular attraction, pressure is reduced at the wall. The amount by which the pressure is reduced is = 𝒂 𝑽𝟐 So, the final pressure due to the finite particle size and intermolecular attraction: 𝑷 = 𝑹𝑻 𝑽−𝒃 − 𝒂 𝑽𝟐 => 𝑷 + 𝒂 𝑽𝟐 𝑽 − 𝒃 = 𝑹𝑻 It is now gradually accepted that intermolecular forces exist. But the origin and the nature of the forces were not still clear. Understanding of different forces at different length scales were confusing.
  • 5. 5 Cataloguing Forces Gravity– attractive Ideal gas– repulsive Condensed phases– attractive molecules do not collapse; meaning some kinds of repulsive forces. Decreasing length scale Intermolecular forces are not of a simple nature
  • 6. 6 Understanding IMFs… What about the interactions between two molecules. For short range IMFs, n>3 𝑭(𝒓) = − 𝒅𝒘 𝒓 𝒅𝒓 ; 𝒘 𝒓 − 𝒊𝒏𝒕𝒆𝒓𝒎𝒐𝒍𝒆𝒄𝒖𝒍𝒂𝒓 𝒑𝒂𝒊𝒓 𝒑𝒐𝒕𝒆𝒏𝒕𝒊𝒂𝒍 𝒘 𝒓 = − 𝑪𝒎𝟏𝒎𝟐 𝒓𝒏 ; 𝑪 − 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕; 𝒎𝒂𝒕𝒆𝒓𝒊𝒂𝒍 𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕 𝒂𝒏𝒅, 𝑭 = − 𝒅𝒘 𝒓 𝒅𝒓 = − 𝒏𝑪𝒎𝟏𝒎𝟐 𝒓𝒏+𝟏 homework
  • 7. 7 Understanding IMFs… vein Mie pair potential → 𝒘 𝒓 = − 𝑨 𝒓𝒏 + 𝑩 𝒓𝒎 Lennard-Jones pair potential → 𝒘 𝒓 = − 𝑨 𝒓𝟔 + 𝑩 𝒓𝟏𝟐 Attractive component; operates at long distances repulsive component; operates at short distances For interaction between two atoms: A=10-77 Jm6; B=10-134 Jm12 𝑭(𝒓) = − 𝒅𝒘 𝒓 𝒅𝒓
  • 8. 8 Intermolecular Forces (IMFs) In nature, there are different types of IMFs which give rise to macroscopic behaviour of materials 0.0 Steric repulsion (Pauli exclusion principle) 0.1 Coulombic Interaction (Charge-Charge/dipole) 1 Dipole-Dipole (Keesom or orientational interaction) 2 Dipole-Induced dipole (Debye or Inductive) 3 Induced dipole- induced dipole (London Dispersion) }van der Waals
  • 9. 9 Intermolecular Forces (IMFs) Dipole-Dipole Dipole- Induced Dipole Induced Dipole- Induced Dipole w(r)= − 𝑢1𝑢2 3 4𝜋𝜖0 2𝑘𝑇 𝑟6 u→ electric dipole moment 𝝐𝟎→dielectric permittivity of vacuum k→ Boltzmann constant w(r)= − 𝑢𝛼 4𝜋𝜖0 2 𝑟6 𝜶→ electric polarizability w(r)= − 3 ℎν𝛼2 4 4𝜋𝜖0 2 𝑟6 𝝂→ ionization freq.
  • 10. 1 0 Surface Forces (SFs) 1 van der Waals (vdW) force between surfaces (adhesion and cohesion) 2 Electric double layer force (EDL) 3 Steric forces 4 Capillary forces (vdW force between molecules in a meniscus) 5 Friction and lubrication forces }DLVO }Entropically driven forces
  • 12. 1 2 Capillary bridge and adhesion θ R 𝑹′ h/2 θ
  • 13. 1 3 Capillary bridge and adhesion R1 = R and R2 = R’ 𝑹’ = ൗ 𝒉 𝟐 𝒄𝒐𝒔𝜽 𝜟𝒑 = 𝝈 ( 𝟏 𝑹 − 𝒄𝒐𝒔𝜽 ൗ 𝒉 𝟐 ) Capillary pressure within the bridge: 𝜟𝒑 = 𝝈 ( 𝟏 𝑹𝟏 + 𝟏 𝑹𝟐 )
  • 14. 1 4 Capillary bridge and adhesion A= π R2 Force due to capillary pressure: FC = 𝜟𝒑 𝑨 FC = π R 2 𝝈 ( 𝟏 𝑹 − 𝒄𝒐𝒔𝜽 ൗ 𝒉 𝟐 ) If R >> h ; ‫׀‬ FC ‫׀‬ ~ π R 2 ( 𝟐𝝈𝒄𝒐𝒔𝜽 𝒉 )
  • 15. 1 5 Capillary bridge and adhesion concave cylinder convex sphere Attractive capillary force FC = 0
  • 16. 16 Drop bouncing and spreading
  • 17. 17 Drop bouncing and spreading Ruiter J, et. al. Nature Physics, 11, 2015.
  • 18. 18 Normal force component in Young equation 𝐜𝐨𝐬 𝜽𝑬 = 𝝈𝑺𝑽 −𝝈𝑺𝑳 𝝈 Young equation ❖ In mechanical equilibrium, all forces must balance each other; otherwise contact line will start to move along the surface. ❖ Gradual increase in σSV will gradually decrease 𝜽𝑬 and at some point, it will reach to zero. This is called wetting transition. ❖ What happens with normal force component of σ?
  • 19. 19 Normal force component in Young equation