This document summarizes two research articles about drag force on spheres moving in yield stress fluids. The first article studied how drag force varied with sphere density and velocity by observing spheres falling in aqueous Carbopol solutions. Three regimes of motion were observed depending on sphere density relative to a critical density. The second article used a Laponite-water mixture and also found three regimes depending on time between sphere releases and vibration frequency. Both approaches examined the fluid's rheological behavior to better understand drag forces on objects in pasty materials.

1. ASSIGNMENT
OF
FLUID MECHANICS-1
SUBMITTED BY:
NS-HUMZA SAJJAD ME-38/A
SUBMITTED TO:
SIR MUBASHAR GULZAR
January 1, 2018

2. DRAG FORCE ON A SPHERE IN YIELD STRESS FLUID
Research article by “Hervé Tabuteau, Philippe Coussot, and John R. de Bruyn”:
Thisarticle isbasedon the actionof drag force on the sphere movingina yieldstressfluid. Yieldsstress
fluidsare the oneswhichonlyflowwhentheyare acteduponbyminimumstressknownascritical
stress.Forinstance cementpaste, toothpaste, natural mudsandsolutioncontainingsuspendedparticles
are categorizedasyieldstressfluids.
In orderto findoutthe variationof drag force on differentobjectsandvelocityof objectsasa function
of time andsphere density,the researcherhasconductedfew experimentsin awell-equipped
environmentbyinstallinghighspeedcamerasandcontrolledstressrheometers inwhichtwoaqueous
solutionsof Carbopol ETD 2050 withbyweightconcentrationof 0.5%and 2% respectivelyare used.
Sphereswithvariousdensitiesare allowedtofall inafluidcontainerandthere motioninobserved
carefully. Initially,the vibrationswereproducedinthe depthof the fluidwhichhinderedthe recording
of observations.Once the vibrational effectsvanished,the motionof fluidwasobservedwhichhad
three regimesdependinguponthe densitiesof the spheresused.The sphereswithdensitiesgreater
than critical density(ƿc) reacheduniformvelocityandtheirdepthkeptonincreasinguniformlywith
time.However, the sphereswithdensitieslessthan ƿc rapidlycame to restaftertheywere injectedin
the fluid.Andinthe thirdregime of motion,the velocitiesof the sphereswithintermediate densities
kepton decreasingsteadilywithtime.Howeverthe depthkeptonincreasing.
Afterperformingthe experimentsandanalyzing the outcomesthathave come out,it isconcludedthat
the results obtained show coherence with the existing theories on the Newtonian Fluids.
Research article by T. Ferroir, H. T. Huynh, X. Chateau:
The article is aboutfindingdragforce byusinga pastymaterial asa yieldstressfluid
In thisexperimentthe yieldstressfluidwaspreparedbymixingof distilledwater andLaponite,a
syntheticclayina tank.Afterthe propermixing,the sphere of densityƿwasallowedtofall inthe fluid
at differenttime intervalsof rest.Justlike previousexperiment,three regimesappear;forshorttime of
restthe sphere fallswithhighvelocity;incontrastitmoveswithnegligible velocityatlongertimesof
restand withintermediate velocityatintermediate timesof rest. Forthe vibrationtests fall of the
sphere ina Newtonianliquidcommercial honey wasobserved,apparentlyconstantvelocitywithand
withoutvibrationsatanyfrequency.Withthe laponite suspensionthe resultsof vibrationtestsat
differentimposedfrequenciesappearedtobe similartothose forthe fluidatrestunderdifferentinitial
restructuringtimes:The three regimesare obtained,respectively,forhigh,low andintermediate
frequencies.
It was concludedthatthe fall of the objectinpastymaterial wasmuch complex andcomplicated.The
fall wastime dependent.The rheological behaviorof the pastymaterial hadgreatsignificance tofinding
out the exactrheological behaviorof the material isatediousjobwhichrequiresmucheffort.
In the end,to summarize,we saythe twodifferentapproacheswereadoptedtofindoutthe dragforce
and the time dependence of velocity.Differentrheological behaviorswere examinedusingthe lawsand
the theoriesof fluidmechanicsandphysics.

3. References:
http://sor.scitation.org/doi/pdf/10.1122/1.2401614
Akers,B.,and A.Belmonte,“Impactdynamicsof asolidsphere fallingintoaviscoelasticmicellarfluid,”J.
Non-NewtonianFluidMech. 135, 97–108 2006.
http://aip.scitation.org/doi/pdf/10.1063/1.1640372