Drag force on a sphere in yield stress fluid
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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.
Drag force on a sphere in yield stress fluid
- 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