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Fluid Dynamics – Viscosity

Dave FosterDave FosterDepartment of Chemical EngineeringDepartment of Chemical EngineeringUniversity of RochesterUniversity of RochesterEmail: Email: dafosterdafoster@@cheche..rochesterrochester..eduedu

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Chemical Engineering What do Chemical Engineers Do?

ManufacturingManufacturingResearchResearch

Chemical

BiotechMedical

Pharmaceutical

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OK, first a little background

Fluid Mechanics is the study of fluids either in Fluid Mechanics is the study of fluids either in motion (Fluid Dynamics) or at rest (Fluid Statics)motion (Fluid Dynamics) or at rest (Fluid Statics)

Fluids are either gas or liquidFluids are either gas or liquid

Solids are NOT fluidsSolids are NOT fluids

Properties of the fluid are things like density, Properties of the fluid are things like density, pressure, temperature, and pressure, temperature, and VISCOSITYVISCOSITY!!

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Fluid – a definition

A substance that deforms continuously under A substance that deforms continuously under the action of shear stressthe action of shear stress

Gas or LiquidGas or Liquid

Solids can resist a shear stress, a fluid canSolids can resist a shear stress, a fluid can’’tt

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Applications of Fluid Mechanics

Explains Explains blood flow in capillaries of a few in capillaries of a few microns in diameter to crude oil flowcrude oil flowthrough an 800 mile long, 4 ft diameter pipethrough an 800 mile long, 4 ft diameter pipeExplains why Explains why airplaness are streamlined are streamlined with smooth surfaceswith smooth surfacesExplains why Explains why golf balls are made will are made will dimpled surfaces for most efficient traveldimpled surfaces for most efficient travel

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Effect of Dimples on Golf Balls

00.050.1

0.150.2

0.250.3

0.350.4

0.450.5

0 100 200 300 400

Velocity (Feet per Second)

Dra

g (P

ound

s of F

orce

)

Drag for SphereDrag for Golf Ball

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A List of Some Applications

CoatingCoatingBreathingBreathingBlood flow/pipe flowBlood flow/pipe flowSwimmingSwimmingPumps (traditional and Pumps (traditional and your heart)your heart)FansFansTurbinesTurbines

Airplanes & RocketsAirplanes & RocketsMissilesMissilesShipsShipsKidney dialysis machinesKidney dialysis machinesHeartHeart--Lung bypass Lung bypass machinesmachinesMembrane Membrane oxygenatorsoxygenatorsEnginesEnginesAnd lots more!And lots more!

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For everything “FLUID” -

Flow is keyFlow is keyHow fastHow fastWhat directionWhat directionHow changing with time (differential How changing with time (differential equations)equations)

Flow properties deal with things like the Flow properties deal with things like the velocity, changes in temperature, velocity, changes in temperature, concentration.concentration.

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Isaac Newton

Key player in much of basic scienceKey player in much of basic scienceThree Three ““LawsLaws””

1.1. A body will remain at rest or in motion A body will remain at rest or in motion unless acted upon by an external forceunless acted upon by an external force

2.2. ΣΣ F = m aF = m a3.3. For every action there is an equal and For every action there is an equal and

opposite reactionopposite reaction

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Newton’s Law of Viscosity:

dydvµτ =

Shear stress viscosity Shear Strain

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Viscosity – What is it?

A property of a fluid to resist the rate of A property of a fluid to resist the rate of deformation deformation –– a quantitative measure of a fluida quantitative measure of a fluid’’s s resistance to flow (water vs. syrup)resistance to flow (water vs. syrup)Takes place when a fluid is acted upon by a shear Takes place when a fluid is acted upon by a shear stressstressSimply stated, itSimply stated, it’’s how s how ““thickthick”” a fluid isa fluid is

We easily move through airWe easily move through airItIt’’s more difficult to move through water which s more difficult to move through water which is 50X higher in viscosity than airis 50X higher in viscosity than air

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A couple common examples:

Air < Water < Paint < Pancake Syrup < Tooth PasteAir < Water < Paint < Pancake Syrup < Tooth Paste

Least Viscous

Most Viscous

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Units(yep – units, very important)

If we talk about how deep a If we talk about how deep a swimming pool is and I tell you swimming pool is and I tell you that itthat it’’s s ““1010””, would you dive in?, would you dive in?Not if itNot if it’’s 10 inchess 10 inchesBut you might if it was 10 feetBut you might if it was 10 feet

Units are key in all of science, never Units are key in all of science, never accept a number without a unit if itaccept a number without a unit if it’’s s supposed to have onesupposed to have one

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Units of Viscosity

Poise (the most common units used to Poise (the most common units used to describe viscosity, but not the only one)describe viscosity, but not the only one)

Named after the French physician Named after the French physician ––Jean Louis Poiseuille (1799 Jean Louis Poiseuille (1799 -- 1869)1869)

OneOne--hundredth of a Poise is a centipoise or hundredth of a Poise is a centipoise or ““cPcP””

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Viscosity of Some “Common” Materials(all are in units of Centi-Poise)

Hydrogen Hydrogen 0.00880.0088Carbon DioxideCarbon Dioxide 0.0150.015Air Air 0.0180.018BloodBlood 0.400.40GasolineGasoline 0.290.29Water Water 1.01.0MercuryMercury 1.51.5Corn OilCorn Oil 7272SAE 30 oilSAE 30 oil 290290Heinz KetchupHeinz Ketchup 50,00050,000

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Changing a Material’s Viscosity

Easiest ways:Easiest ways:

Change the Temperature Change the Temperature –– Heat it Up !Heat it Up !Strong EffectStrong Effect

Change the Pressure Change the Pressure –– not as easynot as easy……Weak Effect: Decrease pressure, viscosity Weak Effect: Decrease pressure, viscosity decreasesdecreases

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In a perfect world:

Fluids obey NewtonFluids obey Newton’’s Law of Viscositys Law of ViscosityStraight line passing through the origin

dydvµ=τ

Slope = viscosityτ

(Format: y = m x + b)dv/dy

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Newtonian Fluids

Fluids that obey NewtonFluids that obey Newton’’s Law of Viscositys Law of ViscosityLinear relationship between shear stress and Linear relationship between shear stress and shear strainshear strainSome Examples of Newtonian Fluids:Some Examples of Newtonian Fluids:

WaterWaterSimple AlcoholsSimple AlcoholsSimple Organic SolventsSimple Organic Solvents

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Everything Else is a Non-Newtonian Fluid

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Non-Newtonian Fluids

Examples: Honey, toothpaste, paint, blood, Examples: Honey, toothpaste, paint, blood, ketchup, syrup, many polymersketchup, syrup, many polymers

The list goes on and onThe list goes on and on………………

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Non-Newtonian Fluids

Newtonian

Dilatant –shear-thickening-fluid increases resistance withIncreasing applied stress(ex. Rarely encountered, Cornstarch + water, Silly putty)

Pseudoplastic – shear-thinning-Fluid decreases resistance withincreasing stress.(ex: hair gel)

τ

dv/dy

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Why do we care?

The primary parameter correlating the The primary parameter correlating the viscous behavior of Newtonian Fluids is the viscous behavior of Newtonian Fluids is the dimensionless Reynolds Number:dimensionless Reynolds Number:

viscositydistance*velocityRe =

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Why do we care?

The first thing a fluids researcher should do The first thing a fluids researcher should do is estimate the Reynolds Number range of is estimate the Reynolds Number range of flow under study. flow under study.

Low Re = laminar flow Low Re = laminar flow (no change with time)(no change with time)

High Re = turbulent flow High Re = turbulent flow (changes with time)(changes with time)

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Reynolds Number and Viscosity

Viscosity ReViscosity Re

Viscosity ReViscosity Re

viscositydistance*velocityRe =

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How can we use Viscosity (and Fluid Dynamics)?

Flow measurements in human bodyFlow measurements in human bodyHeart valve flow volumesHeart valve flow volumes

Coating technologiesCoating technologiesLots of applicationsLots of applications

Moving fluids from one place to anotherMoving fluids from one place to anotherBlood flow in your bodyBlood flow in your bodyChemicals in pipesChemicals in pipes

Moving objects through fluidsMoving objects through fluids

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Thanks !!Thanks !!

Any Questions ?Any Questions ?