Friction and Shear n Gas u Origin of

Friction (and Shear) n Gas u Origin of Viscosity u Mix of gases n Liquid u Origin of Viscosity u Effect of foreign materials F Dilute vs Concentrated (sol-gel) u Non-newtonian Fluids F Concentrated F Effect of non-spherical dispersed materials F Presence of structure IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Gas n Gas u Kinetic Theory of gas u Non polar, low density n Mean Free Path is large Y 3 2 1 V X n Molecular movement between 1 and 2 (and 2 and 1, etc) Momentum Transfer between planes ==> viscosity Increase Temp ==> Increase velocity, Viscosity n Rigid Spheres n n n IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Gas n n Accounting for van der Waals attractive force Lennard-Jones potential n n n Mix of gases IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 n Sigma- collision dia omega- collision integral M -molecular wt

Liquids n n Theory is not as well developed Eyring’s Theory u Inter-molecular forces cause viscosity (NOT moving molecules) u Temp increase ==> more energy for molecule ==> less viscosity n Similar to reaction equilibrium IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Liquid Viscosity n n To go from A to C, the particle should have energy DEAct(Activation Energy) Energy released is heat of reaction DERxn B A C State Force n B For Liquid movement u EA and EC are same u Application of stress shifts A up and C down u ==> Movement from left to right IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 Energy C C’ A A’ State

Dilute solutions n Assume u No interaction between particles u Spherical, uncharged u Liquid velocity on particle surface = particle surface velocity u Newtonian behavior u Emulsions will show lower viscosity particles do not shear, emulsions will F surface contamination will increase emulsion viscosity IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 F

Non newtonian fluids n n n When one or more of the assumptions are violated Usually heterogenous Higher concentration (eg 40% of blood has red blood cells in plasma) ==> interaction between particles Non spherical particles Electrically charged (not discussed here) IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Non newtonian fluids n n High concentration (high is relative) Interaction, structure formation u Structural n viscosity Application of shear stress u breaks structure over time ==> thixotropic u breaks structure quickly, more stress ==> more disintegration ==> pseudoplastic u alternate: cylinders, ellipses align better with flow under higher shear ==> pseudoplastic u thixotropic (60 sec) --> pseudoplastic L D Axis Ratio = L/D IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Non newtonian fluids n Dilatant: Mostly solids with some fluid in between u Low stress ==> lubrication and less viscosity u higher stress ==> insufficient lubrication, more viscosity Bingham Plastic Pseudo plastic Dilatant Stress Newtonian n Bingham Plastic u Minimum yield stress u Newtonian IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 Strain

Non newtonian Fluids: Models IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Non Newtonian Fluids: Models n Viscoelastic: u usually coiled or connected structure u stretched (not broken) by stress u recoil after stress is released u normal stress on pipe != 0 u eg. Pull back after the applied force is removed n Non-newtonian != high viscosity u Many polymers added to reduce friction in water IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

n Fluid flow in a pipe n Hagen-Poiseulle’s law n n r x r n Momentum balance n Pressure drop = friction IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 Assumptions Laminar flow steady state no-slip incompressible

Fluid flow in a pipe n Newtonian n n Flow Rate Average Velocity IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 r x r

Fluid flow in a pipe n Non newtonian: power law fluid n Flow Rate Average Velocity n Double the pressure != double velocity n IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fluid flow in a pipe n Non newtonian: Bingham Plastic n Flow Rate Average Velocity n Double the pressure != double velocity n IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Flow between plates Sample 1 Sample 2 n n n Micro fluidics Identification of DNA fragments (for example) Flow rate depends on u Viscosity u Surface Tension u Sample movement rate depends on affinity IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Flow between plates n n Steady state Incompressible Laminar flow no-slip n Y 2 b Z X Element of width length DX, height DY and width (or depth) of 1 unit IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Flow between plates n n By symmetry, at the center, shear stress =0 Newtonian n n Flow rate Average velocity IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Flow between plates n Non newtonian : Power law fluids n n Flow rate Average velocity IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Examples n n n Pipe flow Fluid flow ~= Current flow DP = Voltage, Vavg = current Non-newtonian fluid: non-linear relation between DP and Vavg Resistance Newtonian fluid: easier prediction of results of changing one or more parameters IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Example n Non newtonian : Bingham Plastic H=10 m D=0. 1 m L=20 m/5 m IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Example n Find the time taken to drain the tank H=10 m n V 2 is a function of H n Tank will not drain completely! IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 D=0. 1 m L=20 m/5 m

Example n Non newtonian : Power law fluid 1 m/s 25 m Long, 1 cm dia n If flow rate has to be doubled, pressure needed IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Example n n n 1 Pbm. 8. 11 8 cm Given, Q=. 273 cm 3/s, d=. 18 cm, 2 Find m/r 55 cm 3 n Assume that pressure drop due to viscosity is high IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Example n n Pbm. 8. 6 Given, L=8 m, DP=207 k. Pa, d=. 635 cm, m, r Find velocity for no friction vs friction Frictional effects IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 1 2

Example L 12 L 23 n Pbm. 8. 2 n Given, L 12=22 km, L 23=18 km, Q, DP known n Consider this as resistance model IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Viscometers n Tube, Cone&Plate, Narrow gap cylinder, infinite gap cylinder IIT-Madras, Momentum Transfer: July 2005 -Dec 2005