1 / 31

Friction (and Shear)

Friction (and Shear). Gas Origin of Viscosity Mix of gases Liquid Origin of Viscosity Effect of foreign materials Dilute vs Concentrated (sol-gel) Non-newtonian Fluids Concentrated Effect of non-s pherical dispersed materials Presence of structure. Gas. 3. 2. Gas

valiant
Download Presentation

Friction (and Shear)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Friction (and Shear) • Gas • Origin of Viscosity • Mix of gases • Liquid • Origin of Viscosity • Effect of foreign materials • Dilute vs Concentrated (sol-gel) • Non-newtonian Fluids • Concentrated • Effect of non-spherical dispersed materials • Presence of structure

  2. Gas 3 2 • Gas • Kinetic Theory of gas • Non polar, low density V 1 Y • Mean Free Path is large X • Molecular movement between 1 and 2 (and 2 and 1, etc) • Momentum Transfer between planes • ==> viscosity • Increase Temp ==> Increase velocity, Viscosity • Rigid Spheres

  3. Gas • Accounting for van der Waals attractive force • Lennard-Jones potential • Sigma- collision dia • omega- collision integral • M -molecular wt • Mix of gases

  4. Liquids • Theory is not as well developed • Eyring’s Theory • Inter-molecular forces cause viscosity (NOT moving molecules) • Temp increase ==> more energy for molecule ==> less viscosity • Similar to reaction equilibrium

  5. Force B C C’ A A’ Energy State Liquid Viscosity B • To go from A to C, the particle should have energy DEAct(Activation Energy) • Energy released is heat of reaction DERxn A Energy C State • For Liquid movement • EA and EC are same • Application of stress shifts A up and C down • ==> Movement from left to right

  6. Dilute solutions • Assume • No interaction between particles • Spherical, uncharged • Liquid velocity on particle surface = particle surface velocity • Newtonian behavior • Emulsions will show lower viscosity • particles do not shear, emulsions will • surface contamination will increase emulsion viscosity

  7. Non newtonian fluids • 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)

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

  9. Bingham Plastic Pseudo plastic Dilatant Stress Newtonian Strain Non newtonian fluids • Dilatant: Mostly solids with some fluid in between • Low stress ==> lubrication and less viscosity • higher stress ==> insufficient lubrication, more viscosity • Bingham Plastic • Minimum yield stress • Newtonian

  10. Non newtonian Fluids: Models

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

  12. Assumptions • Laminar flow • steady state • no-slip • incompressible Fluid flow in a pipe • Hagen-Poiseuille’s law r x r • Momentum balance • Pressure drop = friction

  13. r x r Fluid flow in a pipe • Newtonian • Flow Rate • Average Velocity

  14. Fluid flow in a pipe • Non newtonian: power law fluid • Flow Rate • Average Velocity • Double the pressure != double velocity

  15. Fluid flow in a pipe • Non newtonian: Bingham Plastic • Flow Rate • Average Velocity • Double the pressure != double velocity

  16. Sample 1 Sample 2 Flow between plates • Micro fluidics • Identification of DNA fragments (for example) • Flow rate depends on • Viscosity • Surface Tension • Sample movement rate depends on affinity

  17. Flow between plates Y • Steady state • Incompressible • Laminar flow • no-slip 2b Z X • Element of width length DX, height DY and width (or depth) of 1 unit

  18. Flow between plates • By symmetry, at the center, shear stress =0 • Newtonian • Flow rate • Average velocity

  19. Flow between plates • Non newtonian : Power law fluids • Flow rate • Average velocity

  20. Resistance Examples • Pipe flow • Fluid flow ~= Current flow • DP = Voltage, Vavg = current • Non-newtonian fluid: non-linear relation between DP and Vavg • Newtonian fluid: easier prediction of results of changing one or more parameters

  21. Example • Non newtonian : Bingham Plastic H=10 m D=0.1m L=20m/5m

  22. Example • Find the time taken to drain the tank H=10 m D=0.1m • V2 is a function of H L=20m/5m • Tank will not drain completely!

  23. Example • Non newtonian : Power law fluid 1m/s 25 m Long, 1cm dia • If flow rate has to be doubled, pressure needed

  24. Example L23 L12 • Pbm. 8.2 • Given, L12=22 km, L23=18 km, Q, DP known • Consider this as resistance model

  25. Viscometers • Tube,Cone&Plate,Narrow gap cylinder, infinite gap cylinder

  26. A Y • Goal: Shear Stress, Velocity Profile, Torque Viscometers • Cone and Plate Viscometer • Ref: BSL, pbm 2B.11 X • Fluid between two plates, linear profile

  27. Shear Stress at cone: Viscometers • Shear stress vs Velocity: Spherical Co-ordinates • Force, Torque • Practical Y0 ~ 1o

  28. Viscometers • Cylindrical viscometer • Vary W, obtain Torque and velocity gradients for plots

  29. Continuity (Velocity Divergence) Differential momentum balance:Navier-Stokes Equation • Newtonian Fluids ONLY • Assumptions/applicability: • Isothermal conditions • both Compressible/Incompressible • both laminar/turbulent • Stokes assumption for bulk-viscosity (needed for compressible fluids)

  30. Appendix 1 2 • Pbm. 8.6 • Given, L=8m,DP=207kPa, d=.635 cm, m,r • Find velocity for no friction vs friction • Frictional effects

  31. Appendix: Blood Flow in Arteries • 40% red blood cells in plasma, non-newtonian • Pulsating motion, varying pressure • Re = 600, during exercise 6000 • Blood vessel dilation , short term, long term • Shear stress vs platelet activation (wound vs stenosis); ultrasonic detection • Tensile vs compressive stress; structure of blood vessel • Collapse of vessel during BP measurement • Collapse near stenosis and cardiac arrest • Mass & heat transport

More Related