1-Fludic-Basic Principles

Fluids – Basic Principles

Fawwaz Habbal School of Engineering and Applied Sciences Harvard University Topics

• Fluids and Solids • Type of Flow • Reynolds number • Diffusion • Surface Tension • Capillary Forces Fluids

• Fluid • Has volume, but no shape • Any substance that deforms continuously under the application of shear • Fluid behaves as a continuum • Fluid ‘sticks’ to surfaces (no-slip condition)

• Microfluidics is the fluid dynamics in microscopic domains and very small volumes

3 Basic Properties

• Type of Fluids • Newtonian • non- Newtonian • Fluid Flow • Laminar Flow • Turbulence • Parameters • Shear • Viscosity • Surface Tension 4 Viscosity

Viscosity is a measure of ?? of the fluid to the flow

Symbols: η or µ

5 Viscosity

Viscosity is a measure of resistance (friction) of the fluid to the flow

This determines “flow rate”

Symbols: η or µ

6 Stress - Strain for a Fluid

du ⎛ F ⎞ τ = µ ⎜τ = ⎟ dy ⎝ A ⎠ 7 Non-Newtonian Fluids

du τ = µ dy

⎛ F ⎞ ⎜τ = ⎟ ⎝ A ⎠ Viscosity (µ)

• “inverse fluidity”, “measure of fluid resistance to flow” • Ratio of the shear stress to the strain rate:

du ⎛ F ⎞ τ = µ ⎜τ = ⎟ dy ⎝ A ⎠

• Units: Poise “P” (g/cm·s) or Pa·s • Dependent on temperature: • Liquids: µ↓ as T↑ • Gases: µ↑ as T↑ 9 Viscosity (µ)

• Constant • Only for Newtonian Fluids du τ = µ (shear-thinning) dy Yield stress (shear-thickening) • Water, ethanol, gasoline • Non-Newtonian Fluids • Bingham Plastic • Ketchup, peanut butter • Pseudo-plastic (shear-thinning) • Latex paint, blood • Dilatant (shear-thickening) • Starch solution, AWD coupling fluid 10 Example: Dilatant Fluid

“Walking over water (plus some corn starch)!”

(Steve Spangler on The Ellen Show) hp://www.youtube.com/watch?v=RUMX_b_m3Js 11 Summary Newtonian Foods

Examples: • Water Shear stress • Milk • Vegetable oils • Fruit juices Shear rate • Sugar and salt solutions Pseudoplastic (Shear thinning) Foods

Examples: Shear stress • Applesauce • Banana puree • Orange juice concentrate Shear rate • Oyster sauce Dilatant (Shear thickening) Foods

Examples: Shear stress • Liquid Chocolate • 40% Corn starch solution Shear rate Bingham Plastic Foods

Examples: Shear stress • Tooth paste • Tomato paste

Shear rate Fluid Movement

• Gravity pumped • Vacuum pumps • Electro-osmotic Flow • Thermal Flow

17 Fluids - Types of Flow

• Laminar Flow (Steady)

• Turbulent Flow

• Laminar Flow ---> Turbulent Flow

18 Fluids - Types of Flow

• Laminar Flow (Steady) • Energy losses are dominated by viscosity effects • Most Flow in MEMS are Laminar

• Turbulent Flow • Most flow in nature are turbulent!

• Laminar Flow ---> Turbulent Flow Reynolds Number Re

Re is a measure of turbulence 19 Reynolds Number

Reynolds number (Re) = inertial forces / viscous forces

Re = Kinetic energy / energy dissipated by shear Implies inertia relatively important

L Re = ρVD η

VD = Drag velocity, L = characteristic length, η = viscosity,

ρ = density 20 21 Flow Regimes

• Laminar Flow • Viscous forces dominate (µ). • Observed in small conduits or at low flow rates. • Like concentric liquid cylinders in a pipe • Turbulent Flow Turbulent • Inertial forces are significant (ρ). • Observed in large conduits or at high flow rates. Transitional

• Unpredictable flow due to vortices, Laminar eddies and wakes. • Transitional Flow • Generally turbulent in the center of the channel and laminar near the surfaces. Example: Mixing Viscous Liquids

• Laminar Flow: high viscosity (corn syrup) and relatively low fluid velocity , low Re L Re = ρVD η

http://www.youtube.com/watch?v=p08_KlTKP50 23 Newton’s Second Law for Fluidics

Newton’s 2nd Law Time rate of change of momentum of a system equal to net force acting on system In Fluids dP ΣF = ??? equation dt

Newton’s Second Law for Fluidics

Newton’s 2nd Law Time rate of change of momentum of a system equal to net force acting on system

dP In Fluids ΣF = Navier-Stokes equation dt

Sum of forces acting on a control volume = Rate of momentum efflux from control volume 25

Navier - Stokes Equation

dU η ρ = −∇P + ρg + η∇2U + ∇(∇U ) dt 3

U = Velocity 26 Navier - Stokes Equation

dU η ρ = −∇P + ρg + η∇2U + ∇(∇U ) dt 3 For noncompressible Fluid ∇ iU = 0 dU ρ = −∇P + ρg + η∇2U dt

If inertial forces dominate inertial forces dominate due to small dimensions, even though velocity can be high dU 1 = − ∇P U = Velocity dt ρ 27 Laminar and Turbulent Flows

Laminar Flow: Viscous interaction between the wall and the fluid is strong, and there is no turbulences or vortices

28 Poiseuille Flow

h2∇P 2 Poiseuille ﬂow proﬁle. Average U = = U max 12ηL 3

29 Pressure Driven

30 Diffusion

Stokes - Einstein Equation Diffusion of a particle (gas, fluid) η

K T Translational Diffusivity B Dt = 6πηa

K BT Rotational Diffusivity Dr = 3 8πηa 31 Flow Profiles

32 Fluid Flow in very narrow channels

Laminar ﬂow in narrow channels leads to no “mixing” of the ﬂuids - Good or Bad?

33 Fluid Flow in very narrow channels

Diffusion ~ 1/a Can use the “T” channel as a ﬁlter!

K BT K BT Dt = Dr = 6πηa 8πηa3