Microfluidics for Biologists Fundamentals and Applications

Applications of Stokes Law

• Hydrodynamic separation of cells


• Viscous force calculation


• Calculating shear on cells

This is important because mostly biomolecules and cells are approximately
spherical. Thus Stokes law can be employed with approximation.
Theviscous forceexperienced by each spherical particle is given by

FvZ¼ 3 ηU=2r ð 1 : 45 Þ

Thegravitational forceexperienced by a spherical particle falling in a liquid

Fg¼ 4 ½ðρsρfÞgΠr^3 Š= 3 ð 1 : 46 Þ

where,ρsis particle density,ρfis fluid density, g is gravity constant, r is radius of
particle
Terminal velocityof a spherical particle falling in a liquid under gravity

Uter¼ 2 ½ðρsρfÞgr^2 Š= 9 η ð 1 : 47 Þ

Stokes-Einstein lawrelates kinetics to Stokes law for understandingDiffusion

D¼kBT= 6 Πηr ð 1 : 48 Þ

where, D is diffusion constant, kBis Boltzmann constant, T is temperature of the
system
Drag forceon a particle completely enclosed in fluid is expressed as

FD¼ρU^2 CDA= 2 ð 1 : 49 Þ

where, FDis drag force, CDis drag coefficient, A is the area of reference, U is flow
velocity, andρis fluid density.
Equation (1.49) can be rewritten as

FD¼ρU^2 CAf ReðÞ= 2 ð 1 : 50 Þ

where, f(Re) is function operator for Reynolds number

• Poiseuille principle: Volumetric flow rate and pressure drop

It describes the relation of pressure drop in a moving fluid enclosed within a tube
with the flow resistance and flow rate (Table1.6). It is also known asHagen-
Poiseuille law(Fig.1.8).

1 Fundamentals of Fluidics 21