To study the effect of low Reynold's number flow on a protein or cells, we determine the force acting on

rigid sphere that is exposed to a uniform field under conditions when the Re is extremely small. A slightly

different problem - a sphere moving at constant velocity in a nonmoving fluid - yields a different velocity

field, but same force. The results from this problem are used to analyze the viscous and pressure forces

that act upon biological molecules and cells.

For low Re flow around a sphere of radius R, the velocity varies in the radial and angular direction above

and below the sphere's equator. The velocity components far from the sphere are

P + 00

Vo = -Upsing

Far from the surface, the pressure is uniform at pa. On the surface of the sphere, the no-slip condition

applies and velocities vanish.

FAR

1 = VS =0

Your first goal is to find the equations needed to determine the velocity profile, assuming steady flow and

an incompressible fluid and symmetry about the equator (no variation in the 0 direction). To do so:

a. Draw system presented above (flow around a sphere)

b. Present postulate

C.

d.

Simplify continuity equation

Simplify Navier-Stokes Equation (equation of motion), neglecting pressure around the sphere due

to gravity

e.

Present boundary conditions