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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

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