# Interdisciplinary Applied Mathematics

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g(h),

368 (h/a)3 + 559 (h/a)2 + 81 (h/a) 368(h/a)3 + 779(h/a)2 + 250(h/a)

and the hindered particle diffusion in the normal direction to the wall is given as (Bevan and Prieve, 2000)

D(h)

g(h)

kBT

6npa

g(h),

6(h/a)2 + 2 (h/a)

6 (h/a)2 + 9 (h/a) + 2’

where h is the particle-wall distance.

We now consider particleparticle interactions. Relative motion of two spheres toward each other, squeezing flow, was solved in (O’Neill and Ma-jumdar, 1970). A rational function approximation of drag force for this case is given by

Fd

f (h)

6npV a

~JW’

54 (h/a)3 + 71 (h/a)2 + 8 (h/a)

54 (h/a)3 + 154 (h/a)2 + 60 (h/a) + 4 ’

where h is the separation distance between the two spheres. In the asymptotic limits the above relation gives

lim fe(h) ^ 1,    lim fe(h) ^ 2h/a.

h——ж    h——0

Collective motion of two spheres with the same velocity V parallel to their line    of    centers    so    that    there is    no    relative    velocity    between    them

was solved analytically in (Stimson and Jeffery, 1926). A rational function approximation of drag force for this case is given by

Fd

f(h)

6npV a

~JW’

2 (h/a)3 + 14 (h/a)2 + 31 (h/a)

2 (h/a)3 + 11 (h/a)2 + 20 (h/a) + 4 ’