The resistance functions that relate the forces, couples, and stresslets exerted on ambient fluid by two unequal rigid spheres in low Reynolds number flow are calculated for the case in which the spheres are immersed in an ambient linear flow. In conjuction with earlier works, this paper completes the tabulation of all of the two‐sphere resistance functions at present needed in investigations of the mechanics of suspensions. Each function is calculated first as a series in inverse powers of the center‐to‐center separation, and then, in order to handle the singular behavior caused by lubrication forces, the asymptotic form which the function takes when the spheres are close is combined with the series expansion into a single expression valid for all separations of the spheres.

1.
S. Kim and S. J. Karrila, Microdynamics: Principles and Selected Applications (Butterworth-Heinemann, London, 1991).
2.
L.
Durlofsky
,
J. F.
Brady
, and
G.
Bossis
, “
Dynamic simulation of hydrodynamically interacting particles
,”
J. Fluid Mech.
180
,
21
(
1987
).
3.
L.
Durlofsky
and
J. F.
Brady
, “
Dynamic simulation of bounded suspensions of hydrodynamically interacting particles
,”
J. Fluid Mech.
200
,
39
(
1989
).
4.
D. J.
Jeffrey
and
Y.
Onishi
, “
Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow
,”
J. Fluid Mech.
139
,
261
(
1984
).
5.
R. M.
Corless
and
D. J.
Jeffrey
, “
Stress moments of nearly touching spheres in low Reynolds number flow
,”
J. Appl. Math. Phys.
39
,
874
(
1988
).
6.
D. J.
Jeffrey
, “
Stresslet resistance functions for low Reynolds number flow using deforming spheres
,”
J. Appl. Math. Phys.
40
,
163
(
1989
).
7.
D. J.
Jeffrey
, “
Higher-order corrections to the axisymmetric interactions of nearly touching spheres
,”
Phys. Fluids A
1
,
1740
(
1989
).
8.
D. J.
Jeffrey
, “
The lubrication analysis for two spheres in a two-dimensional pure-straining motion
,”
Phys. Fluids A
3
,
1819
(
1991
).
9.
D. J.
Jeffrey
and
R. M.
Corless
, “
Forces and stresslets for the axisymmetric motion of nearly touching unequal spheres
,”
Physico Chem. Hydrodyn.
10
,
461
(
1988
).
10.
S.
Kim
and
R. T.
Mifflin
, “
The resistance and mobility functions of two equal spheres in low-Reynolds-number flow
,”
Phys. Fluids
28
,
2033
(
1985
).
11.
J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Martinus Nijhoff, Dordrecht, 1973).
12.
G. K. Batchelor, An Introduction to Fluid Mechanics (Cambridge U.P., Cambridge, 1967).
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