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Resistance functions for two spherical particles with the Navier slipboundary condition in general linear flows, including rigid translation, rigidrotation, and strain, at low Reynolds number are derived by the method ofreflections as well as twin multipole expansions. In the solutions, particleradii and slip lengths can be chosen independently. In the course ofcalculations, single-sphere problem with the slip boundary condition is solvedby Lamb's general solution and the expression of multipole expansions, andFax\'{e}n's laws of force, torque, and stresslet for slip particle are alsoderived. The solutions of two-body problem are confirmed to recover theexisting results in the no-slip limit and for the case of equal scaled sliplengths.

Resistance functions for two unequal spheres in linear flow at low Reynolds number with the Navier slip boundary condition