It is demonstrated that the intrinsic hydrodynamic resistance of a rigid particle of arbitrary shape, immersed in an arbitrary quasistatic Stokes flow extending to infinity, may be represented by a pair of symbolic, dyadic operators. When multiplied by the viscosity coefficient, these symbolic entities "operate" on the algebraic difference between the particle velocity and the fluid velocity at infinity to yield the hydrodynamic force and torque, respectively, on the particle. These force and torque operators are intrinsic geometric properties of the particle and serve to uniquely characterize its viscous resistance, independently of the kinematical and dynamical properties and state of motion of the fluid. Their use provides an alternative and simpler method of describing hydrodynamic resistance than the polyadic scheme proposed in Part IV. Remarkably simple, closed-form expressions for these operators are obtained for spherical and ellipsoidal particles.
The operator technique is extended to multiparticle systems and to systems which are partially bounded by container wails.