Viscoelasticity of rigid macromolecules with irregular shapes in the limit of overwhelming Brownian motion

We consider viscoelastic properties of complex rigid macromolecules in fluids undergoing steady or sinusoidal linear shearing. An arbitrary body is hydrodynamically described by six tensors to allow for irregular shapes that couple rotational and translational motions to each other and to the shear field. The viscosity increment ν is obtained for infinitely dilute suspensions in the limit of overwhelming Brownian motion by balancing drag forces and torques with entropic forces and torques. For sinusoidal shearing, ν is a complex number that exhibits five resonances at frequencies matching the j = 2 eigenvalues of the rotational diffusion equation for a stationary fluid. The resonance amplitudes are conveniently expressed in terms of a second‐rank body‐fixed tensor χ that characterizes alignment by the shear field, and special cases of symmetry are considered which reduce the number of contributing terms. Steadyshear methods, which assume a body matches the translational and rotational motions of the fluid element it replaces, are shown to slightly overestimate ν when complex shapes are involved. An algebraic criterion is found to locate the center of viscosity needed in these other methods although our treatment is independent of the choice of position in the body used for calculations. Bead‐model expressions are derived in order to provide numerical treatments of complicated structures. As an example, we examine a long bent rod.