  Suspensions of anisotropic particles are commonly encountered in a wide
spectrum of applications, including industrial and architectural coatings,
targeted drug delivery and manufacturing of fiber-reinforced composites. A
grand challenge in the field of chemical and material processing is robust
production of strongly aligned fibers at the microscopic level, as this is
routinely linked with enhanced mechanical properties at the macroscopic level.
While the investigation of the microstructure of anisotropic colloids in shear
flows has garnered a lot of theoretical and experimental attention, the case of
extensional flow remains poorly understood due to several experimental
challenges. In this article, we present a theoretical framework for predicting
the steady and transient orientations of anisotropic particles in a flowing
liquid undergoing precisely defined steady and time-dependent planar
extensional flow at the stagnation point of a Stokes trap device. In
particular, we analytically solve the Fokker-Planck equation for estimating the
probability distribution function describing the orientation dynamics of
rod-like objects as a function of flow strength (Peclet number, Pe) and probing
frequency (Deborah number, De). The theoretical results are compared with
recent experiments and reasonable agreement is found. We also discuss the
challenges involved in obtaining a full closed-form solution for the transient
dynamics of anisotropic particles in oscillatory time-dependent extensional
flow. Overall, our theoretical framework provides a way to compare the
orientation dynamics of rod-like particles with experiments that have been
performed using a new experimental technique involving the Stokes trap and
precise flow-control over the orientation of particles.
