Universal flow-induced orientational ordering of colloidal rods in planar shear and extensional flows: Dilute and semidilute concentrations

The design of flow processes to build a macroscopic bulk material from rod-shaped colloidal particles has drawn considerable attention from researchers and engineers. Here, we systematically explore and show that the characteristic strain rate of the flow universally determines the orientational ordering of colloidal rods. We employed the fluctuating lattice Boltzmann method by simulating hydrodynamically interacting Brownian rods in a Newtonian liquid moving under various flow types. By modeling a rigid rod as a chain of nonoverlapping solid spheres with constraint forces and torque, we elucidate rigid rod dynamics with an aspect ratio (⁠$L/d$⁠) either 4.1 or 8.1 under various rotational Péclet number (⁠$Per$⁠) conditions. The dynamics of colloidal rods in dilute (⁠$nL3=0.05$⁠) and semidilute suspensions (⁠$nL3=1.1$⁠) were simulated for a wide range of $Per$ (⁠$0.01<Per<1000$⁠) under shear flows including Couette and Poiseuille flows in a planar channel geometry, and an extensional and mixed-kinematics flow in a periodic four-roll mill geometry, where $n$ is the number density, and $d$ and $L$ are the diameter and length of the rod, respectively. By evaluating the degree of orientational alignment of rods along the flows, we observed that there is no significant difference between flow types, and the flow-induced ordering of rods depends on the variation of $Per$ up to moderate $Per$ (⁠$Per<100$⁠). At a high $Per$ (⁠$Per>100$⁠), the degree of orientational ordering is prone to diversify depending on the flow type. The spatial inhomogeneity of the strain-rate distribution leads to a substantial decrease in the orientational alignment at high $Per$⁠.