Colloidal rod dynamics under large amplitude oscillatory extensional flow

We perform a combined experimental and theoretical investigation of the orientational dynamics of rod-like colloidal particles in dilute suspension as they are subjected to a time-dependent homogeneous planar elongational flow. Our experimental approach involves the flow of dilute suspensions of cellulose nanocrystals (CNC) within a cross-slot-type stagnation point microfluidic device through which the extension rate is modulated sinusoidally over a wide range of P\'{e}clet number amplitudes ($Pe_0$) and Deborah numbers ($De$). The time-dependent orientation of the CNC is assessed via quantitative flow-induced birefringence measurements. For small $Pe_0 \lesssim 1$ and small $De \lesssim 0.03$, the birefringence response is sinusoidal and in phase with the strain rate, i.e., the response is linear. With increasing $Pe_0$, the response becomes non-sinusoidal (i.e., nonlinear) as the birefringence saturates due to the high degree of particle alignment at higher strain rates during the cycle. With increasing $De$, the CNC rods have insufficient time to respond to the rapidly changing strain rate, leading to asymmetry in the birefringence response around the minima and a residual effect as the strain rate passes through zero. These varied dynamical responses of the rod-like CNC are captured in a detailed series of Lissajous plots of the birefringence versus the strain rate. Experimental measurements are compared with simulations performed on both monodisperse and polydisperse systems, with rotational diffusion coefficients $D_r$ matched to the CNC. A semiquantitative agreement is found for simulations of a polydisperse system with $D_r$ heavily weighted to the longest rods in the measured CNC distribution. The results will be valuable for understanding, predicting, and optimizing the orientation of rod-like colloids during transient processing flows such as fiber spinning and film casting.