Colloidal rod dynamics under large amplitude oscillatory extensional flow

We perform a combined experimental and theoretical investigation of the orientational dynamics of colloidal rods subjected to time-dependent homogeneous planar elongational flow. Our experimental approach involves the flow of dilute suspensions of cellulose nanocrystals (CNC) within a cross-slot-type microfluidic device through which the extension rate is modulated sinusoidally over a wide range of Péclet number amplitudes (Pe₀) and Deborah numbers (De). The time-dependent orientation of the CNC is assessed via quantitative flow-induced birefringence measurements. For small Pe₀ ≲ 1 and small De ≲ 0.03, the birefringence response is sinusoidal and in phase with the strain rate. With increasing Pe₀, 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 approaches zero. These dynamical responses of the 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 polydisperse simulations 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.