Colloidal rod dynamics under large amplitude oscillatory extensional flow

TL;DR

This work investigates how rigid rod-like colloids orient under large amplitude oscillatory extensional flow using a cross-slot microfluidic device and flow-induced birefringence. The authors combine precise LAOE experiments with Jeffery-type orientation-distribution simulations, including both monodisperse and polydisperse rod populations, to map the dynamic response across Péclet and Deborah numbers. Key findings show linear birefringence at low Pe and De, with pronounced nonlinear saturation and residual alignment at higher amplitudes and frequencies; polydisperse simulations, especially the length-weighted $A_3$ case, best reproduce experiments. The results reveal hysteresis in Lissajous curves and establish conditions under which persistent alignment persists, providing insights for transient processing flows such as fiber spinning and film casting.

Abstract

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 Péclet 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.

Figures (12)

• Figure 1: CNC characterization. (a) Histogram of the characteristic contour length $l_{\mathrm{c}}$ distribution using $N=10$ bins, as obtained from AFM counting of 976 isolated particles (see Ref. Calabrese2021). (b) Distribution of the rotational diffusion coefficient $D_r$, calculated from the data in (a) using Eq. \ref{['eq_Dr']}, with $l_{\mathrm{c}}$ corresponding to that of each bin.
• Figure 2: Rheological responses of the CNC test fluids in shear and uniaxial extension. (a) Shear viscosity as a function of the applied shear rate. (b) Representative curves of the thinning filament diameter during capillary thinning in a CaBER experiment. The legend in (a) indicates the CNC concentration in vol.%. The inset in (b) displays a representative snapshot of the filament for the $\unit[0.1]{\%}$ CNC suspension, where the white scale bar represents [2]mm.
• Figure 3: Overview of the experimental setup. (a) Schematic illustration of the optimized shape cross-slot extensional rheometer (OSCER) geometry. The geometry has a height of $2H$ and features two pairs of opposing inlet and outlet channels aligned along the ${x}$ and ${y}$ axes, respectively, each with a width of $2W$. (b) Representation of the normalized set extension rate profiles $\dot{\varepsilon}_{\mathrm{x,set}}/\dot{\varepsilon}_{\mathrm{0,set}}$ and $\dot{\varepsilon}_{\mathrm{y,set}}/\dot{\varepsilon}_{\mathrm{0,set}}$ in the ${x}$ and ${y}$ directions, respectively, shown over one normalized period $t/T$.
• Figure 4: Flow velocimetry obtained with the $\unit[0.1]{\%}$ CNC dispersion under steady flow conditions. (a) Normalized velocity field with superimposed streamlines at $\dot{\varepsilon}_{\mathrm{set}}=\unit[1]{s^{-1}}$ (left) and $\dot{\varepsilon}_{\mathrm{set}}=\unit[100]{s^{-1}}$ (right). (b) Normalized velocity components along the ${x}$ and ${y}$ directions representatively shown for $\dot{\varepsilon}_{\mathrm{set}}=\unit[100]{s^{-1}}$. Black dashed lines represent linear fits over $\lvert y/W \rvert \leq 6$ and $\lvert x/W \rvert \leq 6$, which are used to calculate the extension rates $\dot{\varepsilon}_{\mathrm{x}}$ and $\dot{\varepsilon}_{\mathrm{y}}$, respectively. (c) Extension rates along the ${x}$ and ${y}$ directions as a function of the set elongation rate. (d) Streamwise velocity profiles normalized by the centerline velocity, measured across an outlet $\unit[7]{mm}$ downstream of the stagnation point at various imposed $\dot{\varepsilon}_{\mathrm{set}}$.
• Figure 5: Birefringence of the CNC dispersions under steady flow conditions. (a) Time-averaged birefringence normalized by the CNC concentration for the same conditions as in Fig. \ref{['FIG_SteadyPIV']}(a). The orientation angle $\theta$ is indicated by the solid segments. The white boxes around the central stagnation point in (a) correspond to regions of $\lvert x\rvert\leq\unit[0.2]{mm}$ and $\lvert y\rvert\leq\unit[0.02]{mm}$, where the spatially-averaged data is calculated. (b) Spatially-averaged orientation angle $\langle \theta \rangle$(top) and birefringence $\langle\Delta n \rangle$ (bottom) for the three samples as a function of the extension rate $\dot{\varepsilon}$. Gray areas in (b) indicate the polarization camera's maximum retardance limit. (c) Spatial averaged birefringence $\langle\Delta n \rangle$ scaled with the CNC volume fraction $\phi$ as a function of Péclet number $Pe$, using $\overline {D}_r = \unit[1.44]{s^{-1}}$. The red solid line shows a fit to the data according to Eq. \ref{['eq_steadyFIB']}.