Interplay of Micellar Architecture and Viscosity Governs Active Droplet Motility

TL;DR

This work investigates how micellar architecture and viscosity govern active droplet motility in CTAB/NaSal solutions. By varying salt-to-surfactant ratio, the authors observe a non-monotonic propulsion speed, with a maximum around $C_s/C_d\approx0.5$, due to competing increases in the micellar interaction lengthscale $\lambda$ and bulk viscosity $\eta_o$, especially when micelles transition to worm-like forms. They develop a theoretical framework combining diffusiophoretic slip and Marangoni stresses with the hydrodynamic drag, using $K$ and $L^*$ derived from rod-like micelles and an interfacial-layer viscosity $\eta_s$ distinct from the bulk; the model reproduces the observed trend. PIV confirms pusher-type flow, and cryo-TEM/MADLS measurements link nanoscale micellar structure to macroscopic propulsion, providing design rules for active droplets in viscoelastic media.

Abstract

The autonomous motion of liquid crystal oil droplets in micellar media arises from spontaneous breaking of time reversal symmetry via nonlinear coupling between Marangoni stresses and surfactant transport. While this phenomenon has been widely studied, the influence of micellar solute structure remains unexplored. By modifying micellar architecture using a structure forming salt, we uncover a pronounced non monotonic dependence of droplet velocity on salt concentration. Increasing salt simultaneously raises the medium viscosity and drives a transition of micelles from spherical to rod-like or worm like morphologies. Using complementary experiments, we quantify the viscosity and micellar interaction lengthscale as functions of the salt to surfactant ratio and develop a theoretical model that consistently reproduces the measured propulsion speeds. Flow fields around the droplets are characterized by particle image velocimetry. Our results demonstrate that salt surfactant composition governs active droplet propulsion by jointly controlling micellar solute interaction lengthscales and medium viscosity.

Figures (8)

• Figure 1: (a) Schematic representation of the variation in the interaction length scale at the droplet interface, governed by changes in the micellar structure. The droplet is positioned at a solute concentration gradient, interacting with the solute via a potential ($\phi$) confined to a diffuse layer with a thickness of several $\lambda$, where $\lambda$ denotes the solute interaction length scale. (b) Representative X-Y trajectories for active 5CB droplets with a diameter nearly identical across different cases, corresponding to concentration ratios $C_\mathrm{s}/C_\mathrm{d} = 0.3$, 0.5, and 1. The trajectories are color-coded by droplet velocity, with the direction of motion indicated by the associated arrows. (c) Optical micrograph showing a snapshot of a 5CB droplet (diameter $\sim 90~\mu$m) motion in a $C_\mathrm{s}/C_\mathrm{d} = 1$, illustrating a low-viscosity trail region (indicated by the red dotted envelope, with local viscosity $\eta_\mathrm{s}$) within a surrounding medium of viscosity $\eta_\mathrm{o}$.
• Figure 2: (a) Mean-square displacement (MSD) and (b) experimentally measured droplet velocity $V_{\mathrm{exp}}$, extracted from the MSD data, as functions of NaSal concentration (or equivalently $C_{\mathrm{s}}/C_{\mathrm{d}}$) at fixed CTAB concentration (10 mM).
• Figure 3: (a) Representative cryo-TEM images at varying NaSal concentrations, expressed as the ratio $C_{\mathrm{s}}/C_{\mathrm{d}}$ (scale bars: $xx~\mu\mathrm{m}$ in each image strip). (b) Solute interaction length scale $\lambda$, measured by MADLS; (c) zero-shear viscosity $\eta_{o}$ of the micellar medium; and (d) Experimentally measured droplet velocity $V_{\mathrm{exp}}$, compared with theoretical predictions of velocity considering spherical (S) solute $V^{\mathrm{S}}_{\mathrm{Th}}$ and rod-like (R) solute $V^{\mathrm{R}}_{\mathrm{Th}}$ where as $V^{\mathrm{S,m}}_{\mathrm{Th}}$ and $V^{\mathrm{R,m}}_{\mathrm{Th}}$ represent viscosity-modified theoretical velocity, as functions of NaSal concentration (or equivalently $C_{\mathrm{s}}/C_{\mathrm{d}}$). The CTAB concentration is 10 mM in all cases.
• Figure 4: (a) Flow profile using PIV measurements at concentration $C_\mathrm{s}/C_\mathrm{d}$ = 1. (b) Tangential flow velocity, obtained from PIV measurements at $C_\mathrm{s}/C_\mathrm{d}= 1$, at the droplet interface, in the co-moving frame of reference. Red line is theoretical fits of $v_\mathrm{\theta}$. (c) $B_1$ and (d) $B_2$ value as a function of $C_\mathrm{s}/C_\mathrm{d}$.
• Figure S1: (a) MADLS data with variation of $C_\mathrm{s}/C_\mathrm{d}$ (b) MADLS data of 10 mM CTAB and 5CB oil saturated 10 mM CTAB containing dimension ($\delta$) of oil filled micelles. (c) Zeta potential of 10 mM CTAB with variation of NaSaI salt ($C_\mathrm{s}/C_\mathrm{d}$).