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A recent experiment by Wanget al.(Soft Matt., vol. 17, 2021, pp. 2985–2993) shows that a self-propelled compound drop in a surfactant-laden solution can autonomously change its motion from a straight line to a spiraling trajectory, enhancing its capability for chemical detection, catalytic reaction and pollutant removal in a large fluid region. To understand the underlying physics of this peculiar motion, we develop a two-dimensional minimal model to study the swimming dynamics of a compound droplet driven by a self-generated Marangoni stress. We find that, depending on the Péclet number ($$Pe$$) and the viscosity and volume ratios of the two compound phases, the drop can swim in a variety of trajectories, including straight lines, circles, zigzag curves and chaotic trajectories. The drop moves in circles when its two components have comparable volumes. Otherwise, it shows other types of motions depending on$$Pe$$. Our simulation results for the circular motion at small$$Pe$$are qualitatively comparable to the experiment. The transition between zigzag and circular trajectories is mainly determined by the orientation of high-order modes with respect to the drop's swimming direction. For most compound drops, the speed decays as$$Pe^{-1/3}$$at high Péclet numbers as it does for a single-phase drop. A drop with two equal components undergoes a run-and-reorient motion due to the competition between the even and odd modes. 

We analyse the electrophoresis of a weakly charged particle with a thin double layer in a dilute polymer solution. The particle velocity in polymer solutions modelled with different constitutive equations is calculated using a regular perturbation in the polymer concentration and the generalized reciprocal theorem. The analysis shows that the polymer is strongly stretched in two regions, the birefringent strand and the high-shear region inside the double layer. The electrophoretic velocity of the particle always decreases with the addition of polymers due to both increased viscosity and fluid elasticity. At a small Weissenberg number ( $Wi$ ), which is the product of the polymer relaxation time and the shear rate, the polymers inside the double layer contribute to most of the velocity reduction by increasing the fluid viscosity. With increasing $Wi$ , viscoelasticity decreases and shear thinning increases the particle velocity. Polymer elasticity alters the fluid velocity disturbance outside the double layer from that of a neutral squirmer to a puller-type squirmer. At high $Wi$ , the strong extensional stress inside the birefringent strand downstream of the particle dominates the velocity reduction. The scaling of the birefringent strand is used to estimate the particle velocity. 

Reactive metals are known to electrodeposit with irregular morphological features on planar substrates. A growing body of work suggest that multiple variables: composition, mechanics, structure, ion transport properties, reductive stability, and interfacial energy of interphases, formed either spontaneously or by design on the metal electrode play important but differentiated roles in regulating these morphologies. We examine the effect of fluorinated thermoset polymer coatings on Li deposition by means of experiment and theoretical linear stability analysis. By tuning the chemistry of the polymer backbone and side chains, we investigate how physical and mechanical properties of polymeric interphases influence Li electrodeposit morphology. It is found that an interplay between elasticity and diffusivity leads to an optimum interphase thickness and that higher interfacial energy augments elastic stresses at a metal electrode to prevent out-of-plane deposition. These findings are explained using linear stability analysis of electrodeposition and provide guidelines for designing polymer interphases to stabilize metal anodes in rechargeable batteries.