Soft-Lubrication Drainage and Rupture in Particle-Driven Vesicles

Abstract

The deformation and rupture of a lipid vesicle due to the forced normal approach of an inclusion are essential for optimizing the design of magnetic giant unilamellar vesicles [magGUVs, Malik et al., Nanoscale 17, 13720 (2025)], with implications for active colloid-membrane interactions and cellular-scale chemical delivery. Here, we investigate vesicles propelled by a force-driven rigid inclusion and reveal a robust elastohydrodynamic mechanism: the inclusion outpaces the vesicle, sustaining a thinning film that drains symmetrically and self-similarly, largely independent of initial shape. For soft membranes and small inclusions, coupling drives a monotonic tension increase that can exceed the lysis tension. Evaluating the maximal tension over a delivery distance, we map an operating window in vesicle reduced area and size relative to the inclusion.

Figures (4)

• Figure 1: A vesicle pushed by an inclusion particle under a constant force deforms and translates. (a) A magGUV under a constant, uniform magnetic field gradient. Scale bars are $10$$\mu$m. (b) Quasi-steady simulated equilibrium shapes from 2D boundary-integral simulations, which produce the (c) flow field around a vesicle pushed by a rigid inclusion (blue circle). The vesicle membrane is color-coded (i) by its tension $\sigma$, and the draining flow in the interstitial space is driven by the pressure gradient (ii).
• Figure 2: (a) Transient dynamics to the quasi-steady equilibrium configurations, and (b,c,d) quasi-steady equilibrium shapes color-coded by $\bar{\sigma}=\sigma/\sigma_{\mathrm{max}}$. (a, i) Particle speed $U_{\mathrm{p}}$ and vesicle speed $U_{\mathrm{v}}$ as a function of time. Schematic showing the polar angle $\theta$ with respect to the forcing direction. (a, ii&iii) Configurations at $t=0$ and $t=400$. (b) A stiff membrane ($\kappa_b=1$ and $\nu=0.95$) and a quadratic film profile in the inset. (c) A soft, less deformable membrane ($\kappa_b=10^{-3}$ and $\nu=0.95$) and a dimple-shaped film profile in the inset. (d) A soft, more deformable membrane ($\kappa_b=10^{-3}$ and $\nu=0.65$) and a dimple-shaped film profile in the inset.
• Figure 3: Quasi-steady thin film characteristics. (a) 2D quasi-steady equilibrium film profiles, and (b) their corresponding tension distributions. Black curves: stiff vesicle; red curves: soft and less deformable vesicle; blue curves: soft and more deformable vesicle. (c) Distribution of equilibrium film profiles in size ratio $\bar{b}$ and reduced area $\nu$ for a stiff membrane ($\kappa_b = 1$). (d) Dimple-shaped film profile with arc-length as a function of the angle $s(\theta)$ around the neck at the rim $\theta=\phi$.
• Figure 4: Scaling of thin-film drainage from simulations. (a) Neck drainage for $\nu=0.95$: $h_0(t)$ decays self-similarly. (b) Pressure gradient–height scaling ($|P_x|$ vs $h_0$) for a soft membrane ($\kappa_b=10^{-3}$) as deformability varies from $\nu=0.95$ (blue) to $\nu=0.65$ (red). (c) Maximum membrane tension $\sigma_{\max}$ for three pairs of size ratio $\bar{b}$ and $\nu$ at $\kappa_b=10^{-3}$; dashed line: lysis tension $\sigma_{\mathrm{lysis}}$ scaled to $|\mathbf F|=5\times10^{-4}\,\mathrm{N\,m^{-1}}$. (d) Map of dimensional $\sigma_{\max}$ (mN m$^{-1}$) over $(\nu,\bar{b})$; the black dashed contour is $\sigma_{\max}=\sigma_{\mathrm{lysis}}=4\,\mathrm{mN\,m^{-1}}$. Rupture is predicted above this contour.