Shape transitions of sedimenting confined droplets and capsules: from oblate to bullet-like geometries

TL;DR

This work investigates shape transitions of sedimenting confined droplets and capsules, revealing a universal oblate-to-bullet-like transition governed by confinement and, for capsules, by hydrodynamic pressure rather than flexibility. Using experiments and coupled lattice Boltzmann–immersed boundary simulations, the authors identify two regimes: a viscous-dominated regime at low confinement and a pressure-dominated regime at high confinement, with a critical confinement near $k_c\approx 0.37$ (scaling $h_0\sim2a$ yields $k_c$ around $1/3$). A 2D lubrication analysis provides analytical support for the crossover, showing pressure contributions dominate as walls constrict the gap, independent of Bond number in the studied range. These findings enhance understanding of fluid–structure interactions in confined environments and have potential implications for biomedical diagnostics, filtration, and multiphase flows.

Abstract

The transport and deformation of confined droplets and flexible capsules are central to diverse phenomena and applications, from biological flows in microcapillaries to industrial processes in porous media. Inspired by experiments, we perform numerical simulations to investigate their shape dynamics under varying levels of confinement and particle flexibility. A transition from an oblate to a bullet-like shape is observed at a confinement threshold, independent of flexibility, which agrees with our analytical calculations. A fluid-structure interaction analysis reveals two regimes: a pressure-dominated and a viscous-dominated regime. For highly flexible particles, the pressure-dominated regime prevails and the deformation is enhanced. These findings offer new insights into the transport of flexible particles in confined environments, with implications for biomedical applications, filtration technologies, and multiphase fluid mechanics.

Figures (13)

• Figure 1: (a) Shapes of sedimenting droplets (experiments and simulations) and capsules (simulations) at high confinement $k$. In the first row, we show droplets of dyed glycerol sedimenting in silicone oil. We use different volumes $12 \mu$L-- $22 \mu$L and surface tensions $\sigma$$\{19, 9, 4\}$ mN/m (left to right). Whereas the small droplets with high surface tension remain spherical, the larger droplets with the lowest surface tension become bullet-shaped (pink colour). The grey vertical lines in the first row are the tube edges. AR stands for aspect ratio of the steady shape. (b) Shape transitions for capsules for different values of confinement parameter $k$(between 0.05 and 0.6) and Bond number $\mathrm{Bo}$between 0.079 and 790 obtained numerically (the parameters are available in the SM).
• Figure 2: Shape transitions for capsules differing in flexibility, determined by the Bond number $\mathrm{Bo}$. Higher $\mathrm{Bo}$ corresponds to higher flexibility. The aspect ratio AR increases with the confinement parameter as $k \to 0$ (unconfined capsule) and decreases as $k \to 1$ (ultraconfinement). For illustration, we show different capsule shapes at different flexibilities and levels of confinement. The green capsule is on the green curve for Bo = 7.9.
• Figure 3: Ratio between the pressure and viscous contributions to the drag force. Here $\lambda_p =F^{D}_{p} /(\mu V_t)$, $\lambda_v = F^{D}_{v} /(\mu V_t)$ and $\lambda_t = \lambda_p + \lambda_v$. The subscripts $p$, $v$ and $t$ stand for pressure, viscous and total.
• Figure 4: Force vector and steady shape for different values of confinement and Bond number. The force vectors are scaled according to their magnitude. The results are in lattice units. The calculation of the force vectors from fluid stresses is detailed in the SM. The colorbar indicates the force magnitude, whose values are multiplied by $10^{-4}$.
• Figure 5: The main experimental setup. A water tank of dimensions $10 \times10 \times 50 {\rm cm}^3$ in which a thin capillary (diameter $5$ mm, length $40$ cm) is held.