We investigate the equilibrium properties of a single area-minimising bubble trapped between two narrowly-separated parallel curved plates. We begin with the simple case of a a bubble trapped between concentric spherical plates. We develop a model that shows that the surface tension energy of the bubble is lower when confined between spherical plates as compared to a bubble trapped between flat plates. We confirm our findings by comparing against Surface Evolver simulations. Next, we derive a simple model for a bubble between arbitrarily curved parallel plates. The energy is found to be higher when the local Gaussian curvature of the plates is negative and lower when the curvature is positive. To check the validity of the the model we consider a bubble trapped between concentric tori. In the toroidal case we find that the sensitivity of the bubble's energy to the local curvature acts as a geometric potential capable of driving bubbles from regions with negative to positive curvature.
Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow with relative velocity parallel to the interface between them. The interface is unstable due to a Kelvin-Helmholtz type of instability in which fluid flow couples with inertial effects to cause an initial small perturbation to grow. Large amplitude disturbances form stable solitons. We consider the effects of applied magnetic fields when one of the two fluids is a ferrofluid. The dispersion relation governing mode growth is modified so that the magnetic field can destabilize the interface even in the absence of inertial …
Solvent exchange (also called solvent shifting or Ouzo effect) is a generally used bottom-up process to mass-produce nanoscale droplets. In this process, a good solvent for some oil is displaced by a poor one, leading to oil nanodroplet nucleation and subsequent growth. Here we perform this process on a hydrophobic substrate so that sessile droplets so-called surface nanodroplets-develop, following the work of Zhang et al. [Zhang, X.; Lu, Z.; Tan, H.; Bao, L.; He, Y.; Sun, C.; Lohse, D. Proc. Natl. Acad. Sci. U.S.A. 2015, 122, 9253-9257]. In contrast to what was done in that paper, we chose a …
In this paper we study the effects of dynamic wetting on the immiscible displacement of a high viscosity fluid subject to the radial injection of a less viscous fluid in a Hele-Shaw cell. The displaced fluid can leave behind a trailing film that coats the cell walls, dynamically affecting the pressure drop at the fluid interface. By considering the non-linear pressure drop in a boundary element formulation, we construct a Picard scheme to iteratively predict the interfacial velocity and subsequent displacement in finite mobility ratio flow regimes. Dynamic wetting delays the onset of finger bi…
In this paper, the interaction between two immiscible fluids with a finite mobility ratio is investigated numerically within a Hele-Shaw cell. Fingering instabilities initiated at the interface between a low viscosity fluid and a high viscosity fluid are analysed at varying capillary numbers and mobility ratios using a finite mobility ratio model. The present work is motivated by the possible development of interfacial instabilities that can occur in porous media during the process of CO$_2$ sequestration, but does not pretend to analyse this complex problem. Instead, we present a detailed stu…
Viscous Bending Mitigates the Spontaneous Meandering of Rivulets in Hele-Shaw Cells
Matière et Systèmes Complexes UMR 7057, Université Paris Cité, CNRS（复杂物质与系统联合研究实验室，巴黎西岱大学，法国国家科学研究中心）；Laboratory of Fluid Mechanics and Instabilities, EPFL（流体力学和不稳定性实验室，洛桑联邦理工学院）
