Related papers: Systematic weakly nonlinear analysis of interfacia…
We investigated the two-dimensional flows of a viscoplastic fluid in symmetric channels with impermeable walls under no-slip boundary conditions. As response functions for the Cauchy stress tensor of the viscoplastic fluid, we considered…
We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in…
We introduce two new lowest order methods, a mixed method, and a hybrid Discontinuous Galerkin (HDG) method, for the approximation of incompressible flows. Both methods use divergence-conforming linear Brezzi-Douglas-Marini space for…
We investigate the convective instability resulting from the dissolution of carbon dioxide (CO$_{2}$) into water in a heterogeneous Hele-Shaw cell utilizing both experimental and numerical approaches. Experiments are conducted in a…
We analyze a recent experiment of Sharon \textit{et al.} (2003) on the coarsening, due to surface tension, of fractal viscous fingering patterns (FVFPs) grown in a radial Hele-Shaw cell. We argue that an unforced Hele-Shaw model, a natural…
In this paper we revisit the derivation of a nonlocal interfacial Hamiltonian model for systems with short-ranged intermolecular forces. Starting from a microscopic Landau-Ginzburg-Wilson Hamiltonian with a double parabola potential, we…
This paper concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where…
We study the Couette flow of a quasi-2d soft-glassy material in a Hele-Shaw geometry. The material is chosen to be above the jamming point, where a yield stress $\sigma_Y$ emerges, below which the material deforms elastically and above…
The slow viscous flow through a doubly-periodic array of cylinders does not have an analytical solution. However, as a reduced model for the flow within fibrous porous media, this solution is important for many real-world systems. We…
The accurate and stable simulation of viscoelastic flows remains a significant computational challenge, exacerbated for flows in non-trivial and practical geometries. Here we present a new high-order meshless approach with variable…
Having a finite interfacial thickness, the phase-field models supply a way to model the fluid interfaces, which allows the calculations of the interface movements and deformations on the fixed grids. Such modeling is applied to the…
We consider a Hele-Shaw model that describes tumor growth subject to nutrient supply. The model is derived by taking the incompressible limit of porous medium type equations, and the boundary instability of this model was recently studied…
We address pattern selection problems in nonlinear interface dynamics by maximizing the entropy of the most probable (classical) scenario associated with the processes. This variational principle we applied to well-known selection problems…
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
Knowledge of the underlying mechanisms of multiphase flow dynamics in porous media is crucial for optimizing subsurface engineering applications like geological carbon sequestration. However, studying the micro-mechanisms of multiphase…
Using the anelastic approximation of linearised hydrodynamic equations, we investigate the development of axially symmetric small perturbations in thin Keplerian discs. The sixth-order dispersion equation is derived and numerically solved…
Analytical solutions for both a finite assembly and a periodic array of bubbles steadily moving in a Hele-Shaw channel are presented. The particular case of multiple fingers penetrating into the channel and moving jointly with an assembly…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
We report experimental evidences of anomalous kinetic roughening in the stable displacement of an oil-air interface in a Hele-Shaw cell with strong quenched disorder. The disorder consists on a random modulation of the gap spacing…
This study investigates three-dimensional, steady-state, and non-Newtonian flows within a very thin porous medium (VTPM). The medium is modeled as a domain confined between two parallel plates and perforated by solid cylinders that connect…