Related papers: Stabilizing effect of tip splitting on the interfa…
The displacement of a fluid by another less viscous one in a quasi-two dimensional geometry typically leads to complex fingering patterns. In an isotropic system, dense-branching growth arises, which is characterized by repeated…
We study the linear stability of an isotropic active fluid in three different geometries: a film of active fluid on a rigid substrate, a cylindrical thread of fluid, and a spherical fluid droplet. The active fluid is modeled by the…
The three-layer Saffman-Taylor problem introduces two coupled moving interfaces separating the three fluids. A very recent weakly nonlinear analysis of this problem in a radial Hele-Shaw cell setup has shown that the morphologies of the…
To find the regularities of formed fingers in gravity driven coating flows on upper cylinder and sphere, the mathematical formulation to model the fingering instability on cylindrical or spherical surface which consists of a capillary wave…
When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the…
We demonstrate that topological insulators exhibit an intrinsic interfacial instability that amplifies small interface fluctuations, resulting in chaotic behavior during interface growth. This mechanism is fundamentally different from…
Cell division and death can be regulated by the mechanical forces within a tissue. We study the consequences for the stability and roughness of a propagating interface, by analysing a model of mechanically-regulated tissue growth in the…
A pair of concentric spheres separated by a small gap form a spherical Hele-Shaw cell. In this cell an interfacial instability arises when two immiscible fluids flow. We derive the equation of motion for the interface perturbation…
The spreading of a thin film of suspension on a spinning disk and the accompanying contact line instability is studied through flow visualization experiments. The critical radius for the onset of instability shows an increase with increase…
Inspired by river networks and other structures formed by Laplacian growth, we use the Loewner equation to investigate the growth of a network of thin fingers in a diffusion field. We first review previous contributions to illustrate how…
An instability may arise when a hot viscous fluid enters a thin gap and cools through heat transfer to a colder surrounding environment. Fluids whose viscosity increases strongly upon cooling create a positive feedback in which warmer…
Viscous fingering patterns can form at the interface between two immiscible fluids confined in the gap between a pair of flat plates; whenever the fluid with lower viscosity displaces the one of higher viscosity the interface is unstable.…
This work is intended to be a contribution to the study of the morphology of the rising convective columns, for a better representation of the processes of entrainment and detrainment. We examine technical methods for the description of the…
Interfaces between stratified epithelia and their supporting stromas commonly exhibit irregular shapes. Undulations are particularly pronounced in dysplastic tissues and typically evolve into long, finger-like protrusions in carcinomas. In…
We show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhang equation and the Lai-Das Sarma equation) and related atomistic models of epitaxial growth…
We investigate the linear stability of a flat interface that separates a liquid layer from a fully-developed turbulent gas flow. In this context, linear-stability analysis involves the study of the dynamics of a small-amplitude wave on the…
A systematic analytic treatment of fluctuations in Laplacian growth is given. The growth process is regularized by a short-distance cutoff $\hbar$ preventing the cusps production in a finite time. This regularization mechanism generates…
Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We…
It is shown that step moving to meet solution flow can be unstable against lateral perturbations. The instability of long-wavelength perturbations occurs at values of the solution flow intensity less than some critical value depending on…
Impact of a droplet on an undercooled surface is a complex phenomenon as it simultaneously instigates several physical processes that cover a broad spectrum of transport phenomena and phase-transition. Here, we report and explain an…