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Related papers: Bubbles and Filaments: Stirring a Cahn-Hilliard Fl…

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We present an extensive direct numerical simulation of statistically steady, homogeneous, isotropic turbulence in two-dimensional, binary-fluid mixtures with air-drag-induced friction by using the Cahn-Hilliard-Navier-Stokes equations. We…

Fluid Dynamics · Physics 2016-11-16 Nairita Pal , Prasad Perlekar , Anupam Gupta , Rahul Pandit

The Cahn-Hilliard model with reaction terms can lead to situations in which no coarsening is taking place and, in contrast, growth and division of droplets occur which all do not grow larger than a certain size. This phenomenon has been…

Analysis of PDEs · Mathematics 2025-11-07 Harald Garcke , Kei Fong Lam , Robert Nürnberg , Andrea Signori

A phase-field model for two-phase immiscible, incompressible porous media flow with surface tension effects is considered. The pore-scale model consists of a strongly coupled system of Stokes-Cahn-Hilliard equations. The fluids are…

Analysis of PDEs · Mathematics 2023-01-25 Nitu Lakhmara , Hari Shankar Mahato

We study a Cahn--Hilliard two-phase model describing the flow of two viscoelastoplastic fluids, which arises in geodynamics. A phase-field variable indicates the proportional distribution of the two fluids in the mixture. The motion of the…

Analysis of PDEs · Mathematics 2025-10-01 Fan Cheng , Robert Lasarzik , Marita Thomas

We measure the liquid content, the bubble speeds, and the distribution of bubble sizes, in a vertical column of aqueous foam maintained in steady-state by continuous bubbling of gas into a surfactant solution. Nearly round bubbles…

Soft Condensed Matter · Physics 2007-05-23 K. Feitosa , Olivia L. Halt , Randall D. Kamien , D. J. Durian

The Cahn-Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to many different contexts in several scientific fields. In this survey article, we…

Analysis of PDEs · Mathematics 2022-06-22 Hao Wu

We call a system bouncing ball billiard if it consists of a particle that is subjected to a constant vertical force and bounces inelastically on a one-dimendional vibrating periodically corrugated floor. Here we choose circular scatterers…

Chaotic Dynamics · Physics 2007-05-23 L. Matyas , R. Klages

Cavitation and bubble dynamics are central concepts in engineering, the natural sciences, and the mathematics of fluid mechanics. Due to the nonlinear nature of their dynamics, the governing equations are not fully solvable. Here, the…

Fluid Dynamics · Physics 2014-10-15 Alexander R. Klotz

A Cahn-Hilliard equation with stochastic multiplicative noise and a random convection term is considered. The model describes isothermal phase-separation occurring in a moving fluid, and accounts for the randomness appearing at the…

Analysis of PDEs · Mathematics 2021-04-21 Luca Scarpa

In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where…

Fluid turbulence is commonly associated with stronger drag, greater heat transfer, and more efficient mixing than in laminar flows. In many natural and industrial settings, turbulent liquid flows contain suspensions of dispersed bubbles and…

Fluid Dynamics · Physics 2020-05-29 Varghese Mathai , Detlef Lohse , Chao Sun

We investigate by direct numerical simulations the flow that rising bubbles cause in an originally quiescent fluid. We employ the Eulerian-Lagrangian method with two-way coupling and periodic boundary conditions. In order to be able to…

Fluid Dynamics · Physics 2009-12-29 Irene Mazzitelli , Detlef Lohse

A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface…

Analysis of PDEs · Mathematics 2024-07-24 Nitu Lakhmara , Hari Shankar Mahato

We consider the Cahn-Hilliard equation, which models phase separation in binary fluids, on the two-dimen\-sional torus in the presence of advection by a given background shear flow, satisfying certain conditions and of sufficiently large…

Analysis of PDEs · Mathematics 2026-05-12 Yu Feng , Yuanyuan Feng , Anna L. Mazzucato , Xiaoqian Xu

The bubble size distribution below a breaking wave is of paramount interest when quantifying mass exchanges between the atmosphere and oceans. Mass fluxes at the interface are driven by bubbles that are small compared to the Hinze scale…

Fluid Dynamics · Physics 2021-12-14 A. Rivière , D. Ruth , W. Mostert , L. Deike , S. Perrard

In this paper we propose a mathematical model of phase separation for a quasi-incompressible binary mixture where the spinodal decomposition is induced by an heat flux governed by the Cattaneo-Maxwell equation. As usual, the phase…

Mathematical Physics · Physics 2013-06-04 A. Berti , I. Bochicchio , M. Fabrizio

The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic…

Analysis of PDEs · Mathematics 2021-04-27 Patrik Knopf , Kei Fong Lam , Chun Liu , Stefan Metzger

We hypothesize that dynamical systems concepts used to study the transition to turbulence in shear flows are applicable to other transition phenomena in fluid mechanics. In this paper, we consider a finite air bubble that propagates within…

Fluid Dynamics · Physics 2020-07-01 J. S. Keeler , A. B. Thompson , G. Lemoult , A. Juel , A. L. Hazel

An initially homogeneous freely evolving fluid of inelastic hard spheres develops inhomogeneities in the flow field (vortices) and in the density field (clusters), driven by unstable fluctuations. Their spatial correlations, as measured in…

Statistical Mechanics · Physics 2009-10-30 J. A. G. Orza , R. Brito , T. P. C. Van Noije , M. H. Ernst

We investigate a new diffuse-interface model that describes creeping two-phase flows (i.e., flows exhibiting a low Reynolds number), especially flows that permeate a porous medium. The system of equations consists of a Brinkman equation for…

Analysis of PDEs · Mathematics 2025-09-15 Pierluigi Colli , Patrik Knopf , Giulio Schimperna , Andrea Signori