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The Saffman-Taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele-Shaw cell. Experiments in radial flow geometry form fan-like patterns, in which…
We report on the filaments that develop self-consistently in a new numerical simulation of cloud formation by colliding flows. As in previous studies, the forming cloud begins to undergo gravitational collapse because it rapidly acquires a…
We experimentally study the viscous fingering instability in a fluid-fluid phase separated colloid-polymer mixture by means of laser scanning confocal microscopy and microfluidics. We focus on three aspects of the instability. (i) The…
The immiscible displacement of a fluid by another one inside a porous medium produces different types of patterns depending on the capillary number Ca and viscosity ratio M. At high Ca, viscous fingers resulting from the viscous instability…
I show that the evolution of a two dimensional surface in a Laplacian field can be described by Hamiltonian dynamics. First the growing region is mapped conformally to the interior of the unit circle, creating in the process a set of…
The finger-like branching pattern that occurs when a less viscous fluid displaces a more viscous one confined between two parallel plates has been widely studied as a classical example of a mathematically-tractable hydrodynamic instability…
A new model of Laplacian stochastic growth is formulated using conformal mappings. The model describes two growth regimes, stable and turbulent, separated by a sharp phase transition. The first few Fourier components of the mapping define…
Purely repulsive active particles spontaneously undergo motility-induced phase separation (MIPS) into condensed and dilute phases. Remarkably, the mechanical tension measured along the interface between these phases is negative. In…
In this work we study the global solvability of moisture dynamics with phase changes for warm clouds. We thereby in comparison to previous studies [Hittmeir-Klein-Li-Titi (2017)] take into account the different gas constants for dry air and…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
We use a lattice gas cellular automata model in the presence of random dynamic scattering sites and quenched disorder in the two-phase immiscible model with the aim of producing an interface dynamics similar to that observed in Hele-Shaw…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
Excess pore pressure in granular--fluid mixtures can transiently suppress frictional contacts and dramatically enhance flow mobility, yet its evolution is commonly modeled using constant effective diffusivities. Here we show that the…
Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
Moist processes are among the most important drivers of atmospheric dynamics,and scale analysis and asymptotics are cornerstones of theoretical meteorology. Accounting for moist processes in systematic scale analyses therefore seems of…
Traditional mathematical models of Hele--Shaw flow consider the injection (or withdrawal) of an air bubble into (or from) an infinite body of viscous fluid. The most commonly studied feature of such a model is how the Saffman-Taylor…
We consider the process of convective dissolution in homogeneous and isotropic porous media. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is…
Understanding dynamical facilitation in nonequilibrium glass-forming systems driven by active forces remains an open challenge. In particular, it is unclear whether facilitation survives in active glasses, where persistent self-propulsion…
Condensational growth of cloud droplets due to supersaturation fluctuations is investigated by solving the hydrodynamic and thermodynamic equations using direct numerical simulations with droplets being modeled as Lagrangian particles. The…