Related papers: Hele-Shaw flow for parity odd three-dimensional fl…
We study the linear stability of the displacement of three Stokes fluids with constant viscosity in a porous medium when the middle fluid is contained in a bounded region. We use the Hele-Shaw model. The eigenfunctions of the stability…
In this paper, the interfacial motion between two immiscible viscous fluids in the confined geometry of a Hele-Shaw cell is studied. We consider the influence of a thin wetting film trailing behind the displaced fluid, which dynamically…
A rest fluid displaced by a less viscous fluid in a porous medium triggers the so-called Saffman-Taylor instability at their contact front and hence forms complicated finger-like patterns. When the two fluids are miscible, the surface…
We study the spreading and leveling of a gravity current in a Hele-Shaw cell with flow-wise width variations as an analog for flow {in fractures and horizontally heterogeneous aquifers}. Using phase-plane analysis, we obtain second-kind…
In this note, we discuss the quantum Hele-Shaw flow, a random measure process in the complex plane introduced by the physicists P.Wiegmann, A. Zabrodin, et al. This process arises in the theory of electronic droplets confined to a plane…
We perform a linear stability analysis of three-layer radial porous media and Hele-Shaw flows with variable viscosity in the middle layer. A nonlinear change of variables results in an eigenvalue problem that has time-dependent coefficients…
Fractured porous media or double porosity media are common in nature. At the same time, accurate modeling remains a significant challenge due to bi-modal pore size distribution, anisotropy, multi-field coupling, and various flow patterns.…
Existing theoretical analyses of Faraday waves in Hele-Shaw cells rely on the Darcy approximation and assume a parabolic flow profile in the narrow direction. However, Darcy's model is known to be inaccurate when convective or unsteady…
Over 125 years ago, Henry Selby Hele-Shaw realized that the depth-averaged flow in thin gap geometries can be closely approximated by two-dimensional (2D) potential flow, in a surprising marriage between the theories of viscous-dominated…
A plane turbulent mixing in a shear flow of an ideal homogeneous fluid confined between two relatively close rigid walls is considered. The character of the flow is determined by interaction of vortices arising at the nonlinear stage of the…
The Darrieus--Landau instability of premixed flames propagating in a narrow Hele-Shaw channel in the presence of a strong shear flow is investigated, incorporating also the Rayleigh--Taylor and diffusive-thermal instabilities. The flow…
We fill a viscous liquid in a vertically stood cell of millimeter thickness, called the Hele-Shaw cell, and insert a disk in the liquid whose thickness is smaller than the cell thickness. The disk starts falling in the liquid due to gravity…
We study capillary-gravity surface waves for fluid flows governed by Darcy's law. This includes flows in vertical Hele-Shaw cells and in porous media (the one-phase Muskat problem) with finite or infinite depth. The free boundary is acted…
Exact solutions are presented for a doubly-periodic array of steadily moving bubbles in a Hele-Shaw cell when surface tension is neglected. It is assumed that the bubbles either are symmetrical with respect to the channel centreline or have…
Pushing two fluids with different density one against the other causes the development of the Rayleigh-Taylor instability at their interface, which further evolves in a complex mixing layer. In porous media, this process is influenced by…
In this paper, we study the dynamics of a two-dimensional viscous fluid evolving through a porous medium or a Hele-Shaw cell, driven by gravity and surface tension. A key feature of this study is that the fluid is confined within a vessel…
Predicting the flow of non-Newtonian fluids in porous structure is still a challenging issue due to the interplay betwen the microscopic disorder and the non-linear rheology. In this letter, we study the case of an yield stress fluid in a…
The free boundary problem of a two phase flow in a rotating Hele-Shaw cell with Coriolis effects is studied. Existence and uniqueness of solutions near spheres is established, and the asymptotic stability and instability of the trivial…
The complex behaviour of air-liquid interfaces driven into Hele-Shaw channels at high speeds could arise from oscillatory dynamics; yet, both the physical and dynamical mechanisms that lead to interfacial oscillations remain unclear. We…
We study the deformation and transport of elastic fibers in a viscous Hele-Shaw flow with curved streamlines. The variations of the global velocity and orientation of the fiber follow closely those of the local flow velocity. The ratios of…