A set of experiments of spontaneous imbibition for water displacing oil or a mixture of water and glycerine displacing oil, on flat and rectangular Hele-Shaw cells, is reported. Visualization of the imbibition process allowed the knowledge of the evolution of three basic kinematical variables: the active oil area, the interfacial length and the mean velocity of displacement. A derived kinematic...

Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a Cahn–Hilliard–Navier–Stokes model introduced by Abels, Garcke and Grün (Math. Models Methods Appl. Sci. 2012), which uses a volume averaged velocity, we derive a diffuse interface mo...

Nature, in quest for the best designs has shaped its vital systems into fractal geometries. Effectual way of spontaneous fabrication of scalable, ordered fractal-like structures by controlling Saffman-Taylor instability in a lifted Hele-Shaw cell is deployed here. In lifted Hele-Shaw cell uncontrolled penetration of low-viscosity fluid into its high-viscosity counterpart is known to develop irr...

The Saffman-Taylor viscous fingering problem is investigated for the displacement of a non-Newtonian fluid by a Newtonian one in a radial Hele-Shaw cell. We execute a mode-coupling approach to the problem and examine the morphology of the fluid-fluid interface in the weak shear limit. A differential equation describing the early nonlinear evolution of the interface modes is derived in detail. O...

The Muskat, or Muskat-Leibenzon, problem describes the evolution of the interface between two immiscible fluids in a porous medium or Hele-Shaw cell under applied pressure gradients or fluid injection/extraction. In contrast to the Hele-Shaw problem (the one-phase version of the Muskat problem), there are few nontrivial exact solutions or analytic results for the Muskat problem. For the stable,...

We review the fundamental modeling and numerical simulation for a prediction of fiber orientation during injection molding process of polymer composite. In general, the simulation of fiber orientation involves coupled analysis of flow, temperature, moving free surface, and fiber kinematics. For the governing equation of the flow, Hele-Shaw flow model along with the generalized Newtonian constit...

In this paper we study the long-time behavior of solutions of the one phase Hele-Shaw problem without surface tension. We show that after a finite time solutions of the Hele-Shaw problem become Lipschitz continuous with nondegenerate free boundary speed. It then follows that after a finite time the solution and the free boundary become smooth in space and time. 0 Introduction Let K = {x ∈ IR : ...