A bottom-up approach to construct or deconstruct a fluid instability

Fluid instabilities have been the subject of study for a long time. Despite all the extensive knowledge, they still constitute a serious challenge for many industrial applications. Here, we experimentally consider an interface between two fluids with different viscosities and analyze their relative displacement. We designed the contents of each fluid in such a way that a chemical reaction takes place at the interface and use this reaction to suppress or induce a fingering instability at will. This process describes a road map to control viscous fingering instabilities in more complex systems via interfacial chemical reactions.

Spreading or contraction of viscous drops between plates: single, multiple or annular drops

The behaviour of a viscous drop squeezed between two horizontal planes (a squeezed Hele-Shaw cell) is treated by both theory and experiment. When the squeezing force $F$ is constant and surface tension is neglected, the theory predicts ultimate growth of the radius $a\sim t^{1/8}$ with time $t$. This theory is first reviewed and found to be in excellent agreement with experiment. Surface tension at the drop boundary reduces the interior pressure, and this effect is included in the analysis, although it is negligibly small in the squeezing experiments. An initially elliptic drop tends to become circular as $t$ increases. More generally, the circular evolution is found to be stable under small perturbations. If, on the other hand, the force is reversed ($F<0$), so that the plates are drawn apart (the ‘contraction’, or ‘lifting plate’, problem), the boundary of the drop is subject to a fingering instability on a scale determined by surface tension. The effect of a trapped air bubble at the centre of the drop is then considered. The annular evolution of the drop under constant squeezing is still found to follow a ‘one-eighth’ power law, but this is unstable, the instability originating at the boundary of the air bubble, i.e. the inner boundary of the annulus. The air bubble is realised experimentally in two ways: first by simply starting with the drop in the form of an annulus, as nearly circular as possible; and second by forcing four initially separate drops to expand and merge, a process that involves the resolution of ‘contact singularities’ by surface tension. If the plates are drawn apart, the evolution is still subject to the fingering instability driven from the outer boundary of the annulus. This instability is realised experimentally by levering the plates apart at one corner: fingering develops at the outer boundary and spreads rapidly to the interior as the levering is slowly increased. At a later stage, before ultimate rupture of the film and complete separation of the plates, fingering spreads also from the boundary of any interior trapped air bubble, and small cavitation bubbles appear in the very low-pressure region, far from the point of leverage. This exotic behaviour is discussed in the light of the foregoing theoretical analysis.

MATHEMATICAL SOLUTION OF FINGERING PHENOMENON IN VERTICAL DOWNWARD DIRECTION THROUGH HETEROGENEOUS POROUS MEDIUM

Present study explores the Fingering (Instability) phenomenon's mathematical model that ensues during the process of secondary oil recovery where two not miscible fluids (water and oil) flow within a heterogeneous porous medium as water is injected vertically downwards. Variational iteration method with proper initial and boundary conditions is being used to determine approximate analytic solution for governing nonlinear second order partial differential equation. Whereas MATLAB is applied to acquire the solution's numerical findings and graphical representations.

Solute transport by suspended buoyant particles

The transport of a colouring solute, driven by the buoyant displacement of microscopic suspended particles, and in the absence of net flow, is studied experimentally in a Hele Shaw cell. Initially, a sharp interface between a transparent fluid without particles and an underlying coloured suspension is obtained. From this situation, the suspended particles rise, carrying the solute in the form of a fingering instability across the interface, where a light transmission technique is used to measure the local solute concentration. This one attains an asymptotic value that increases with the solid fraction ϕ of suspended particles, and decreases with the distance to the interface. The solute mass discharge also increases with ϕ, always being relatively small (< 3%). The onset and development of the instability as the mechanism driving the transport of the solute is discussed.

Fingering instability in spreading epithelial monolayers: roles of cell polarisation, substrate friction and contractile stresses

Collective cell migration plays a crucial role in many developmental processes that underlie morphogenesis, wound healing, or cancer progression. In such coordinated behaviours, cells are organised in coherent structures and...

Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments

We show that both the viscosity ratio between the inner and outer fluid and the degree of anisotropy control the symmetry of dendritic patterns in the viscous fingering instability.