Fingering stabilization and adhesion force in the lifting flow with a fluid annulus.

The lifting Hele-Shaw cell flow commonly involves the stretching of a viscous oil droplet surrounded by air, in the confined space between two parallel plates. As the upper plate is lifted, viscous fingering instabilities emerge at the air-oil interface. Such an interfacial instability phenomenon is widely observed in numerous technological and industrial applications, being quite difficult to control. Motivated by the recent interest in controlling and stabilizing the Saffman-Taylor instability in lifting Hele-Shaw flows, we propose an alternative way to restrain the development of interfacial disturbances in this gap-variable system. Our method modifies the traditional plate-lifting flow arrangement by introducing a finite fluid annulus layer encircling the central oil droplet, and separating it from the air. A second-order, perturbative mode-coupling approach is employed to analyze morphological and stability behaviors in this three-fluid, two-interface, doubly connected system. Our findings indicate that the intermediate fluid ring can significantly stabilize the interface of the central oil droplet. We show that the effectiveness of this stabilization protocol relies on the appropriate choice of the ring's viscosity and thickness. Furthermore, we calculate the adhesion force required to detach the plates, and find that it does not change significantly with the addition of the fluid envelope as long as it is sufficiently thin. Finally, we detect no distinction in the adhesion force computed for stable or unstable annular interfaces, indicating that the presence of fingering at the ring's boundaries has a negligible effect on the adhesion force.

Wrinkling and folding patterns in a confined ferrofluid droplet with an elastic interface.

A thin elastic membrane lying on a fluid substrate deviates from its flat geometry on lateral compression. The compressed membrane folds and wrinkles into many distinct morphologies. We study a magnetoelastic variant of such a problem where a viscous ferrofluid, surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. Elasticity comes into play when the fluids are brought into contact, and due to a chemical reaction, the interface separating them becomes a gel-like elastic layer. A perturbative linear stability theory is used to investigate how the combined action of magnetic and elastic forces can lead to the development of smooth, low-amplitude, sinusoidal wrinkles at the elastic interface. In addition, a nonperturbative vortex sheet approach is employed to examine the emergence of highly nonlinear, magnetically driven, wrinkling and folding equilibrium shape structures. A connection between the magnetoelastic shape solutions induced by a radial magnetic field and those produced by nonmagnetic means through centrifugal forces is also discussed.

Kinetic undercooling in Hele-Shaw flows.

A central topic in Hele-Shaw flow research is the inclusion of physical effects on the interface between fluids. In this context, the addition of surface tension restrains the emergence of high interfacial curvatures, while consideration of kinetic undercooling effects inhibits the occurrence of high interfacial velocities. By connecting kinetic undercooling to the action of the dynamic contact angle, we show in a quantitative manner that the kinetic undercooling contribution varies as a linear function of the normal velocity at the interface. A perturbative weakly nonlinear analysis is employed to extract valuable information about the influence of kinetic undercooling on the shape of the emerging fingered structures. Under radial Hele-Shaw flow, it is found that kinetic undercooling delays, but does not suppress, the development of finger tip-broadening and finger tip-splitting phenomena. In addition, our results indicate that kinetic undercooling plays a key role in determining the appearance of tip splitting in rectangular Hele-Shaw geometry.

Adhesion force in fluids: effects of fingering, wetting, and viscous normal stresses.

Probe-tack measurements evaluate the adhesion strength of viscous fluids confined between parallel plates. This is done by recording the adhesion force that is required to lift the upper plate, while the lower plate is kept at rest. During the lifting process, it is known that the interface separating the confined fluids is deformed, causing the emergence of intricate interfacial fingering structures. Existing meticulous experiments and intensive numerical simulations indicate that fingering formation affects the lifting force, causing a decrease in intensity. In this work, we propose an analytical model that computes the lifting adhesion force by taking into account not only the effect of interfacial fingering, but also the action of wetting and viscous normal stresses. The role played by the system's spatial confinement is also considered. We show that the incorporation of all these physical ingredients is necessary to provide a better agreement between theoretical predictions and experiments.

Influence of wetting on fingering patterns in lifting Hele-Shaw flows.

We study the pattern formation dynamics related to the displacement of a viscous wetting fluid by a less viscous nonwetting fluid in a lifting Hele-Shaw cell. A perturbative weakly nonlinear analysis of the problem is presented. We focus on examining how wetting effects influence the morphology of the emerging interfacial patterns at the early nonlinear regime. Our analytical results indicate that wettability has a significant impact on the resulting nonlinear patterns. It restrains finger length variability while inducing the development of structures presenting short, blunt penetrating fingers of the nonwetting fluid, alternated by short, sharp fingers of the wetting fluid. The basic mode-coupling mechanisms leading to such behavior are discussed.

Radial viscous fingering: wetting film effects on pattern-forming mechanisms.

We consider the interfacial motion between two immiscible viscous fluids in the confined geometry of a radial Hele-Shaw cell. In this framework, we investigate the influence of a thin wetting film trailing behind the displaced fluid on the linear and weakly nonlinear dynamics of the system. More specifically, we examine how the interface instability and the pattern formation mechanisms of finger tip splitting and finger competition are affected by the presence of such a film in the low capillary number limit. Our theoretical analysis is carried out by employing a mode-coupling theory, which allows analytic assess to wetting-induced changes in pattern morphology at the onset of nonlinearities.