Mode-coupling approach to near-cuspidal patterns in planar fluid flows.

We investigate the evolution of the interface separating two Newtonian fluids of different viscosities in two-dimensional Stokes flow driven by suction or injection. A second-order, mode-coupling theory is used to explore key morphological aspects of the emerging interfacial patterns in the stage of the flow that bridges the purely linear and fully nonlinear regimes. In the linear regime, our analysis reveals that an injection-driven expanding interface is stable, while a contracting motion driven by suction is unstable.

Boundary-layer effects on electromagnetic and acoustic extraordinary transmission through narrow slits.

We study the problem of resonant extraordinary transmission of electromagnetic and acoustic waves through subwavelength slits in an infinite plate, whose thickness is close to a half-multiple of the wavelength. We build on the matched-asymptotics analysis of Holley & Schnitzer (2019 , 102381 (doi:10.1016/j.

Elastic fingering in three dimensions.

Recent studies on quasi-two-dimensional (2D) fluid flows in Hele-Shaw cells revealed the emergence of the so-called elastic fingering phenomenon. This pattern-forming process takes place when a reaction occurs at the fluid-fluid interface, transforming it into an elastic gel-like boundary. The interplay of viscous and elastic forces leads to the development of pattern morphologies significantly different from those seen in the conventional, purely hydrodynamic viscous fingering problem.

Generalized elastica patterns in a curved rotating Hele-Shaw cell.

We study a family of generalized elasticalike equilibrium shapes that arise at the interface separating two fluids in a curved rotating Hele-Shaw cell. This family of stationary interface solutions consists of shapes that balance the competing capillary and centrifugal forces in such a curved flow environment. We investigate how the emerging interfacial patterns are impacted by changes in the geometric properties of the curved Hele-Shaw cell.

Capillary and geometrically driven fingering instability in nonflat Hele-Shaw cells.

The usual viscous fingering instability arises when a fluid displaces another of higher viscosity in a flat Hele-Shaw cell, under sufficiently large capillary number conditions. In this traditional framing, the reverse flow case (more viscous fluid displacing a less viscous one) and the viscosity-matched situation (fluids of equal viscosities) are stable. We revisit this classical fluid dynamic problem, now considering flow in a nonflat Hele-Shaw cell.

Viscous fluid fingering on a negatively curved surface.

Viscous fingering formation in flat Hele-Shaw cells is a classical and widely studied fluid mechanical problem. We examine the development of viscous fluid fingering on a two-dimensional surface of constant negative Gaussian curvature, the hyperbolic plane H(2). A perturbative mode-coupling formalism is applied to study the influence of the negative surface curvature on the two most important pattern formation mechanisms of the system: fingertip splitting and finger competition.

Suppression of viscous fingering in nonflat Hele-Shaw cells.

Viscous fingering formation in flat Hele-Shaw cells is a classical and widely studied fluid mechanical problem. Recently, instead of focusing on the development of the fingering instability, researchers have devised different strategies aiming to suppress its appearance. In this work, we study a protocol that intends to inhibit the occurrence of fingering instabilities in nonflat (spherical and conical) Hele-Shaw cell geometries.

Interfacial pattern formation in confined power-law fluids.

The interfacial pattern formation problem in an injection-driven radial Hele-Shaw flow is studied for the situation in which a Newtonian fluid of negligible viscosity displaces a viscous non-Newtonian power-law fluid. By utilizing a Darcy-law-like formulation, we tackle the fluid-fluid interface evolution problem perturbatively, and we derive second-order mode-coupling equations that describe the time evolution of the perturbation amplitudes. This allows us to investigate analytically how the non-Newtonian nature of the dislocated fluid determines the morphology of the emerging interfacial patterns.

Stretch flow of confined non-Newtonian fluids: nonlinear fingering dynamics.

We employ a weakly nonlinear perturbative scheme to investigate the stretch flow of a non-Newtonian fluid confined in Hele-Shaw cell for which the upper plate is lifted. A generalized Darcy's law is utilized to model interfacial fingering formation in both the weak shear-thinning and weak shear-thickening limits. Within this context, we analyze how the interfacial finger shapes and the nonlinear competition dynamics among fingers are affected by the non-Newtonian nature of the stretched fluid.