Field-induced patterns in confined magnetorheological fluids

Field-controlled flow and shape of a magnetorheological fluid annulus

We investigate the behavior of a magnetorheological (MR) fluid annulus, bounded by a nonmagnetic fluid and confined in a Hele-Shaw cell, under the simultaneous effect of in-plane, external radial and azimuthal magnetic fields. A second-order mode-coupling theory is used to study the early nonlinear stage of the pattern-forming dynamics. We examine changes in the morphology of the MR fluid annular structure as a function of its magnetic-field-tunable rheological properties, as well as the combined magnetic field's intensities, and thickness of the ring. Our weakly nonlinear perturbative results show that, depending on the system control parameters, the MR fluid annulus adopts various stationary shapes. These equilibrium annular structures present slightly bent, asymmetric fingered protrusions which may emerge on the inner, outer, or even on both boundaries of the magnetic fluid ring. On top of these morphological changes, we find that the resulting permanent shape patterns rotate with a well defined angular velocity. We focus on analyzing how the overall shape of the fingered patterns, in particular their sharpness and asymmetric form, as well as the number of resulting fingers are impacted by the magnetic-field-dependent yield stress of the MR fluid annulus. The influence of the magnetically controlled rheological properties of the MR fluid on the angular velocity of the rotating annulus is also scrutinized.

Ferrofluid patterns in Hele-Shaw cells: Exact, stable, stationary shape solutions

We investigate a quasi-two-dimensional system composed of an initially circular ferrofluid droplet surrounded by a nonmagnetic fluid of higher density. These immiscible fluids flow in a rotating Hele-Shaw cell, under the influence of an in-plane radial magnetic field. We focus on the situation in which destabilizing bulk magnetic field effects are balanced by stabilizing centrifugal forces. In this framing, we consider the interplay of capillary and magnetic normal traction effects in determining the fluid-fluid interface morphology. By employing a vortex-sheet formalism, we have been able to find a family of exact stationary N-fold polygonal shape solutions for the interface. A weakly nonlinear theory is then used to verify that such exact interfacial solutions are in fact stable.

Interfacial patterns in magnetorheological fluids: Azimuthal field-induced structures

Despite their practical and academic relevance, studies of interfacial pattern formation in confined magnetorheological (MR) fluids have been largely overlooked in the literature. In this work, we present a contribution to this soft matter research topic and investigate the emergence of interfacial instabilities when an inviscid, initially circular bubble of a Newtonian fluid is surrounded by a MR fluid in a Hele-Shaw cell apparatus. An externally applied, in-plane azimuthal magnetic field produced by a current-carrying wire induces interfacial disturbances at the two-fluid interface, and pattern-forming structures arise. Linear stability analysis, weakly nonlinear theory, and a vortex sheet approach are used to access early linear and intermediate nonlinear time regimes, as well as to determine stationary interfacial shapes at fully nonlinear stages.

Radial viscous fingering in yield stress fluids: onset of pattern formation

We report analytical results for the development of interfacial instabilities in a radial Hele-Shaw cell in which a yield stress fluid is pushed by a Newtonian fluid of negligible viscosity. By dealing with a gap averaging of the Navier-Stokes equation, we derive a Darcy-law-like equation for the problem, valid in the regime of high viscosity compared to yield stress effects. A mode-coupling approach is executed to examine the morphological features of the fluid-fluid interface at the onset of nonlinearity. Within this context, mechanisms for explaining the rising of tip-splitting and side-branching events are proposed.

Weakly nonlinear study of normal-field instability in confined ferrofluids

Similar to the classic three-dimensional Rosensweig instability, a ferrofluid confined in a vertical Hele-Shaw cell subjected to an in-plane normal magnetic field develops a periodic array of peaked interfacial structures. We perform a weakly nonlinear analysis that is able to reproduce the morphology of such pattern formation phenomenon at lowest nonlinear order. A mode-coupling theory is applied to compare the early nonlinear evolution of the interface with static shapes obtained when relevant forces equilibrate. Our nonlinear results indicate that the time-evolving shapes tend to approach stable stationary solutions.

Stationary shapes of confined rotating magnetic liquid droplets

We study the family of steady shapes which arise when a magnetic liquid droplet is confined in a rotating Hele-Shaw cell and subjected to an azimuthal magnetic field. Two different scenarios are considered: first, the magnetic fluid is assumed to be a Newtonian ferrofluid, and then it is taken as a viscoelastic magnetorheological fluid. The influence of the distinct material properties of the fluids on the ultimate morphology of the emerging stationary patterns is investigated by using a vortex-sheet formalism. Some of these exact steady structures are similar to the advanced time patterns obtained by existing time-evolving numerical simulations of the problem. A weakly nonlinear approach is employed to examine this fact and to gain analytical insight about relevant aspects related to the stability of such exact stationary solutions.