Synthesis of layered double hydroxides: Investigating the impact of stirring conditions and reactor design parameters.

The synthesis by coprecipitation of Layered Double Hydroxides (LDHs) is governed by the stages of nucleation and crystal growth associated with the efficiency of the mixing and dispersion process of the reagents. Mixing efficiency is related to process variables, such as agitation speed, type of impeller and baffles presence, among others. In this context, this work proposes an analysis of these variables in a batch reactor, using a 23 factorial design employing the factors: acceleration speed (200 and 1000 rpm), mixing time (2 and 18 h) and presence or absence of baffles. The results were evaluated quantitatively (amount of LDH produced, time and amount of base for the formation of LDHs to begin) and qualitatively (mixing aspects, sedimentation ad grinding). The significant factors affecting the amount of LDH produced (51.94-80.81 g) were agitation speed and aging time. These factors were also correlated with the structural characteristics of the materials produced, such as crystallinity, crystallite size (70.99-174.79 nm), surface area (69.81-97.62 m2/g), pore volume (0.28-0.59 cm3/g), and pore diameter (11.40-34.66 nm). LDHs produced at higher agitation rates (1000 rpm) and longer aging times (18 h) yielded higher quantities of materials (80.81 g) with improved structural characteristics. The study highlights the importance of systematically exploring the synergistic effect between process variables, emphasizing the research potential in this area.

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. Moreover, we find that the linear growth rate associated with this suction-driven instability is independent of the viscosity contrast between the fluids. However, second-order results tell a different story, and show that the viscosity contrast is crucial in determining the morphology of the interface. Our theoretical description is applicable to the entire range of viscosity contrasts, and provides insights on the formation of near-cusp pattern-forming structures. Reproduction of fully nonlinear, n-fold symmetric near-cuspidal shapes previously obtained through conformal mapping techniques substantiates the validity of our mode-coupling approach.

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 Wave Motion 91, 102381 (doi:10.1016/j.wavemoti.2019.102381)), who considered a single-slit system assuming an idealized formulation where dissipation is neglected and the electromagnetic and acoustic problems are analogous. We here extend that theory to include thin dissipative boundary layers associated with finite conductivity of the plate in the electromagnetic problem and viscous and thermal effects in the acoustic problem, considering both single-slit and slit-array configurations. By considering a distinguished boundary-layer scaling where dissipative and diffractive effects are comparable, we develop accurate analytical approximations that are generally valid near resonance; the electromagnetic-acoustic analogy is preserved up to a single parameter that is provided explicitly for both scenarios. The theory is shown to be in excellent agreement with GHz-microwave and kHz-acoustic experiments in the literature.

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. In this work, we investigate the occurrence of elastic fingering for radial fluid displacements in a 3D uniform porous medium. A perturbative third-order mode-coupling approach is employed to examine how the combined action of viscous and elastic effects influences the linear stability of the interface, and the weakly nonlinear pattern formation in such a 3D environment. In addition, a variational method is used to determine how to minimize the growth of interfacial perturbation amplitudes via a time-dependent injection rate scheme.

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. A vortex-sheet formalism is used to calculate the two-fluid interface curvature, and a gallery of possible shapes is provided to highlight a number of peculiar morphological features. A linear perturbation theory is employed to show that the most prominent aspects of these complex stationary patterns can be fairly well reproduced by the interplay of just two interfacial modes. The connection of these dominant modes to the geometry of the curved cell, as well as to the fluid dynamic properties of the flow, is discussed.

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. For a specific nonflat environment, we show that both the reverse and the viscosity-matched flows can become unstable, even at low capillary number. This peculiar fluid fingering instability is driven by the combined action of capillary effects and geometric properties of the nonflat Hele-Shaw cell. Our theoretical results indicate that the Hele-Shaw cell geometry significantly impacts the linear stability and nonlinear pattern-forming dynamics of the system. This suggests that the geometry of the medium plays an important role in favoring the occurrence of fingering patterns in nonflat, confined fluid flows.

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. We also report on a time-dependent control strategy placed on the injection rate, which is able to minimize viscous fingering growth on H(2).

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. By using a mode-coupling theory to describe interfacial evolution, plus a variational controlling technique, we show that viscous fingering phenomena can be minimized in such a confined, curved environment by properly manipulating a time-dependent injection flow rate Q(t). Explicit expressions for Q(t) are derived for the specific cases of spherical and conical cells. The suitability of the controlling method is verified for linear and weakly nonlinear stages of the flow.

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. If the pushed fluid is shear-thinning, our results indicate the development of side-branching structures. On the other hand, if the displaced fluid is shear-thickening, one detects the formation of petal-like shapes, markedly characterized by strong tip-splitting events. Finally, a time-dependent injection protocol is presented that is able to restrain finger proliferation via side-branching and tip-splitting. This permits the emergence of symmetric n-fold interfacial shapes for which the number of fingers remains fixed as time progresses. This procedure generalizes existing controlling strategies for purely Newtonian flow circumstances to the case of a non-Newtonian, displaced power-law fluid.

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.