Search Results (11)

We study the large-time behavior of solutions to Darcy–Boussinesq equations with a non-vanishing scalar acceleration coefficient, which model buoyancy-driven flows in porous media with spatially varying gravity. First, we show that the system admits steady-state solutions of the form $(\mathbf{u},\rho ,p)=(\mathbf{0},{\rho }_s,p_s)$, where ${\rho }_s$ is characterised by the hydrostatic balance $\nabla p_s=-{\rho }_s\nabla \mathrm{\Psi }$. Second, we prove that the steady-state solution satisfying $\nabla {\rho }_s=\delta (x,y)\nabla \mathrm{\Psi }$ is linearly stable provided that $\delta (x,y)<{\delta }_0<0$, while the system exhibits Rayleigh–Taylor instability if $\mathrm{\Psi }=gy$, ${\rho }_s={\delta }_{0}g$ and ${\delta }_0>0$. Finally, despite the inherent Rayleigh–Taylor instability that may trigger exponential growth in time, we prove that for any sufficiently regular initial data, the solutions of the system asymptotically converge towards the vicinity of a steady-state solution, where the velocity field is zero, and the new state is determined by hydrostatic balance. This work advances porous media modeling for geophysical and engineering applications, emphasizing the critical interplay of gravity, inertia, and boundary conditions. Full article

Reaction fronts propagating in liquids separate reacted from unreacted fluid. These reactions may release heat, increasing the temperature of the propagating medium. As fronts propagate, they will induce density changes leading to convection. Exothermic fronts that propagate upward increase the temperature of the reacted fluid located underneath the front. For positive expansion coefficients, the warmer fluid will tend to rise due to buoyancy. In the opposite case, for fronts propagating downward with the warmer fluid on top, an unexpected thermally driven instability can also take place. In this work, we carry out a linear stability analysis introducing perturbations of fixed wavelength. We obtain a dispersion relation between the perturbation wave number and its growth rate. For either direction of propagation, we find that the front is stable for very short wavelengths, but is unstable for large enough wavelengths. We carry out a numerical solution of a cubic reaction–diffusion–advection equation coupled to Navier–Stokes hydrodynamics in a two-dimensional rectangular domain. We find transitions between the non-axisymmetric and axisymmetric fronts increasing with the width of the domain. Full article

The characteristics of a stationary flow of a volatile liquid driven by a co-current gas flux in a flat horizontal mini-channel upon the non-zero transverse temperature drop are studied. We use an exact solution of the thermosolutal convection equations for describing the heat and mass transfer caused by the combined action of gas pumping, buoyancy, thermocapillarity and linear heating of the channel walls in a two-layer system. The influence of heating from above on the parameters of the ground state and the stability characteristics of the basic flow is explored using an example of the ethanol–air system. We evaluate the thresholds of the linear stability and select the most dangerous modes. Heating from above results in flow stabilization. Instability appears in the form of oscillatory cellular convective patterns. Full article

Recently, we found that a two-layer miscible system placed in a vertical slab reactor shows an occurrence of a density shock-wave-like pattern. This wave resembles a turbulent bore separating immobile fluid and an area of intense mixing. It travels away from the convective core of the system and is highly dependent on the intensity of a gravity-dependent chemoconvection in the cocurrent flow. The novelty of this work is that we demonstrate that the change in angle between gravity and wave direction allows controlling the chemoconvection intensity and, consequently, the rate of a spatially-extended reaction. We study both experimentally and numerically the effect of the spatial orientation of a slab reactor to a gravity field on a flow structure induced by a neutralization reaction. In experiments, we use aqueous mixtures of nitric acid and sodium hydroxide. We apply the Fizeau interferometry to visualize the flow and use the PIV method to measure the fluid velocity. The mathematical model includes reaction–diffusion–convection equations that describe 3D flows. We study the flow modifications with a change in the inclination angle from 0 to 90 degrees. At small angles (up to 30), the cocurrent flow becomes spatially heterogeneous, and the fields of salt and acid are separated. If the inclination exceeds 50 degrees, the wavefront is deformed, and the wave breaks up, resulting in a sharp decrease in the reaction rate. Full article

Alongside classical effects driven by gravity or surface tension in non-isothermal fluids, the present experimental study concentrates on other exotic (poorly known) modes of convection, which are enabled in a fluid layer delimited from below by a hot plate and unbounded from above when its container is inclined to the horizontal direction. By means of a concerted approach based on the application of a thermographic visualization technique, multiple temperature measurements at different points and a posteriori computer-based reconstruction of the spatial distribution of wavelengths, it is shown that this fluid-dynamic system is prone to develop a rich set of patterns. These include (but are not limited to), spatially localized (compact) cells, longitudinal wavy rolls, various defects produced by other instabilities and finger-like structures resulting from an interesting roll pinching mechanism (by which a single longitudinal roll can be split into two neighboring rolls with smaller wavelength). Through parametric variation of the tilt angle, the imposed temperature difference and the volume of liquid employed, it is inferred that the observable dynamics are driven by the ability of gravity-induced shear flow to break the in-plane isotropy of the system, the relative importance of surface-tension-driven and buoyancy effects, and the spatially varying depth of the layer. Some effort is provided to identify universality classes and similarities with other out-of-equilibrium thermal systems, which have attracted significant attention in the literature. Full article

An observed sea fog event over the Eastern Yellow Sea on 15–16 April 2012 was reproduced in the Weather Research and Forecasting (WRF) simulation with high-resolution to investigate the roles of physical processes and synoptic-scale flows on advection fog with phase transition. First, it was verified by a satellite-based fog detection algorithm and in situ observation data. In the simulation, longwave (infrared) radiative cooling (LRC) with a downward turbulent sensible heat flux (SHF), due to the turbulence after sunset, triggered cloud formation over the surface when warm-moist air advection occurred. At night, warm air advection with continuous cooling due to longwave radiation and SHF near the surface modulated the change of the SHF from downward to upward, resulting in a drastic increase in the turbulent latent heat flux (LHF) that provided sufficient moisture at the lower atmosphere (self-moistening). This condition represents a transition from cold-sea fog to warm-sea fog. Enhanced turbulent mixing driven by a buoyancy force increased the depth of the sea fog and the marine atmospheric boundary layer (MABL) height, even at nighttime. In addition, cold air advection with a prevailing northerly wind at the top of the MABL led to a drastic increase in turbulent mixing and the MABL height and rapid growth of the height of sea fog. After sunrise, shortwave radiative warming in the fog layers offsetting the LRC near the surface weakened thermal instability, which contributed to the reduction in the MABL height, even during the daytime. In addition, dry advection of the northerly wind induced dissipation of the fog via evaporation. An additional sensitivity test of sea surface salinity showed weaker and shallower sea fog than the control due to the decrease in both the LHF and local self-moistening. Detailed findings from the simulated fog event can help to provide better guidance for fog detection using remote sensing. Full article

The outputs from a submesoscale permitting hindcast simulation from 1990 to 2016 are used to investigate the interannual to decadal variations of submesoscale motions. The region we focus on is the subtropical Northwestern Pacific including the subtropical countercurrent. The submesoscale kinetic energy (KE) is characterized by strong interannual and decadal variability, displaying larger magnitudes in 1996, 2003, and 2015, and smaller magnitudes in 1999, 2009, 2010, and 2016. These variations are partially explained by those of the available potential energy (APE) release at submesoscale driven by mixed layer instability in winter. Indeed, this APE release depends on the mixed layer depth and horizontal buoyancy gradient, both of them modulated with the Pacific Decadal Oscillation (PDO). As a result of the inverse KE cascade, the submesoscale KE variability possibly leads to interannual to decadal variations of the mesoscale KE (eddy KE (EKE)). These results show that submesoscale motions are a possible pathway to explain the impact associated with the PDO on the decadal EKE variability. The winter APE release estimated from the Argo float observations varies synchronously with that in the simulation on the interannual time scales, which suggests the observation capability to diagnose the submesoscale KE variability. Full article

This work presented a series of three-dimensional unsteady numerical simulations on the characteristics of the mixed oscillation flows of binary mixture in a Czochralski crystal growth model. The silicon-germanium melt is investigated and the capillary ratio is minus one. The simulation results showed that, for the special capillary ratio, the thermal and solutocapillary forces are imposed in opposite directions and counteract each other. With the effect of buoyancy, the balance between the capillary forces is disturbed. Mixed with the forced convection driven by rotation, the capillary-buoyancy convection is complex. The basic mixed flow streamlines are presented as various rolling cells. The directions of the rolls are dependent on the combinations of surface and body forces. With the increase of temperature gradient, the basic flow stability is broken, and the oscillations occur. The crucible rotation has an effective influence on the stability enhancement. However, affected by the crystal rotation, the critical condition experiences an increase to a turning point, and then undergoes a sharp reduction to zero. Once the instability is incubated, the surface oscillations are analyzed. For the three-dimensional steady flow, only spatial oscillations are observed circumferentially, and the surface patterns of spokes, rosebud, and pulsating ring are obtained. For the unsteady oscillation flow, the spiral hydrosoultal waves, rotating waves, and superimposition of spirals and spokes are observed, and the oscillation behaviors are also discussed. Full article

The selection of polymorphs of the organic compound 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile, ROY, is studied experimentally in the confined space between two horizontal glass plates when an acetone solution of ROY of variable concentration is injected at a variable flow rate into water. Depending on the local concentration within the radial flow, a polymorph selection is observed such that red prisms are favored close to the injection center while yellow needles are the preferred polymorph close to the edge of the injected ROY domain. At larger flow rates, a buoyancy-driven instability induces stripes at the outer edge of the displacement pattern, in which specific polymorphs are seen to crystallize. Our results evidence the possibility of a selection of ROY polymorph structures in out-of-equilibrium flow conditions. Full article

This article deals with the stability problem that arises in the modeling of the geological sequestration of carbon dioxide. It provides a more detailed description of the alternative approach to tackling the stability problem put forth by Vo and Hadji (Physics of Fluids, 2017, 29, 127101) and Wanstall and Hadji (Journal of Engineering Mathematics, 2018, 108, 53–71), and it extends two-dimensional analysis to the three-dimensional case. This new approach, which is based on a step-function base profile, is contrasted with the usual time-evolving base state. While both provide only estimates for the instability threshold values, the step-function base profile approach has one great advantage in the sense that the problem at hand can be viewed as a stationary Rayleigh–Bénard problem, the model of which is physically sound and the stability of which is not only well-defined but can be analyzed by a variety of existing analytical methods using only paper and pencil. Full article

This paper reviews the past and recent studies on thermocapillarity in relation to microfluidics. The role of thermocapillarity as the change of surface tension due to temperature gradient in developing Marangoni flow in liquid films and conclusively bubble and drop actuation is discussed. The thermocapillary-driven mass transfer (the so-called Benard-Marangoni effect) can be observed in liquid films, reservoirs, bubbles and droplets that are subject to the temperature gradient. Since the contribution of a surface tension-driven flow becomes more prominent when the scale becomes smaller as compared to a pressure-driven flow, microfluidic applications based on thermocapillary effect are gaining attentions recently. The effect of thermocapillarity on the flow pattern inside liquid films is the initial focus of this review. Analysis of the relation between evaporation and thermocapillary instability approves the effect of Marangoni flow on flow field inside the drop and its evaporation rate. The effect of thermocapillary on producing Marangoni flow inside drops and liquid films, leads to actuation of drops and bubbles due to the drag at the interface, mass conservation, and also gravity and buoyancy in vertical motion. This motion can happen inside microchannels with a closed multiphase medium, on the solid substrate as in solid/liquid interaction, or on top of a carrier liquid film in open microfluidic systems. Various thermocapillary-based microfluidic devices have been proposed and developed for different purposes such as actuation, sensing, trapping, sorting, mixing, chemical reaction, and biological assays throughout the years. A list of the thermocapillary based microfluidic devices along with their characteristics, configurations, limitations, and improvements are presented in this review. Full article