Capillary Convection Research Articles

Level‐set based numerical simulation of a migrating and dissolving liquid drop in a cylindrical cavity

AbstractIn the present paper the dissolution of a binary liquid drop having a miscibility gap and migrating due to thermo‐solutal capillary convection in a cylindrical cavity is studied numerically. The interest in studying this problem is twofold. From a side, in the absence of gravity, capillary migration is one of the main physical mechanisms to set into motion dispersed liquid phases and from the other side, phase equilibria of multi‐component liquid systems, ubiquitous in applications, often exhibit a miscibility gap. The drop capillary migration is due to an imposed temperature gradient between the cavity top and bottom walls. The drop dissolution is due to the fact that initial composition and volume values, and thermal boundary conditions are only compatible with a final single phase equilibrium state. In order to study the drop migration along the cavity and the coupling with dissolution, a previously developed planar two‐dimensional code is extended to treat axis‐symmetric geometries. The code is based on a finite volume formulation. A level‐set technique is used for describing the dynamics of the interface separating the different phases and for mollifying the interface discontinuities between them. The level‐set related tools of redistancing and off‐interface extension are used to enhance code resolution in the critical interface region. Migration speeds and volume variations are determined for different drop radii. Copyright © 2004 John Wiley & Sons, Ltd.

Photopatterning of Dry Polymer Films: on the Relative Involvement of Diffusive and Capillary Convection in the Self-Corrugation Process

Dry poly(vinyl alcohol) (PVA) formulations are widely used in the field of micro-optics for holographic recording and fabrication of micro-optical elements, but very little is known about the recording mechanism and even less in systems generating relief elements through a self-developing process. Thus, the recording of relief gratings with pitches ranging from 5 to 120 l/mm was examined with reference to the average weight of PVA and degree of hydrolysis. The slit width to pitch ratio in the amplitude mask used for photopatterning appeared to be also a controlling factor in the response of sensitive materials. A semiquantitative model was introduced to account for the final shape of the photogenerated relief. It determined the respective parts played by diffusion and capillary convection, i.e., convection processes resulting from gradients of chemical potential and surface tension, respectively, and identified the experimental key parameters governing their interrelation. This work sheds new light on the optimization of the patterning conditions of amplitude masks and is expected to open up new vistas in the replication of computer-generated holograms.

Doppler tomography of mass-transfer processes in condensed media induced by femtosecond laser pulses

A femtosecond laser scheme for studying laser-induced mass transfer is proposed. A Doppler velocity meter using a femtosecond Ti: sapphire laser is created. A thermal capillary convection initiated by this laser in paraffin is investigated (with a spatial resolution of 15 μm).

Oscillatory thermo capillary convection in a spinning cylindrical liquid bridge under micro-gravity condition

In a viscous liquid column thermocapillary convection arises under the action of an axial temperature gradient. If this temperature gradient is oscillatory it induces surface oscillations and may lead to large amplitudes, if the frequency of the temperature fluctuation is in resonance with that of the liquid column.

Capillary and gravitational convection in a droplet immersed in a nonuniformly heated liquid

Under the conditions of the Plato technique, the problem of convection in a droplet immersed in a nonuniformly heated liquid is solved analytically. The influence of gravitational convection on the thermocapillary flow is studied. In the linear approximation with respect to the Marangoni and Grashof numbers and their product, the shape of the droplet and the displacement of its center of the mass are obtained.

Extrinsic effects in the dynamics and selection of cellular arrays

In addition to convection in the liquid phase, which can be made negligible in microgravity, other extrinsic effects should be suppressed, or at least controlled, in order to be able to actually relate the dynamics and selection of cellular arrays that result from the pure morphological instability of a planar solidification front to the processing parameters: growth velocity V, thermal gradient G, and solute concentration C0. Therefore, we successively analyzed the influence of four major extrinsic sources of parasitic effects in cellular solidification and, when complementary, in Benard convection with a free surface. The container imposes confinement and wall conditions. Cellular doublets or spatiotempora l chaos are favored by the presence of grain boundaries. When the solute is volatile, gas pores may nucleate, which then provoke capillary convection and whose growth can either suppress morphological instability or form localized duplexes, upon coupling with a cellular or dendritic envelope. Finally, the experimental procedure, essentially through the initial conditions that are applied, determines the initial transient and sometimes prevents the asymptotic state to be reached, possibly by dynamically locking the system in an intermediate configuration, characterized by a significant amount of noise.

Interface dynamics and coupled growth in directional solidification in presence of bubbles

The formation and dynamics of gas bubbles in Bridgman growth of succinonitrile-acetone alloys is examined. The experimental results show for the first time the rich dynamics that are associated with the formation and propagation of bubbles during directional solidification of alloys. The strong coupling of bubbles with the solid-liquid interface is found to result in the growth of elongated bubbles, either attached to a flat solidification front or forming localized cellular as well as dendritic duplexes (bubbles wrapped by a solid envelope). The coupling of the bubble with the solidification front is shown to cause oscillations in the bubble, which are characterized by fast Fourier transforms. When several duplexes are formed, coupled growth and screening may occur. The basic factors that give rise to oscillations, namely competition between source and sink of acetone assisted by capillary convection at the bubble cap, are discussed qualitatively through the development of an internal oscillator model. Coherent sidebranching observed on dendritic duplexes is shown to be due to resonant modes between the bubble cap and the solid envelope.

Computationally efficient algorithms for convection-permeation-diffusion models for blood-tissue exchange.

Analysis of data on tissue depositions obtained by positron tomographic or NMR imaging, or of multiple tracer outflow dilution curves, requires fitting data with models composed of aggregates of capillary-tissue units. These units account for heterogeneities of flows and multisolute exchanges between longitudinally distributed regions across capillary and cell barriers within an organ. Because the analytic solutions to the partial differential equations require convolution integration, solutions are obtained relatively efficiently by a fast numerical method. Our approach centers on the use of a sliding fluid element algorithm for capillary convection, with the time step set equal to the length step divided by the fluid velocity. Radial fluxes by permeation between plasma, interstitial fluid, and cells and axial diffusion exchanges within each time step are calculated analytically. The method enforces mass conservation unless there is regional consumption. Solution for a 2-barrier, 3-region model, accurate to within 0.5%, are 100 to 1000 times faster than the corresponding, purely analytic solution, and over 10,000 times for a 4-region model. Applications include multiple indicator dilution studies of kinetics of transcapillary exchange and positron emission tomographic studies of the mechanisms of substrate transport into cells of organs in vivo.

Thermocapillary instability of the equilibrium of a flat layer containing internal heat sources

In the absence of body forces, a factor which has a strong influence on the equilibrium stability of a nonuniformly heated liquid is the dependence of the coefficient of surface tension on the temperature and the thermocapillary effect generated by it. If the equilibrium temperature gradient is sufficiently great, then the presence of the thermocapillary forces on the free surface can lead to the occurrence of convective motion. The monotonie instability of the equilibrium of a flat layer was investigated in [1–3]. Analysis of nonmonotonic disturbances [4] showed that in the case of an undeformable free surface there is no oscillatory instability. In [5] it was found that oscillatory instability is possible if there is a nonlinear dependence of the coefficient of surface tension on the temperature. The present paper is devoted to numerical investigation of the equilibrium stability of a flat layer with respect to arbitrary disturbances. It is shown that for a deformable free boundary there appears an additional neutral curve, which corresponds to monotonie capillary instability. In addition, when the capillary convection mechanism is taken into account, there appears an oscillatory instability, which becomes the most dangerous in the region of small Prandtl and wave numbers.

A model of oxygen exchange between an arteriole or venule and the surrounding tissue.

A mathematical model is developed to study the effect of capillary convection on oxygen transport around segments of arterioles and venules that are surrounded by capillaries. These capillaries carry unidirectional flow perpendicular to the vessel. The discrete capillary structure is distributed in a manner determined by the capillary blood flow and capillary density. A nonlinear oxyhemoglobin dissociation curve described by the Hill equation is used in the analysis. Oxygen flux from the vessel is expressed as a relationship between Sherwood and Peclet numbers, as well as other dimensionless combinations involving parameters of the capillary bed. A numerical solution is obtained with a finite difference method. The numerical results obtained within the physiological range of parameters allow the prediction of longitudinal gradients of hemoglobin-oxygen saturation along the arterioles and venules.

Capillary convection in a liquid layer on exposure to laser radiation

The dimensions of a convection cell, the profile of the depression on the layer surface, the velocity of the steady-state liquid motion, and the dynamics of the development of the convection in liquid layers with different viscosity are determined.

Thermocapillary cell in a horizontal moving liquid layer with heating from above

The problem of thermocapillary convection that develops in a thin stationary liquid layer, heated locally from above,hasbeen considered in [i] in the constant layer thickness approximation. The exact solution of eouations of capillary convection that had been obtained in [I] for large blarangoni numbers (M >> i) made it possible to determine the convection rate and the dimensions of the convective cell. The solution given in [I], which holds for the Prandtl numbers Pr ~> i, has been generalized in [2] to encompass the case of liquid metals (Pr < I). The problem from [i] was considered in its rigorous statement in [3] with an allowance for the curvature of the free liGuid surface. This made it possible to determine the effect of gravity and surface deformation on the cell structure and define the applicability scope of the simple analytical solution [I, 2]. On the basis of the results obtained in [1-3], a dyanmic thermocapillary model of the vacuum-arc cathode spot has been proposed in [4]. This model relates the high speed of a cathode spot moving over the electrode surface to the high rate of convective heat transfer. It is interesting to examine the problem of steady-state thermocapillary convection in a thin, horizontal moving liquid layer with local heating from above.