Convection induced by composition gradients in miscible systemsConvection induite par des gradients de composition dans les systèmes miscibles

When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, a large concentration (and density) gradient exists, which relaxes through diffusion. With a mathematical model based on the Korteweg stress, we show that convection can occur which is analogous to surface-tension induced convection (STIC) or Marangoni convection. Specifically, we show that with realistic parameters significant flows can occur with plane interfaces and that drops of miscible fluids can act like their immiscible counterparts. Regarding plane interfaces, an experimental confirmation of this phenomenon is planned for the International Space Station. To cite this article: V.A. Volpert et al., C. R. Mecanique 330 (2002) 353–358.     

Oscillatory Marangoni convection around the air bubble in a vertical surfactant stratificationConvection de Marangoni oscillante autour d'une bulle d'air dans une stratification verticale surfactante

The solutocapillary Marangoni convection around a gas bubble in the inhomogeneous binary mixture of miscible fluids with a vertical surfactant concentration gradient was studied experimentally. A new phenomenon, the oscillatory instability of the surfactant mass transfer, near the bubble boundary, was detected and investigated. The interpretation of this effect as an interaction between the surfactant adsorption at the bubble free surface and solutocapillary and buoyancy convective mechanisms is proposed. The experimental data on oscillation period in relation to bubble dimensions, time, liquid layer thickness, physico-chemical fluid parameters and concentration gradients are presented and discussed. To cite this article: K. Kostarev et al., C. R. Mecanique 332 (2004).     

Turbulent forced convection heat transfer of non-Newtonian nanofluids

Forced convection heat transfer of non-Newtonian nanofluids in a circular tube with constant wall temperature under turbulent flow conditions was investigated experimentally. Three types of nanofluids were prepared by dispersing homogeneously γ-Al₂O₃, TiO₂ and CuO nanoparticles into the base fluid. An aqueous solution of carboxymethyl cellulose (CMC) was used as the base fluid. Nanofluids as well as the base fluid show shear-thinning (pseudoplastic) rheological behavior. Results indicate that the convective heat transfer coefficient of nanofluids is higher than that of the base fluid. The enhancement of the convective heat transfer coefficient increases with an increase in the Peclet number and the nanoparticle concentration. The increase in the convective heat transfer coefficient of nanofluids is greater than the increase that would be observed considering strictly the increase in the effective thermal conductivity of nanofluids. Experimental data were compared to heat transfer coefficients predicted using available correlations for purely viscous non-Newtonian fluids. Results show poor agreement between experimental and predicted values. New correlation was proposed to predict successfully Nusselt numbers of non-Newtonian nanofluids as a function of Reynolds and Prandtl numbers.     

Equation of convective diffusion of a multicomponent mixture in a capillary for an arbitrary velocity field

It is shown that the convective transport in a binary mixture in the presence of vortex convection can be described in terms of Fick’s law with an effective diffusion coefficient independent of the concentration. The form of the effective diffusion coefficient is found for arbitrary convection in the mixture. A generalization of the Stefan-Maxwell diffusion equation is proposed to include an arbitrary rotational mixture velocity field. The characteristics of convective transport are considered with reference to a three-component mixture. A solution of the equation of three-component mixture transport through a long capillary in the presence of convection homogeneous along the capillary axis is presented. It is established that for sharply different component diffusion coefficients a mixture density extremum may appear inside the capillary and then change or disappear depending on the convective flow intensity.     

Stability of two-layer systems with respect to convective mixing

The occurrence and development of convection in a two-layer system heated below has been investigated [1–5] under the assumption that the interface of the fluids is horizontal and is not subject to deformations. However, this assumption may not be satisfied if the surface tension on the interface is small and the fluids have either nearly equal densities or the heavier fluid is situated at the top. In the present paper, an attempt is made to study the convection regimes in a two-layer system with deformation of the interface when there is heating from below or above. The simultaneous influence of the convective and Rayleigh-Taylor instability mechanisms is taken into account; the surface tension on the interface is assumed to be infinitesimally small, and thermocapillary effects are ignored. A two-fluid variant of the method of markers and cells [6–9] is used for the numerical solution of the convection equations. A diagram of the regimes is constructed. It is shown that depending on the values of the parameters the system either preserves its two-layer structure, or the development of the conveetive motion leads to the breakup of the interface and complete mixing of the fluids.     

Thermocapillary convection in a two-layer system

Finite-amplitude convective motions that arise in a two-layer system under the influence of the thermocapillary mechanism are studied. Numerical calculations have been made by the grid method for different relationships between the parameters of the fluids. A new type of instability of equilibrium is found — thermocapillary oscillations. The evolution of the oscillatory motions as the Marangoni number changes is studied. The following forms of transitions between convection regimes are established: transition from oscillatory to steady motion through an unbounded increase in the period; bifurcation of the period, accompanied by rearrangement of the three-dimensional structure of the flow. It is shown that the thermogravitational instability mechanism leads to suppression of the oscillations.     

Shear flow induced interface instability

 A system of two stratified layers at a free surface, consisting of distilled water above a layer of salty water separated by an interface, is studied under laboratory conditions involving uniform temperature heating from below. Shadowgraph and particle images have been used with temperature and salt concentration measurements to investigate the interface instability induced by convection when it is developing in the upper and lower layer. It is found that the interface is governed by local shear flow that induces a Kelvin–Helmholtz instability. Moreover, the entrainment interface is subject to a combination of two closely related effects: (1) double diffusion and convective motion and (2) double diffusion and Kelvin–Helmholtz instability. Received: 22 December 1999/Accepted: 31 October 2000     

Convection of magnetic fluids in connected channels heated from below

The convective flows of a binary mixture in connected channels heated from below are studied experimentally. In contrast to homogeneous fluids, in magnetic colloids “hard” convection excitation, specific transient flows, and oscillatory convection regimes can be observed. The temperature fields and concentration inhomogeneities are measured.     

Stability of Thermosolutal Natural Convection in Superposed Fluid and Porous Layers

This article deals with the onset of thermosolutal natural convection in horizontal superposed fluid and porous layers. A linear stability analysis is performed using the one-domain approach. As in the thermal convection case, the results show a bimodal nature of the marginal stability curves where each mode corresponds to a different convective instability. At small wave numbers, the convective flow occurs in the whole cavity (“porous mode”) while perturbations of large wave numbers lead to a convective flow mainly confined in the fluid layer (“fluid mode”). Furthermore, it is shown that the onset of thermosolutal natural convection is characterized by a multi-cellular flow in the fluid region for negative thermal Rayleigh numbers. For positive thermal Rayleigh numbers, the convective flow takes place both in the fluid and porous regions. The influence of the depth ratio and thermal diffusivity ratio is also investigated for a wide range of the thermal Rayleigh numbers.     

Nonlinear investigation of anti-convection and Rayleigh–Benard convection in systems with heat release at the interface

Anti-convection and Rayleigh–Benard convection generated by the joint action of external heating and heat sources (sinks) on the interface in layers with finite thicknesses are studied. Numerical simulations of the finite-amplitude convective regimes have been mage for the real two-liquid system (silicone oil 10 cs – ethylenglycol), convenient for the performance of experiments. The nonlinear boundary value problem was solved by means of the finite-difference method. Anti-convective structures in fluid systems subject to anti-convective instability only in the presence of heat sources (sinks) on the interface, have been obtained. This new type of the anti-convective motion appears in the case where one layer is strongly heated from above, while the temperature gradient in another layer is very weak.     

Convective linear stability analysis of two-layer coextrusion flow for molten polymers

The interface instability of the coextrusion flow of a polyethylene and a polystyrene is studied both experimentally and theoretically in a slit geometry. For prototype industrial conditions, we have found a stable/unstable transition which bounds the occurrence of stable/unstable sheets at die exit. By investigating a large range of processing conditions, we have shown that this transition is controlled by both temperature and flow rate ratios. Close to the transition, we used a transparent die to measure spatial amplification of different controlled perturbations at die inlet and pointed out the convective nature of the instability which exhibits a dominant mode (for which the instability is the most severe). We have then found that a convective stability analysis, using the White–Metzner constitutive equation, is able to account for the spatial amplification rate experimentally measured on controlled perturbation experiments. By considering that the instability is controlled by its dominant mode, we performed a convective stability analysis for all studied prototype industrial conditions and showed that such an analysis is able to forecast the occurrence of defects at die exit.     

对流扩散方程的迎风变换及相应有限差分方法

本文提出所谓迎风变换,将对流扩散方程分解为对流迎风函数和扩散方程,并构造相应的有限差分格式。对流迎风函数以简明的指数解析形式反映对流扩散现象的迎风效应,原则上消除了源于不对称对流算子的困难,能够便利对流扩散方程的数值求解。有限差分格式具有二阶精度和无条件稳定性,算例表明其准确性、收敛速度及对边界层效应的适应能力均明显优于中心差分格式和迎风差分格式。     

The effect of vertical vibrations on the onset of convection in a planar rotating layer

The effect of vertical vibrations on the convection in a rotating planar fluid layer heated from below was studied. In this case a modulation parameter, the acceleration due to gravity, appears in the problem. The modulation of the parameter may have a significant effect on the onset of convective instability. Parameter modulation in nonrotating layers has been investigated in earlier work [1–3]. The presence of rotation significantly increases the complexity of the mathematical problem, introducing an additional dependence of the solution on the Taylor number Ta and the Prandtl number Pr. Furthermore, an oscillatory convection regime can occur at the stability limit in rotating fluids with Pr < 1. Parameter modulation in the rotating fluid may not only lead to a change in the stability limit and critical wavelength but also to a change in the eigenfrequency of the oscillatory convection. Rauscher and Kelly [4] examined the effect of parameter modulation on the convective stability of a rotating fluid only for the particular case of a sinusoidal variation in the temperature gradient with a small amplitude for Pr = 1, i.e., the effect of modulation was studied on only a steady convection regime.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 12–22, July–August, 1984.     

Combined action of anticonvective and thermocapillary mechanisms of instability in multilayer systems

The nonlinear regimes of convection in the system of three immiscible viscous fluids heated from above are investigated. The interfaces are assumed to be flat. The boundary value problem is solved by the finite-difference method. Transitions between convective motions with different spatial structures are investigated. The common diagram of instability regimes is constructed. The new phenomena caused by direct and indirect interaction of anticonvective and thermocapillary mechanisms of instability are considered. Specifically, different oscillatory configurations where anticonvection arises mainly near the upper interface and thermocapillary convection appears mainly near the lower interface have been found.     

Benard convection in a non-linear magnetic fluid under the influence of a non-vertical magnetic field

This work examines the convective instability of a horizontal layer of magnetohydrodynamic fluid of variable permeability when subjected to a non-vertical magnetic field. We use a model proposed by P. H. Roberts [9] in the context of neutron stars but the results obtained are aso relevant to the area of ferromagnetic fluids. The presence of the variable permeability has no effect on the development of instabilities through the mechanism of stationary convection but influences the threshold of overstable convection which is often the preferred mechanism in non-terrestrial applications. In the context of ferromagnetic fluids, both stationary and overstable instability can be expected to be realisable possibilities.     

Effect of the nonmonotonic temperature dependence of water density on convection under uniform heating

This paper presents the results of an experimental study of free convection in a closed rectangular tank with fresh water whose initial temperature is lower than the constant temperature of air outside the tank. Convective instability is shown to play a significant role in the process of heat transfer from the boundary layers on the walls to the bulk of water. In the case where the initial water temperature is higher than the temperature at which the density is maximal (about 4°C), convective instability occurs only in the boundary layer at the bottom of the tank. At a water temperature below 4°C convective instability also exists for some time in the boundary layer on the cover. Quantitative information is given on the variations in temperature and water density in time and on the vertical coordinate.     

The Onset of Double-Diffusive Convection in a Superposed Fluid and Porous Layer Under High-Frequency and Small-Amplitude Vibrations

We numerically simulate the initiation of an average convective flow in a system composed of a horizontal binary fluid layer overlying a homogeneous porous layer saturated with the same fluid under gravitational field and vibration. In the layers, fixed equilibrium temperature and concentration gradients are set. The layers execute high-frequency oscillations in the vertical direction. The vibration period is small compared with characteristic timescales of the problem. The averaging method is applied to obtain vibrational convection equations. Using for computation the shooting method, a numerical investigation is carried out for an aqueous ammonium chloride solution and packed glass spheres saturated with the solution. The instability threshold is determined under two heating conditions—on heating from below and from above. When the solution is heated from below, the instability character changes abruptly with increasing solutal Rayleigh number, i.e., there is a jump-wise transition from the most dangerous shortwave perturbations localized in the fluid layer to the long-wave perturbations covering both layers. The perturbation wavelength increases by almost 10 times. Vibrations significantly stabilize the fluid equilibrium state and lead to an increase in the wavelength of its perturbations. When the fluid with the stabilizing concentration gradient is heated from below, convection can occur not only in a monotonous manner but also in an oscillatory manner. The frequency of critical oscillatory perturbations decreases by 10 times, when the long-wave instability replaces the shortwave instability. When the fluid is heated from above, only stationary convection is excited over the entire range of the examined parameters. A lower monotonic instability level is associated with the development of perturbations with longer wavelength even at a relatively large fluid layer thickness. Vibrations speed up the stationary convection onset and lead to a decrease in the wavelength of most dangerous perturbations of the motionless equilibrium state. In this case, high enough amplitudes of vibration are needed for a remarkable change in the stability threshold. The results of numerical simulation show good agreement with the data of earlier works in the limiting case of zero fluid layer thickness.     

Convective stability of fluid in a rotating horizontal annulus

The convective stability of quasi-equilibriumof a fluid layer formed by two horizontal coaxial cylindrical surfaces which have different temperatures and rotate at the same angular velocity about the axis of symmetry is investigated theoretically and experimentally. Consideration is carried out from the standpoint of thermal vibrational convection caused by the average lifting force generated as a result of vibrations of a nonisothermal fluid with respect to the cavity. The vibrations are induced by an external field. The action of the centrifugal force field is also taken into account. Stability of mechanical quasi-equilibrium with respect to monotonic plane perturbations, which are, as shown experimentally, the most dangerous, is studied within the framework of the linear analysis. The stability boundaries are constructed for layers of various relative thickness in the plane of control parameters, the centrifugal and vibrational Rayleigh numbers. The thresholds of excitation of two-dimensional convective structures obtained experimentally are in good agreement with the theoretical ones.     

A multi‐dimensional monotonic finite element model for solving the convection–diffusion‐reaction equation

In this paper, we develop a finite element model for solving the convection–diffusion‐reaction equation in two dimensions with an aim to enhance the scheme stability without compromising consistency. Reducing errors of false diffusion type is achieved by adding an artificial term to get rid of three leading mixed derivative terms in the Petrov–Galerkin formulation. The finite element model of the Petrov–Galerkin type, while maintaining convective stability, is modified to suppress oscillations about the sharp layer by employing the M‐matrix theory. To validate this monotonic model, we consider test problems which are amenable to analytic solutions. Good agreement is obtained with both one‐ and two‐dimensional problems, thus validating the method. Other problems suitable for benchmarking the proposed model are also investigated. Copyright © 2002 John Wiley & Sons, Ltd.     

Convective self-oscillations near an air-bubble surface in a horizontal rectangular channel

The concentration convection in an isothermal fluid near an air bubble clamped between the vertical walls of a horizontal channel with a rectangular cross-section is studied experimentally and numerically. The channel is filled with an aqueous solution of a surfactant with a nonuniform concentration. As a result of the competition between the gravitational convection in the cavity volume and the Marangoni convection near the bubble surface, an oscillation flow regime is established. This regime is observed experimentally over several hours. In the numerical experiment, the oscillations are obtained in the presence of an initial horizontal surfactant concentration gradient. Against the background of gravitational convection, short bursts of Marangoni convection with ten times greater intensity are observed. The convective flow patterns and the oscillation periods obtained experimentally and numerically are in fairly good agreement.