Growth of binary fluid convection: role of the concentration field

Traveling-wave convection in a binary fluid mixture under high-frequency vertical vibrations

The convective stability thresholds and nonlinear spatiotemporal evolution of convective rolls in a plane horizontal layer subject to steady gravity and high-frequency transversal vibration are numerically investigated considering a laterally periodic convective cell with rigid, impermeable horizontal boundaries. Simulations are performed for parameters adapted to laboratory experiments with an ethanol-water mixture with negative Soret coupling between temperature and concentration gradients. The characteristics of the wave and steady patterns are investigated depending on heat and vibration intensities. The weakly nonlinear traveling wave and modulated traveling wave are found as stable solutions within certain domains of parameters. Temporal Fourier decomposition is used together with other diagnostic tools to analyze the complex bifurcation and spatiotemporal properties that are caused by the interplay of the high-frequency vibrations, Soret induced gradients, and mixing of the fluid.

Traveling-wave convection in colloids stratified by gravity

Thresholds of convection excitation and nonlinear convective flow patterns in a horizontal colloidal-mixture layer heated from below are investigated. We take into consideration the fact that, provided the barometric stratification has been reached prior to imposing the temperature gradient, only oscillatory disturbances develop. The influence of separation ratio, sedimentation length, and Prandtl number on the thresholds of oscillatory convection is studied. To examine the complex nonlinear dynamics of the system, numerical simulations with realistic boundary conditions have been carried out using a finite difference method. Long-wave and cellular instability modes as well as transitions between the conductive state and the traveling-wave regime are discussed. It is shown that the traveling-wave regime is stable within a specified range of heating intensity (the Rayleigh number interval). Complex bifurcation and spatiotemporal properties of dissipative structures caused by the interaction of the gravity-induced concentration gradient, nonlinear advection, and mixing of the fluid with nanoparticles are considered.

Stationary and oscillatory convection of binary fluids in a porous medium

We investigate numerically stationary convection and traveling wave structures of binary fluid mixtures with negative separation ratio in the Rayleigh-Bénard system filled with a porous medium. The bifurcation behavior of these roll structures is elucidated as well as the properties of the velocity, temperature, and concentration fields. Moreover, we discuss lateral averaged currents of temperature and concentration. Finally, we investigate the influence of the Lewis number, of the separation ratio, and of the normalized porosity on the bifurcation branches.

Binary-fluid-mixture convection with low-frequency modulated heating

The response behavior of binary fluid convection to low-frequency temporal modulation of the heating is studied for the case of a negative Soret coupling between temperature and concentration gradients. Numerical simulations using a finite difference method are carried out for ethanol-water mixtures subject to realistic boundary conditions. We study in particular the response when the Rayleigh number periodically drops below the saddle node in the bifurcation diagram of convective solutions under stationary heating, i.e., into a regime where convection would die out in the absence of modulation. Quasiperiodic traveling waves, several different periodic traveling waves, and synchronously modulated patterns with fixed spatial phase are found as stable solutions depending on parameters. The symmetry properties of the different periodic traveling waves are discussed. Anomalous variations of the mixing behavior relative to advection are observed and explained. Lateral and temporal Fourier decompositions are used together with other diagnostic tools to analyze the complex bifurcation and spatiotemporal properties that are caused by the interplay of modulated heating, nonlinear advection, Soret induced gradients, and mixing of the fluid.

Soret effect in molecular mixtures

A theoretical approach to the description of the Soret effect in binary nonpolar liquids is proposed. The temperature gradient of the partial pressure is determined as the driving force of thermal diffusion. The hard-sphere fluid is chosen as a reference system and an explicit relation for the Soret coefficient is found. Two additive contributions owing to steric repulsions and attractive interactions form the so-called chemical contribution to S_{T} [C. Debuschewitz and W. Köhler, Phys. Rev. Lett. 87, 055901 (2001)]. The parameters of interparticle interactions are defined with the help of the solvation theory. In particular, the van der Waals constant of cross interactions is expressed via the excess volume of mixture. The proposed theory is applied to the benzene-cyclohexane system. A reasonable agreement of theoretical and experimental results is revealed for the Soret coefficient and its temperature dependence.

Convection in binary fluid mixtures with modulated heating

The response behavior of strongly nonlinear binary fluid convection to temporal modulation of the heating is investigated for the case of a negative Soret coupling between temperature and concentration gradients. Finite difference numerical simulations are performed for ethanol-water parameters subject to realistic boundary conditions. Traveling waves with modulated amplitudes and phase velocities, subharmonic standing waves, and synchronously modulated patterns with fixed spatial phase are found as stable solutions. The hysteretic transitions between subcritical traveling and standing waves that coexist bistably with the quiescent fluid state are investigated. Various diagnostic analysis tools are used to elucidate the complex spatiotemporal and bifurcation properties that are ultimately caused by nonlinear advection and mixing of concentration being very strong.

Onset of convection in Soret-driven instability

It is common knowledge that light fluids rise while heavy fluids sink in the gravity field. The most obvious case is the isothermal Rayleigh-Taylor instability when a heavy fluid is placed on top of a light one. In the nonisothermal case, while heating from above, the density stratification is stable in a pure liquid. However, unstable density stratification might be established in a binary mixture with a negative Soret effect in the case of heating from above: the heavier liquid is accumulated on the top of the lighter one. Due to the large differences between viscous, thermal, and diffusion times the system has a tendency to fingering buoyant instabilities. At some moment the flow may be initiated. Near the onset of convection the flow pattern has a columnar convective structure: for a relatively low applied temperature difference Delta T the lighter and colder liquid is drawn up in the central part of the cell and the heavier liquid flows down along the walls. For finite size systems the situation is reversed at higher Delta T. Here we present results of three-dimensional direct numerical simulations of heat and mass transfer in a system with a negative Soret effect. While the development of Soret-induced convection is similar for a wide class of liquids: water based mixtures, colloidal, and polymer solutions, the parameters of the chosen system correspond to a realistic binary mixture of water (90%) and isopropanol (10%) enabling comparison of theoretical predictions with planned experimental studies.

Traveling wave fronts and localized traveling wave convection in binary fluid mixtures

Nonlinear fronts between spatially extended traveling wave (TW) convection and quiescent fluid and spatially localized traveling waves (LTWs) are investigated in quantitative detail in the bistable regime of binary fluid mixtures heated from below. A finite-difference method is used to solve the full hydrodynamic field equations in a vertical cross section of the layer perpendicular to the convection roll axes. Results are presented for ethanol-water parameters with several strongly negative separation ratios where TW solutions bifurcate subcritically. Fronts and LTWs are compared with each other and similarities and differences are elucidated. Phase propagation out of the quiescent fluid into the convective structure entails a unique selection of the latter while fronts and interfaces where the phase moves into the quiescent state behave differently. Interpretations of various experimental observations are suggested.

Onset of convection in colloids stratified by gravity

Settling of the equilibrium (barometric) distribution of colloidal grains in a liquid requires a very long time in comparison with that necessary for temperature equilibrium establishment. This mismatch enables different scenarios for the onset of thermal convection. If the stratified state has had no time to be settled, the colloid behaves as a pure fluid where only stationary convection arises. On the contrary, if the barometric concentration profile has been reached before the temperature gradient is imposed, only oscillatory convection occurs. Thereafter, the oscillations last as long as it takes the convection to wash away the initial concentration profile. Then the fluid becomes homogeneous and stationary convection is eventually established. The influence of the Soret effect upon the onset of convection is also taken into account and discussed.

Oscillatory convection in binary mixtures: thermodiffusion, solutal buoyancy, and advection

The role of thermodiffusive generation of concentration fluctuations via the Soret effect, their contribution to the buoyancy forces that drive convection, the advective mixing effect of the latter, and the diffusive homogenisation are compared and elucidated for oscillatory convection. Numerically obtained solutions of the field equations in the form of spatially extended relaxed traveling waves, of standing waves, and of the transient growth of standing waves and their transition to traveling waves are discussed as well as spatially localized convective states of traveling waves that are surrounded by the quiescent fluid.

Standing-wave oscillations in binary mixture convection: from the onset via symmetry breaking to period doubling into chaos

Oscillatory solution branches of the hydrodynamic field equations describing convection in the form of a standing wave (SW) in binary fluid mixtures heated from below are determined completely for several negative Soret coefficients psi. Galerkin as well as finite-difference simulations were used. They were augmented by simple control methods to obtain also unstable SW states. For sufficiently negative psi, unstable SWs bifurcate subcritically out of the quiescent conductive state. They become stable via a saddle-node bifurcation when lateral phase pinning is exerted. Eventually their invariance under timeshift by half a period combined with reflection at midheight of the fluid layer gets broken. Thereafter, they terminate by undergoing a period-doubling cascade into chaos.

Localized waves without the existence of extended waves: oscillatory convection of binary mixtures with strong soret effect

Spatially confined solutions of traveling convection rolls are determined numerically for binary mixtures such as ethanol-water. The appropriate field equations are solved in a vertical cross section of the rolls perpendicular to their axes subject to realistic horizontal boundary conditions. The localized convective states are stably and robustly sustained by strongly nonlinear mixing and complex flow-induced concentration redistribution. We elucidate how this enables their existence for strongly negative separation ratios at small subcritical heating rates below the saddle node of extended traveling convection rolls where the quiescent fluid is strongly stable.