Volume 36, Issue 3

A particulate medium model is used to investigate the onset of Rayleigh–Bénard convection in a colloidal suspension of inert solid particles. The model accounts for the effects of thermophoresis, sedimentation and Brownian diffusion. Depending on the size of the particles, the problem has up to four time scales. These are due to thermal diffusion, particle diffusion, particle migration due to thermophoresis and particle sedimentation. The ratios of these time scales lead to the emergence of three parameters, one of which is the Lewis number τ . The smallness of the latter makes the differential eigenvalue system governing convection onset singular. The other two are the density number Γ and the dimensionless migration velocity β . For a given experimental set-up, β has a quadratic functional dependence on the particles radius. A combination of asymptotics and numerical computation is used to capture the effect of the resulting thin particle concentration boundary layers on the leading order instability thresholds. Results, which are depicted as function of Γ and β , reveal a non-monotonic dependence of the critical Rayleigh number ℛ c on β . The curve ℛ c ( β ) is bimodal and it exhibits a maximum , the value of which increases very sharply with |Γ| while the critical wavelength decreases. Experimental conditions can be fixed so that occurs at β values that correspond to nanoparticles. Therefore, experimental parameters can be controlled so that the mixing of a small amount of nano-size particles has a substantial stabilizing effect. An investigation of the flow patterns in the range of parameters associated with this sharp increase in ℛ c reveals a decrease in the effective thickness of the stratified layer.

The system of interest is a dilute binary mixture, in which we consider that the species have different temperatures as an initial condition. To study their time evolution, we use the full version of the Boltzmann equation, under the hypothesis of partial local equilibrium for both species. Neither a diffusion force nor mass diffusion appears in the system. We also estimate the time in which the temperatures of the components reach the full local equilibrium. In solving the Boltzmann equation, we imposed no assumptions on the collision term. We work out its solution by using the well-known Chapman–Enskog method to first order in the gradients. The time in which the temperatures relax is obtained following Landau's original idea. The result is that the relaxation time for the temperatures is much smaller than the characteristic hydrodynamic times but greater than a collisional time. The main conclusion is that there is no need to study binary mixtures with different temperatures when hydrodynamic properties are sought.

Experiments are to be performed on board the ISS to understand the thermodiffusion behavior in ternary hydrocarbon mixtures of n-dodecane/isobutylbenzene/tetralin. This will be followed by additional experiments with these components as well as mixtures of n-hexane/n-heptane/n-dodecane and n-decane/isobutylbenzene/tetralin. For these additional experiments, the temperature of the mixture is yet to be determined. In a three part series, by applying the theory in the literature, thermodiffusion coefficients of all these mixtures have been determined. The predictions have been made using the thermodiffusion model of Firoozabadi as well as two correlations from the literature. In this first part, thermodiffusion coefficients of twelve mixtures of n-dodecane/isobutylbenzene/tetralin have been estimated. From the results it is proposed that the future experiments be performed at 318 K and 1 atm. Certain mixtures have also been identified as important experiments due to conflicting predictions by the theoretical methods.

Thermodiffusion along molecular diffusion is one of the major mechanisms of transport phenomena. They have an important role in displacement of hydrocarbon fluid components in an oil reservoir. Free volume controls the diffusivity of the molecule in diffusion-limited systems. It states that the transfer kinetics of molecules depends greatly on molecular size and shape as well as the concentration. A new proposed model based on Fujita-type model is used to predict the thermodiffusion coefficients in ternary mixtures such as n-dodecane (nC 12 ), n-butane (nC 4 ), methane (C 1 ), n-dodecane (nC 12 ), isobutylbenzene (IBB), tetrahydronaphtalene (THN) and n-octane (C 8 ), n-decane (nC 10 ), 1-methylnaphtalene (MN). The ratio of evaporation energy to activation energy required for estimating the thermodiffusion coefficients is calculated by the available free volume theory. In particular, the combination of available free volume theory and Shukla and Firoozabadi's model is applied to predict the thermodiffusion coefficient. The results show a good performance of the new approach in estimating the thermodiffusion coefficients.

The Onsager heat of transport Q * for carbon dioxide at the surface of water has been determined by measuring the total gas pressure as a function of the temperature difference across a 6-mm vapour gap above the water surface, and subtracting previously measured water–vapour pressures. The metal surface above the vapour gap was conditioned with carbon dioxide prior to the measurements, to enable efficient thermal accommodation for CO 2 molecules striking that surface, so that plots of ΔP against ΔT were linear for ΔT values up to at least 6 K. For liquid surface temperatures ranging from 0 to 5°C, we find Q * = –6.9 ±1.7 kJ mol –1 . Within experimental error, the results were independent of pH over the range from 6.50 to 9.04, and of CO 2 partial pressure between 13 and 46 Torr. The factor Q * / RT is –3, which implies that the fractional temperature gradient is at least three times as important as the fractional partial-pressure gradient in controlling the magnitude and direction of the steady-state CO 2 flux through a water surface.

The thermodynamic theory of anisotropic rigid heat conductors with gradient constitutive equations is revisited in the framework of both extended irreversible thermodynamics and rational thermodynamics. The Second Law is exploited through a generalized Coleman–Noll procedure. Some interesting physical properties of the entropy flux and the entropy production are pointed out.