Growth of an ice disk: dependence of critical thickness for disk instability on supercooling of water.

The appearance of an asymmetrical pattern that occurs when a disk crystal of ice grows from supercooled water was studied by using an analysis of growth rates for radius and thickness. The growth of the radius is controlled by transport of latent heat and is calculated by solving the diffusion equation for the temperature field surrounding the disk. The growth of the thickness is governed by the generation and lateral motion of steps and is expressed as a power function of the supercooling at the center of a basal face. Symmetry breaking with respect to the basal face of an ice disk crystal is observed when the thickness reaches a critical value; then one basal face becomes larger than the other and the disk loses its cylindrical shape. Subsequently, morphological instability occurs at the edge of the larger basal face of the asymmetrical shape (Shimada, W.; Furukawa, Y. J. Phys. Chem. 1997, B101, 6171-6173). We show that the critical thickness is related to the critical condition for the stable growth of a basal face. A difference of growth rates between two basal faces is a possible mechanism for the appearance of the asymmetrical shape.

Diffuse-reflection boundary conditions for a thermal lattice Boltzmann model in two dimensions: evidence of temperature jump and slip velocity in microchannels.

We discuss the implementation of diffuse reflection boundary conditions in a thermal lattice Boltzmann model for which the upwind finite difference scheme is used to solve the set of evolution equations recovered after discretization of the velocity space. Simulation of heat transport between two parallel walls at rest shows evidence of temperature jumps at the walls that increase with Knudsen number. When the walls move in opposite directions with speeds +/- u(W), fluid velocity slip is observed at the walls, together with temperature jumps.

Mass and thermal diffusivity algorithms: reduced algorithms for mass and thermal diffusivity determinations.

Mass and thermal diffusivity measurements conducted on Earth are prone to contamination by uncontrollable convective contributions to the overall transport. Previous studies of mass and thermal diffusivities conducted on spacecraft have demonstration the gain in precision, and lower absolute values, resulting from the reduced convective transport possible in a low-gravity environment. We have developed and extensively tested real-time techniques for diffusivity measurements, where several measurements may be obtained on a single sample. This is particularly advantageous for low gravity research were there is limited experiment time. The mass diffusivity methodology uses a cylindrical sample geometry. A radiotracer, initially located at one end of the host is used as the diffusant. The sample is positioned in a concentric isothermal radiation shield with collimation bores located at defined positions along its axis. The intensity of the radiation emitted through the collimators is measured versus time with solid-state detectors and associated energy discrimination electronics. For the mathematical algorithm that we use, only a single pair of collimation bores and detectors are necessary for single temperature measurements. However, by employing a second, offset, pair of collimation holes and radiation detectors, diffusivities can be determined at several temperatures per sample. For thermal diffusivity measurements a disk geometry is used. A heat pulse is applied in the center of the sample and the temperature response of the sample is measured at several locations. Thus, several values of the diffusivity are measured versus time. The exact analytic solution to a heat pulse in the disk geometry leads to a unique heated area and measurement locations. Knowledge of the starting time and duration of he heating pulse is not used in the data evaluation. Thus, this methodology represents an experimentally simpler and more robust scheme.

Generalized potentials for a mean-field density functional theory of a three-phase contact line.

We investigate generalized potentials for a mean-field density functional theory of a three-phase contact line. Compared to the symmetrical potential introduced in our previous article [Phys. Rev. E 85, 011120 (2012)], the three minima of these potentials form a small triangle located arbitrarily within the Gibbs triangle, which is more realistic for ternary fluid systems. We multiply linear functions that vanish at edges and vertices of the small triangle, yielding potentials in the form of quartic polynomials. We find that a subset of such potentials has simple analytic far-field solutions and is a linear transformation of our original potential. By scaling, we can relate their solutions to those of our original potential. For special cases, the lengths of the sides of the small triangle are proportional to the corresponding interfacial tensions. For the case of equal interfacial tensions, we calculate a line tension that is proportional to the area of the small triangle.

Mean-field density functional theory of a three-phase contact line.

A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the contact line. We employ a triangular grid and use a successive overrelaxation method to find numerical solutions in the entire domain for the special case of equal interfacial tensions for the two-phase interfaces. We use the Kerins-Boiteux formula to obtain a line tension associated with the contact line. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change.