Lewis E. Johns

THE DIFFUSIONAL LIMITATION ON THE TEMPERATURE RISE IN THE ABSORPTION OF CHEMICALLY REACTIVE GASES

The interfacial temperature is important in gas absorption because it sets the solubility. If the gas undergoes an exothermic reaction this temperature ordinarily exceeds the bulk liquid temperature. For a bimolecular reaction the pseudo-first-order approximation leads to a serviceable model; yet it must overestimate the temperature rise under fast reaction conditions. We correct this estimate by accounting for the depletion of the liquid-phase reactant near the surface. To do this we use an enhancement factor based on the van Krevelen-Hoftijzer approximation. This implies a simple formula for the temperature rise not unlike that based on the pseudo-first-order approximation. We investigate this formula and show that it exhibits either one or three solutions. We deduce criteria for predicting, a priori, both what the multiplicity is and whether or not the maximum temperature rise corresponding to instantaneous reaction obtains.

The Rayleigh–Taylor instability of a surface of arbitrary cross section with pinned edges

We determine the critical points of the Rayleigh–Taylor instability of a surface of arbitrary cross section having pinned edges. Often these points coincide with the diffusion eigenvalues but sometimes they do not.

The Frank-Kamenetskii approximation

Etude des cinetiques chimiques de reactions non-isothermes, et ou la constante de vitesse est liee a la temperature

Can an adverse density difference across a surface be stabilized by heating from above

We investigate the possibility of stabilizing a Rayleigh-Taylor experiment by imposing a small upward temperature gradient. We find that if the two fluids have equal thermal conductivities nothing can be accomplished. If either thermal conductivity is much greater than the other, the small gradient is always stabilizing. If the thermal conductivities are of the same order of magnitude the small gradient can be stabilizing or destabilizing depending on the thermal expansion coefficients. We have used a Darcy model so that we can derive formulas and present a physical explanation of what we find.

Can convection induced by heating delay a thermal explosion

A thermal explosion is said to occur in a region if heat generated steadily therein cannot be conducted to its boundaries. Our interest is in the effect of natural convection on the conditions for thermal explosion. It is surprising that adding a second mechanism for heat loss lowers the steady rate of heat generation and, therefore, that natural convection appears to do little to change the point of explosion. This is due to the fact that the flow, by lowering the heat generation, is self-weakening.

Growth Constants in Solidification

In phase-change problems, there are domain and surface contributions to the dynamics of a moving front. It is ordinarily assumed that the surface contributions are in complete control. This is likely to be true in the case of planar fronts, but it may or may not be true in the cylindrical case. We study the growth rates of disturbances imposed on the surface of a cylindrical solid in equilibrium with its melt and deduce the conditions under which time derivatives of bulk-phase variables are important. They are important in the case of a whisker and are even more important if a solute is added.

CRITICAL POINTS IN THE SOLIDIFICATION OF A PURE MATERIAL

Patterns in the solidification of a pure material are dealt with in this article. Results, deduced from a simple model based on heat conduction in the two phases and the effect of surface tension on the equilibrium temperature at the moving front, present a guide for experimental work. By introducing far-field conditions imitating what can be achieved in an experiment, we explain how the depths of the phases and the width of the container influence the patterns that can be seen if one advances the control variable to the critical point and then just beyond. Our new result is the existence of a third critical point. It occurs at small wave numbers and it is independent of surface tension. It appears because we take the depths of the phases into account. These depths are input values that offer the possibility of controlling crest-to-trough conduction, stabilizing in the solid, destabilizing in the liquid. The new critical point, and the patterns attending its appearance, can be found in cells of easily attainable widths.