Center for low-gravity fluid mechanics and transport phenomena

Research projects in several areas are discussed. Mass transport in vapor phase systems, droplet collisions and coalescence in microgravity, and rapid solidification of undercooled melts are discussed

Berle VIII: Benefit Corporations and the Firm Commitment Universe

Benefit corporation law is a critical tool to allow private capital to be invested in a manner that creates shared and durable value for everyone. But a tool is only as good as the person who uses it. As highlighted in Rick Alexander’s essay, shareholders must understand the value of firm commitment, and, more importantly, the ultimate source of wealth for universal investors, which is thriving financial markets and a healthy, peaceful, and prosperous planet. These goals can only be attained and maintained for the long term if private capital is allocated and invested in a manner that creates value for everyone. So investors must learn to use benefit corporation law as a tool to require the companies they own to create value in a responsible and sustainable manner

The influence of reactant consumption on the critical conditions for homogeneous thermal explisions

The spatially homogeneous model of a high activation energy thermal explosion is studied when the heat loss parameter a is close to the classically-defined critical value a = e. Asymptotic solutions are developed which describe the time- history of the temperature and reactant depletion. It is shown that there is a critical time period, large with respect to the characteristic conduction time, in which the temperature variation is described by a Riccati equation. The solution properties of this nonlinear equation permit one to define a value of A = a — e which separates subsequent subcritical and supercritical behaviour

Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined

Effects of temperature dependent viscosity on Bénard convection in a porous medium using a non-Darcy model

Temperature-dependent viscosity variation effect on Benard convection, of a gas or a liquid, in an enclosure filled with a porous medium is studied numerically, based on the general model of momentum transfer in a porous medium. The exponential form of viscosity-temperature relation is applied to examine three cases of viscosity-temperature relation: constant (mu = mu(C)), decreasing (down to 0.13 mu C) and increasing (up to 7.39 mu(C)). Effects of fluid viscosity variation on isotherms, streamlines, and the Nusselt number are studied. Application of the effective and average Rayleigh number is examined. Defining a reference temperature, which does not change with the Rayleigh number but increases with the Darcy number, is found to be a viable option to account for temperature-dependent viscosity variation. (C) 2007 Published by Elsevier Ltd