A new equation for macroscopic description of capillary rise in porous media

Capillary rise in porous media is frequently modeled using the Washburn equation. Recent accurate measurements of advancing fronts clearly illustrate its failure to describe the phenomenon in the long term. The observed underprediction of the position of the front is due to the neglect of dynamic saturation gradients implicit in the formulation of the Washburn equation. We consider an approximate solution of the governing macroscopic equation, which retains these gradients, and derive new analytical formulae for the position of the advancing front, its speed of propagation, and the cumulative uptake. The new solution properly describes the capillary rise in the long term, while the Washburn equation may be recovered as a special case. (C) 2004 Elsevier Inc. All rights reserved.

Peter Brown's The 'rise of western christendom', second edition: A review essay

Peter Brown, perhaps the world's leading scholar in the field of late antiquity, has produced a substantially revised and expanded edition of one of his major books, drawing on the vast volume of recent work. This essay summarizes its central arguments, especially the significance it attributes to developments away from the Mediterranean and to the seventh century, which together allow the topic to be seen in a compelling new light. It applauds the sustained excellence of Brown's prose, as well as his frame of reference and historical imagination. Some questions are raised concerning his deployment of sources, the importance given to the north, the ability to make decisions that people are credited with, and the coming of Islam. That a scholar of Brown's eminence is able to relish and appropriate effectively work that appeared subsequent to the first edition of this book is a tribute to his stature.

Transient temperature rise in a mouse due to low-frequency regional hyperthermia

A refined nonlinear heat transfer model of a mouse has been developed to simulate the transient temperature rise in a neoplastic tumour and neighbouring tissue during regional hyperthermia using a 150 kHz inductive coil. In this study, we incorporate various bio-energetic enhancements to the heat transfer equation and numerical validations based on experimental findings for the mouse, in terms of nonlinear metabolic heat production, homeothermy, blood perfusion parameters, thermoregulation, psychological and physiological effects. The discretized bio-heat transfer equation has been validated with the commercial software FEMLAB on a canonical multi-sphere object before applying the scheme to the inhomogeneous mouse voxel phantom. The time-dependent numerical results of regional hyperthermia of mouse thigh have been compared with the available experimental temperature results with only a few small disparities. During the first 20 min of local unfocused heating, the temperature in the tumour and the surrounding tissue increased by around 7.5 degrees C. The objective of this preliminary study was to develop a validated electrothermal numerical scheme for inductive hyperthermia of a small mammal with the intention of expanding the model into a complete numerical solution involving ferromagnetic nanoparticles for targeted heating of tumours at low frequencies. In addition, the numerical scheme herein could assist in optimizing and tailoring of focused electromagnetic fields for hyperthermia.