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.

Scaling laws for the critical rupture thickness or common thin films

Despite decades of experimental and theoretical investigation on thin films, considerable uncertainty exists in the prediction of their critical rupture thickness. According to the spontaneous rupture mechanism, common thin films become unstable when capillary waves. at the interfaces begin to grow. In a horizontal film with symmetry at the midplane. unstable waves from adjacent interfaces grow towards the center of the film. As the film drains and becomes thinner, unstable waves osculate and cause the film to rupture, Uncertainty sterns from a number of sources including the theories used to predict film drainage and corrugation growth dynamics. In the early studies, (lie linear stability of small amplitude waves was investigated in the Context of the quasi-static approximation in which the dynamics of wave growth and film thinning are separated. The zeroth order wave growth equation of Vrij predicts faster wave growth rates than the first order equation derived by Sharma and Ruckenstein. It has been demonstrated in an accompanying paper that film drainage rates and times measured by numerous investigations are bounded by the predictions of the Reynolds equation and the more recent theory of Manev, Tsekov, and Radoev. Solutions to combinations of these equations yield simple scaling laws which should bound the critical rupture thickness of foam and emulsion films, In this paper, critical thickness measurements reported in the literature are compared to predictions from the bounding scaling equations and it is shown that the retarded Hamaker constants derived from approximate Lifshitz theory underestimate the critical thickness of foam and emulsion films, The non-retarded Hamaker constant more adequately bounds the critical thickness measurements over the entire range of film radii reported in the literature. This result reinforces observations made by other independent researchers that interfacial interactions in flexible liquid films are not adequately represented by the retarded Hamaker constant obtained from Lifshitz theory and that the interactions become significant at much greater separations than previously thought. (c) 2005 Elsevier B.V. All rights reserved.