Search

We perform a static analysis of a circular cylinder that forms a barrier between surfactant-laden and surfactant-free portions of a liquid–gas interface. In addition to determining the general implications of the balances for forces and torques, we quantify how the imbalance$\unicode[STIX]{x0394}\unicode[STIX]{x1D6FE}=\unicode[STIX]{x1D6FE}_{a}-\unicode[STIX]{x1D6FE}_{b}$between the uniform surface tension$\unicode[STIX]{x1D6FE}_{a}$of the surfactant-free portion of the interface and the uniform surface tension$\unicode[STIX]{x1D6FE}_{b}$of the surfactant-laden portion of the interface influences the load-bearing capacity of a hydrophobic cylinder. Moreover, we demonstrate that the difference between surface tensions on either side of a cylinder with a cross-section of arbitrary shape induces a horizontal force component$f^{h}$equal to$\unicode[STIX]{x0394}\unicode[STIX]{x1D6FE}$in magnitude, when measured per unit length of the cylinder. With an energetic argument, we show that this relation also applies to a rod-like barrier with cross-sections of variable shape. In addition, we apply our analysis to amphiphilic Janus cylinders and we discuss practical implications of our findings for Marangoni propulsion and surface pressure measurements.

The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.

The current entrenched, facile conception of force in terms of “pushes” and “pulls” has fostered a view of force as a “real quantity” rather than a mathematical concept. In the words of P ierce (1934, p. 262): [Force is] “the great conception which, developed in the early part of the seventeenth century from the rude idea of a cause, and constantly improved upon since, has shown us how to explain all the changes of motion which bodies experience, and how to think about physical phenomena; which has given birth to modern science; and which … has played a principal part in directing the course of modern thought … It is, therefore, worth some pains to comprehend it.” Those who believe the notion of force is obvious should read the scientific literature of the period following Newton. T ruesdell (1966) notes that “D'Alembert spoke of Newtonian forces as ‘obscure and metaphysical beings, capable of nothing but spreading darkness over a science clear by itself,’” while J ammer (1957, pp. 209, 215) paraphrases a remark of Maupertis, “we speak of forces only to conceal our ignorance,” and one of Carnot, “an obscure metaphysical notion, that of force.” Within the framework of continuum mechanics, the basic balance laws for linear and angular momentum assert that, given any spatial region P t convecting with the body, (i) the net force on P t is balanced by temporal changes in the linear momentum of P t ; (ii) the net moment on P t is balanced by temporal changes in the angular momentum of P t .