Laplace-Kelvin laws

Tangential stress or Marangoni effect and longitudinal stress or Laplace-Kelvin generalized laws are the fundamental boundary conditions acting on the interfacial layer. 

One must note that the balance equations are not dependent on either the type of material or the type of action the material undergoes. In fact, the balance equations are consequences of the laws of conservation of both linear and angular momenta and, eventually, of the first law of thermodynamics. In contrast, the constitutive equations are intrinsic to the material. As will be shown later, the incorporation of memory effects into constitutive equations either through the superposition principle of Boltzmann, in differential form, or by means of viscoelastic models based on the Kelvin-Voigt or Maxwell models, causes solution of viscoelastic problems to be more complex than the solution of problems in the purely elastic case. Nevertheless, in many situations it is possible to convert the viscoelastic problem into an elastic one through the employment of Laplace transforms. This type of strategy is accomplished by means of the correspondence principle. 

It may be added here that the four basic laws of capillarity, i.e., the equations of Gibbs [(10.2)], Laplace [(10.7)], Kelvin [(10.9)] and Young [(10.10)], all describe manifestations of the same phenomenon the system tries to minimize its interfacial free energy. (Another manifestation is found in the Hamaker equations see Section 12.2.1.) These laws describe equilibrium situations. Moreover, dynamic surface phenomena are of great importance. 

The aim of this book is to show that there is a great deal of science in ice cream, and in particular to demonstrate the link between the microscopic structure and the macroscopic properties. It is naturally biased towards physics, physical chemistry and materials science as these are the areas in which I trained. The book is aimed at schools and universities, and a scientific background is required to understand the more technical sections. I have attempted to make it readable by 16-18-year-olds, and many sections are suitable for adaptation by GCSE science teachers. I have unashamedly made reference to the giants of chemistry and physics such as Newton, Einstein, Boyle, Gibbs, Kelvin, Laplace and Young where the laws and equations that bear their names are relevant. I hope that as a result teachers reading this book will find in ice cream useful illustrations of a number of scientific principles. Some... 

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