Master singular behavior for the Sugden factor of the one-component fluids near their gas-liquid critical point

Abstract

We present the master (i.e. unique) behavior of the squared capillary length - so called the Sudgen factor-, as a function of the temperature-like field along the critical isochore, asymptotically close to the gas-liquid critical point of twenty (one component) fluids. This master behavior is obtained using the scale dilatation of the relevant physical fields of the one-component fluids. The scale dilatation introduces the fluid-dependent scale factors in a manner analog with the linear relations between physical fields and scaling fields needed by the renormalization theory applied to the Ising-like universality class. The master behavior for the Sudgen factor satisfies hyperscaling and can be asymptotically fitted by the leading terms of the theoretical crossover functions for the correlation length and the susceptibility in the homogeneous domain recently obtained from massive renormalization in field theory. In the absence of corresponding estimation of the theoretical crossover functions for the interfacial tension, we define the range of the temperature-like field where the master leading power law can be practically used to predict the singular behavior of the Sudgen factor in conformity with the theoretical description provided by the massive renormalization scheme within the extended asymptotic domain of the one-component fluid "subclass".