Quantitative results for square gradient models of fluids

¹ Department of Applied Mathematics, The University of Western Ontario - London, Ontario N6A 5B8, Canada
² School of Materials Science and Engineering, Shanghai Jiao Tong University - 800 Dongchuan Road, Minhang, Shanghai 200240, China

^a konglt@sjtu.edu.cn
^b cdennist@uwo.ca

Received: 6 October 2010
Accepted: 9 February 2011

Abstract

Square gradient models for fluids are extensively used because they are believed to provide a good qualitative understanding of the essential physics. However, unlike elasticity theory for solids, there are few quantitative results for specific (as opposed to generic) fluids. Indeed the only numerical value of the square gradient coefficients for specific fluids have been inferred from attempts to match macroscopic properties such as surface tensions rather than from direct measurement. We employ all-atom molecular dynamics, using the TIP3P and OPLS force fields, to directly measure the coefficients of the density gradient expansion for several real fluids. For all liquids measured, including water, we find that the square gradient coefficient is negative, suggesting the need for some regularization of a model including only the square gradient, but only at wavelengths comparable to the molecular separation of molecules. The implications for liquid-gas interfaces are also examined. Remarkably, the square gradient model is found to give a reasonably accurate description of density fluctuations in the liquid state down to wavelengths close to atomic size.