Singular behaviour of time-averaged stress fluctuations on surfaces. (21st December 2018)

• Record Type: Journal Article
• Authors: Itami, Masato; Sasa, Shin-ichi
• Is Part Of: Journal of statistical mechanics. (2018:Dec.)
• Publication Date: 2018-12-21
• Subjects: 4 -- 16; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aaf31c
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We provide a method for calculating time-averaged stress fluctuations on surfaces in a viscous incompressible fluid at equilibrium. We assume that (i) the time-averaged fluctuating stress is balanced in equilibrium at each position and that (ii) the time-averaged fluctuating stress obeys a Gaussian distribution on the restricted configuration space given by (i). Using these assumptions with the Green–Kubo formula for the viscosity, we can derive the large deviation function of the time-averaged fluctuating stress. Then, using the saddle-point method for the large deviation function, we obtain the time-averaged surface stress fluctuations. As an example, for a fluid between two parallel plates, we study the time-averaged shear/normal stress fluctuations per unit area on the top plate at equilibrium. We show that the surface shear/normal stress fluctuations are inversely proportional to the distance between the plates.