8th Liquid Matter Conference September 6-10, 2011 Wien, Austria ...

P9.46Tue 611:23-14:00A perturbation theory for friction of a large particleimmersed in a binary solventYuka Nakamura, 1 Akira Yoshimori, 1 and Ryo Akiyama 11 Kyushu Univ. , 6-10-1 Hakozaki, Higashi-ku, 812-8581, Fukuoka, JapanWhen biomolecules such as proteins move in water, they are subjected to friction from water.Though the friction depends on the viscosity of the solvent, a distribution of circumjacent solventparticles can also play an important role. In the case that a solvent consists of two components, thedistribution greatly depends on the mixture ratio. Experiments on actomyosin motors have shownthe effect on the distribution. Therefore, we have developed a new theory of binary solvents tostudy the effects of the distribution of circumjacent solvent particles on the friction. We expandedthe basic equations of a microscopic theory in powers of the ratio between the sizes of solvent andsolute particles. Here, we assumed that a solvent particle is small compared to a solute particle.From this expansion, we derived hydrodynamic equations with new boundary conditions of thesurface on a solute particle. By solving this equation analytically, we obtained an expression of thefriction which includes the mass densities of the binary solvent. Mass densities can be calculatedfrom the radial distribution functions expressing the equilibrium distribution of solvent particlesaround a solute particle. Hence, we can obtain the friction considering the microscopic interactionsbetween solvent and solute particles through the radial distribution functions. By using this theory,we calculated the friction of a hard-sphere system by varying the size and mole fraction. Thecalculated results showed that the friction was 1.08 times as large as that of a one-componentsolvent when a small amount of another component solvent was added (the mole fraction was0.003, and the ratio of the radii was 50 : 1 : 2). Furthermore, the friction increased with the molefraction. For instance, when the mole fraction was 0.03, the friction was twice as large as thatobtained from the Stokes law.46