Kinetic Theory and Shear Viscosity of Dense Dipolar Hard Sphere Liquids

Abstract

Transport properties of dense fluids are fundamentally challenging, because the powerful approaches of equilibrium statistical physics cannot be applied. Polar fluids compound this problem, because the long-range interactions preclude the use of a simple effective diameter approach based solely on hard spheres. Here, we develop a kinetic theory for dipolar hard-sphere fluids that is valid up to high density. We derive a mathematical approximation for the radial distribution function at contact directly from the equation of state, and use it to obtain the shear viscosity. We also perform molecular-dynamics simulations of this system and extract the shear viscosity numerically. The theoretical results compare favorably to the simulations.

Anisotropy of field-controlled shear viscosity of dipolar fluids

“…At a reduced temperature T * = k B T /ϵ = 1.5 in MD simulations this pseudo HS potential reproduces the theoretically predicted shear viscosity of HS fluids [21]. It has also been shown that it describes the HS component of DHS fluids [5] in simulations of viscosity. The long range dipole-dipole interaction potential is used as given in equation (3).…”

“…where J n = (λ/n)(∂I n /∂λ) [5]. The RDF at contact for DHS from the equations above compares well to results of numerical simulations [5].…”

“…where J n = (λ/n)(∂I n /∂λ) [5]. The RDF at contact for DHS from the equations above compares well to results of numerical simulations [5]. In addition, it can be used in combination with equation ( 8) to obtain a better prediction for the viscosity than a purely HS model [5].…”

“…For DHS systems Pousaneh and de Wijn [5] proposed a method to predict the viscosity by starting from the HS approximation of equation (8), and then estimating g(σ) for DHS from the free energy using the logarithmic free energy (LFE) theory of Elfimova et al [17] by making use of the relation…”

“…The long range electrostatic interactions are qualitatively different from short-range interactions that are often approximated as (nearly) hard spheres (HS). Nevertheless, analytical results have been obtained for viscosity of such fluids [4,5]. Despite the theoretical challenges, polar fluids have a lot of potential applications due to their rich chemistry.…”