Carnahan-Starling type equations of state for stable hard disk and hard sphere fluids

Abstract

The well-known Carnahan-Starling (CS) equation of state (EoS) 1 for the hard sphere (HS) fluid was derived from a quadratic relation between the integer portions of the virial coefficients, 𝐵 , , and their orders, 𝑛. Here we extend the method to the full virial coefficients 𝐵 for the general D-dimensional case. We assume a polynomial function of (D-1) th order for the virial coefficients starting from 𝑛 = 4 and EoS's are derived from it. For the hard rob (D=1) case, the exact solution is obtained. For the stable hard disk fluid (D=2), the most recent virial coefficients up to the 10 th 2 and accurate compressibility data 3,4 are employed to construct and test the EoS. For the stable hard sphere (D=3) fluid, a new CS-type EoS is constructed and tested with the most recent virial coefficients 5,2 up to the 11 th and with the highly-accurate simulation data for compressibility [6][7][8] . The simple new EoS's turn out to be as accurate as the highest-level Padé approximations based on all available virial coefficients, and significantly improve the CS-type EoS in the hard sphere case. We also shown that as long as the virial coefficients obey a polynomial function any EoS derived from it will diverge at the non-physical packing fraction, 𝜂 = 1.

Singular limit for the compressible Navier--Stokes equations with the hard sphere pressure law on expanding domains

“…In order to proceed we estimate the quantity |Ω R | −1 τ 0 Ω R p(ρ). We begin by repeating the part of the proof of Theorem 2.1, namely the proof of (20), as b(s) = s satisfies the assumptions of Theorem 2.1, to get…”

“…This model is used for the study of the behavior of dense gases and liquids. The interested reader can find more details regarding the model or its corrections (Percus-Yevick equation, Kolafa correction, Liu correction) in [6,20,19,17]. Singular pressure laws of similar type appeared in modeling of various phenomena, including the collective motion, see [8,9,23], and the traffic flow, see [1,2].…”