Equation of State of a Cell Fluid Model with Allowance for Gaussian Fluctuations of the Order Parameter

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An analytic procedure for calculating the critical temperature and estimating the size of the critical region for a cell fluid model is developed. Our numerical calculations are illustrated by the case of the Morse potential parameters characterizing the alkali metals (sodium and potassium). The critical temperatures found for liquid sodium and potassium as solutions of the resulting quadratic equation agree with experimental data. The expression for the relative temperature determining the critical region size is obtained proceeding from the condition for the critical regime existence. In the cases of sodium and potassium, the value of this temperature is of the order of a few hundredths.

Section: Model For Describing a Fluid Systemmentioning

confidence: 99%

Analytic Calculation of the Critical Temperature and Estimation of the Critical Region Size for a Fluid Model

Pylyuk,

Kozlovskii,

Dobush

2023

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“…We consider a system of 𝑁 interacting particles in the volume 𝑉 conditionally divided into 𝑁 𝑣 cells (𝑉 = 𝑣𝑁 𝑣 , 𝑣 = 𝑐 3 is the cell volume, and 𝑐 is the linear size of a cell) [16][17][18]. In contrast to a cell gas model (where a cell is assumed to contain only one particle or be empty) [19,20], in our approach, a cell may contain more than one particle [21,22]. Besides, the distance between the cells is introduced instead of the distance between the particles.…”

Section: Cell Fluid Model and The Interaction Potentialmentioning

confidence: 99%

Thermodynamic Quantities of Morse Fluids in the Supercritical Region

Pylyuk,

Kozlovskii,

Dobush

2023

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The critical point parameters for liquid alkali metals (sodium and potassium) are calculated accounting for the non-Gaussian order parameter fluctuations and the Morse interaction potential. The behavior of the isothermal compressibility, density fluctuations, and thermal expansion for sodium is studied in the supercritical temperature region. A significant increase in the isothermal compressibility and the density fluctuations near the critical point indicates a substantial density sensitivity to tiny pressure fluctuations. The thermal expansion coefficient for various fixed pressure values shows a typical gas decrease with increasing supercritical temperature. The Widom line separating the gaseous and liquid structures of the fluid at temperatures above the critical one is represented. Note that our calculations are valid in a small neighborhood of the critical point, which is problematic for theoretical and experimental studies.

“…The theoretical and experimental study of the behavior of liquids and their mixtures in a vicinity of their critical point (see, e.g., works [1][2][3][4][5][6][7][8]) is an important and challenging task. In our previous works [9,10], the behavior of fluid was studied in an immediate vicinity of the critical point, and in works [11][12][13] beyond this vicinity. As a result, a wide region near the critical point has been covered.…”

Section: Introductionmentioning

confidence: 99%

Фазовий Перехід Першого Роду В Рамках Коміркової Моделі Плину: Області Зміни Хімічного Потенціалу Та Відповідні Густини

Pylyuk

Kozlovskii

2022

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Роботу присвячено мiкроскопiчному опису поведiнки плинного середовища в безпосередньому околi критичної точки, де теоретичнi та експериментальнi дослiдження важко проводити. Для температур T < TC видiлено i проаналiзовано областi змiни хiмiчного потенцiалу та густини. Рiвняння стану комiркової моделi плину у змiнних температура–хiмiчний потенцiал записано з використанням функцiй Хевiсайда. Дане рiвняння подано також у термiнах змiнних температура–густина. В результатi дослiдження зв’язку мiж густиною та хiмiчним потенцiалом отримано рiвняння для бiнодалi в безпосереднiй близькостi до критичної точки.