Statistical Complexity and Two Van Der Waals’ Phase Transitions

We show that the van der Waals gas does not exhibit just the celebrated liquid-gas 1 transition but also a quantum-classical one. We study the issue with reference to the LMC statistical 2 complexity and in relation to the order-disorder contrast.

Stability of expanding accretion shocks for an arbitrary equation of state

We present a theoretical stability analysis for an expanding accretion shock that does not involve a rarefaction wave behind it. The dispersion equation that determines the eigenvalues of the problem and the explicit formulae for the corresponding eigenfunction profiles are presented for an arbitrary equation of state and finite-strength shocks. For spherically and cylindrically expanding steady shock waves, we demonstrate the possibility of instability in a literal sense, a power-law growth of shock-front perturbations with time, in the range of $h_c< h<1+2 {\mathcal {M}}_2$ , where $h$ is the D'yakov-Kontorovich parameter, $h_c$ is its critical value corresponding to the onset of the instability and ${\mathcal {M}}_2$ is the downstream Mach number. Shock divergence is a stabilizing factor and, therefore, instability is found for high angular mode numbers. As the parameter $h$ increases from $h_c$ to $1+2 {\mathcal {M}}_2$ , the instability power index grows from zero to infinity. This result contrasts with the classic theory applicable to planar isolated shocks, which predicts spontaneous acoustic emission associated with constant-amplitude oscillations of the perturbed shock in the range $h_c< h<1+2 {\mathcal {M}}_2$ . Examples are given for three different equations of state: ideal gas, van der Waals gas and three-terms constitutive equation for simple metals.

An Integral Method for Natural Convection of Van Der Waals Gases over a Vertical Plate

This paper focuses on a study of natural convection in a van der Waals gas over a vertical heated plate. In this paper, for the first time, an approximate analytical solution of the problem was obtained using an integral method for momentum and energy equations. A novel simplified form of the van der Waals equation for real gases enabled estimating the effects of the dimensionless van der Waals parameters on the normalized heat transfer coefficients and Nusselt numbers in an analytical form. Trends in the variation of the Nusselt number depending on the nature of the interaction between gas molecules and the wall were analyzed. The results of computations for a van der Waals gas were compared with the results for an ideal gas.

Numerical Modeling of the Real Van Der Waals Gas Flow in the Shock Tube

В работе проводится математическое моделирование течения реального газа в ударной трубе. Численное решение задачи выполняется на основе метода С. К. Годунова с использованием уравнения состояния Ван-дер-Ваальса. Газодинамические процессы исследуются как в областях классического поведения газа, так и в неклассической области, в которой фундаментальная производная отрицательна. Проведенные расчеты для случаев формирования в идеальном газе двух волн разрежения, двух ударных волн, а также ударной волны и волны разрежения одновременно показали хорошее соответствие результатов аналогичным расчетам и известным теоретическим данным. Для случая неклассического поведения газа исследовалось вещество с большой удельной теплоемкостью по отношению к ее молекулярной массе вблизи критической точки кривой насыщения. Рассматривались три варианта начальных состояний газа, в процессе развития течения в которых формировались области неклассического поведения вещества. Во всех исследуемых вариантах в газе формируется ударная волна, распространяющаяся в сторону меньшего значения давления и волны разрежения, двигающиеся в сторону большего давления в газе. Показано, что в неклассической области течения ударная волна сглаживается, в то время как волны разрежения при отрицательных значениях фундаментальной производной формируют скачок разрежения, и крутизна кривых параметров течения возрастает.

An Analytical Investigation of Natural Convection of a Van Der Waals Gas over a Vertical Plate

The study focused on a theoretical study of natural convection in a van der Waals gas near a vertical plate. A novel simplified form of the van der Waals equation derived in the study enabled analytical modeling of fluid flow and heat transfer. Analytical solutions were obtained for the velocity and temperature profiles, as well as the Nusselt numbers. It was revealed that nonlinear effects considered by the van der Waals equation of state contribute to acceleration or deceleration of the flow. This caused respective enhancement or deterioration of heat transfer. Results for a van der Waals gas were compared with respective computations using an ideal gas model. Limits of the applicability of the simplified van der Waals equations were pinpointed.

Increase in Axial Compressibility in a Spinning Van der Waals Gas

We investigated the adiabatic compression along the axial direction of a spinning Van der Waals gas by applying theoretical analysis and molecular dynamics (MD) simulations. Based on the analytical results, the rotation-induced compressibility increase effect is significant in a Van der Waals gas, while the attraction term in the Van der Waals equation of states (EOS) contributes significantly to the compressibility increase in a spinning system. We conducted MD simulations to the axial compression of a spinning gas, whose state is far from the ideal gas state, and further demonstrated that the rotation-induced compressibility increase effect in a dense state is robust, implying that such a phenomenon can be detected in experiments under high-energy-density conditions.