Mesoscopic metastable liquid in congruent vapor-liquid diagram of argon from about zero up to boyle`s temperature (review of FT-model)

Such paradigms of the coupled classical metastability and nonclassical criticality as the existence of a unified EOS (common for both gas and liquid phases) with its mean-field (mf), so-called Andrews-van der Waals’ critical point (CP) should be questioned to recognize the realistic stratified structure of a mesoscopic liquid phase. It exists supposedly in the wide range of temperatures located between about zero , K and up to the singular first Boyle’s point . Its opposite, also singular second Boyle’s point corresponds to the alternative origin for the crossover continuous bounds separating the specific structural strata of a mesoscopic liquid. The region of a heterogeneous l-phase spanning the whole temperature range can be termed the non-Gibbsian phase (due to its discrete cluster-like structure) without any appeals to the concept of a spinodal decomposition. The respective metastable liquid stratum is formed by three segments of supercritical , subcritical and sublimation metastable states of a formally incompressible liquid constrained by the pair of fixed extensive parameters (N,V). Its location on the CVL-diagram is restricted by the new introduced here ml-bound and by the known Zeno-line (ZL) bound. Thus, all above-mentioned strata belong to the region of soft fluid with the dominance of interparticle attraction. The remaining parts of CVL-diagram are spanned either by the real gas state-points and solid state-points (crystalline and/or amorphous) or by the region of hard fluid in the classification proposed by Ben-Amotz and Herschbach.

On instability of Rayleigh–Taylor problem for incompressible liquid crystals under $L^{1}$-norm

We investigate the nonlinear Rayleigh–Taylor (RT) instability of a nonhomogeneous incompressible nematic liquid crystal in the presence of a uniform gravitational field. We first analyze the linearized equations around the steady state solution. Thus we construct solutions of the linearized problem that grow in time in the Sobolev space $H^{4}$ H 4 , then we show that the RT equilibrium state is linearly unstable. With the help of the established unstable solutions of the linearized problem and error estimates between the linear and nonlinear solutions, we establish the nonlinear instability of the density, the horizontal and vertical velocities under $L^{1}$ L 1 -norm.

RESEARCH AND MODELING OF FLUID MOTION IN THE CASE WHEN THE VOLUME OF THE FLUID DOES NOT CHANGE AND IN THE CASE WHEN THE VOLUME CHANGES

A liquid is a physical body that has the property of fluidity, so it does not have its own shape and takes the form of a vessel that it fills. Liquids are divided into two types: drip and gaseous. Droplet liquids are characterized by high compression resistance (almost complete incompressibility) and low resistance to tensile and tangential forces, due to the insignificance of the coupling forces and friction forces between the liquid particles. An incompressible fluid is a mathematical model of a continuous medium whose density is preserved when the pressure changes. When defining an incompressible liquid, it is assumed that it retains the basic properties of the liquid, in particular, to change shape at a constant volume. The article presents the experiments demonstrating two types of incompressible fluid are presented. The first type is the motion of fluid not changing its volume due to elastic deformation. The second type is the formation of vortices during the expansion of the fluid that has received additional kinetic energy. Formulas for calculating and modeling vortices are proposed.

Simulation of Coagulable Mixtures Dynamics in Incompressible Liquid Considering Clot Cluster Formation

Одной из ключевых проблем, на решение которой направлены ресурсы общества по преодолению заболевания, вызванного новым коронавирусом COVID-19, является проблема нарушения кровотока, связанная, в частности, с процессом тромбообразования. Это явление существенно ограничивает кровоток, снижая доставку кислорода в целом по всему организму. В статье рассмотрены результаты создания математической модели динамики коагулирующих смесей в несжимаемой жидкости c учетом явления формирования кластеров-тромбов. Создание математических моделей процессов коагуляции и тромбообразования в сердечно-сосудистой системе человека обеспечит разработку эффективного управления этими явлениями. В статье описана математическая модель для процессов коагуляции в дисперсных системах — тромбообразования. Представлены результаты численного решения задачи и визуализация аналитического решения задачи, включая такие важнейшие параметры для тромбообразования, как распределение концентрации примеси в жидкости и распределение поля давления. Указанная модель может служить основой для построения иерархической системы образования тромбов в сердечно-сосудистой системе от микроскопического уровня до макроскопических структур. В том числе модель позволит сделать выводы об эффективности использования антикоагулянтов при поступлении пациентов в отделения неотложной помощи и при положительном результате теста на COVID-19. One of the key problems associated with COVID-19 is blood circulation impairment, particularly caused by thrombosis. The impairment significantly reduces the blood flow and restricts oxygen delivery to the entire body. The paper covers the simulation model for the coagulable mixture dynamics in an incompressible liquid considering clot cluster formation. Simulation models for the thrombosis and coagulation processes in the human cardiovascular system will help efficiently manage these phenomena. The study proposes a simulation model of the coagulation processes in disperse systems, i.e., the thrombosis process. The paper presents the numerical solution results and the visualization of the analytical solution. The key thrombosis properties such as impurity concentration distribution in the liquid, and the pressure field 16 В. А. Галкин, Т. В. Гавриленко, А. В. Галкин О математическом моделировании динамики коагулирующих смесей в несжимаемой жидкости c учетом явления формирования кластеров-тромбов distribution, were estimated. The simulation model can become a foundation for developing a multi-tier clot formation system in the cardiovascular system: from the microscopic level to the macroscopic structures. Besides, the model can estimate the efficiency of anticoagulants administered to COVID-19 positive patients at emergency care departments.