No 3 (2024)

The extent of participation of mechanisms such as the active interactions of cells with each other and with the extracellular matrix, the increased hydrostatic pressure in intercellular fluid, and enzymatic activity of cells that lead to the destruction of the extracellular matrix in the process of formation of cavities in clusters of cells formed during cluster vasculogenesis is studied. The problem of evolution of a single cluster of cells immersed in a deformable extracellular matrix is solved within the framework of a previously developed continuum multiphase model of the medium formed by two actively interacting solid phases and a fluid and the role of various cellular mechanisms discussed in the formation of hollow structures is studied. The calculations showed that the dominance of active interactions of the cell-matrix type over the intercellular interactions leads to a displacement of cells towards the outer boundary of the cluster and the creation of conditions for the formation of a cavity inside the cluster. The enzymatic activity of cells helps to free up a headroom for compaction of the cluster, due to the active intercellular interactions, and to slow down the formation of the increasing concentration profile of the cellular phase. An increase in the fluid pressure in the area occupied by cells leads to acceleration of the redistribution of concentrations of the cellular phase and matrix. The fluid pressure promotes accumulation of the cellular phase near the cluster boundary and increase in the matrix concentration in its central part. And only the joint participation of all the mechanisms considered leads to the formation of a structure in which a layer formed by the cellular phase surrounds a fluid-occupied cavity, while the matrix concentration in the cavity demonstrates the trend to its complete disappearance.

The high-speed videorecording method is used to investigate the effect of an electrostatic field (with the potential 0, 16, and 18 kV) on the flow geometry in the case of gravity-induced separation of a drop from a capillary tube. The flow videograms are analyzed and the dimensions of the characteristic structural elements, that is, the drops themselves, a connection, and satellites, are determined. The oscillations of the linear dimensions and the mother liquid volume after drop separation are traced at 0 and 18 kV. Both fundamental frequencies and their harmonics are observable in the spectra. It is found that small (12%) variations in the potential value lead to qualitative variations in the flow pattern and, in particular, to direct separation of the drop from the mother liquid without the formation of a connection. At a constant liquid flow in the capillary the dimensions of the separated drops decrease with increase of the voltage. The experiments show the possibility of the fine controlling of drop flows using electrostatic fields.

A simplified mathematical model of two-phase multicomponent flow in the reservoir – multistage hydraulic fractures – horizontal well system is proposed. The formulation of transport problems in the well and in hydraulic fractures is simplified based on the dimensional analysis and similarity theory. The possibility of transition to a quasi-steady-state problem of distribution of the mixture components in high-permeability hydraulic fractures is shown. The dimension of the problem in reservoir is reduced by decomposing the problem into a set of problems in independent fixed stream tubes. For numerical solution of the problem, the resulting reduction in computer time reaches two orders of magnitude and can be further reduced by using parallel computing. Accelerating the solution of the direct problem is fundamentally necessary for the possibility of solving the inverse problem of identifying the porosity and permeability properties of fractures from the results of interpretation of tracer studies.

The drag crisis in flow past a sphere is modeled within the framework of the recently formulated vortex-resolving hybrid RANS–LES approach, which includes a semi-empirical model of laminar-turbulent transition. The calculations performed in a wide Reynolds number range show that the complex model used yields a qualitatively adequate description of all aspects of the drag crisis including such fine effects, as the growth of the side force oscillation amplitude at near-critical Reynolds numbers. At the same time, the results obtained indicate that it is very fine computation grids that should be used for obtaining qualitatively accurate predictions of the critical Reynolds number and the details of laminar-turbulent transition in near-critical flow regimes.

The disturbances generated by external turbulence in the shear layer on a flat plate suddenly set in motion are found. As the initial conditions, turbulent flow found using direct numerical simulation of the development of isotropic homogeneous turbulence is used. The solution obtained models laminar-turbulent transition in the boundary layer on a flat plate under relatively low free-stream turbulence when the transition is caused by Tollmien-Schlichting waves. The solution makes it possible to describe the process of generating various disturbances, namely, low-frequency streaky structures and instability waves and also their development in the initial stage of laminar-turbulent transition. Based on the processing of the obtained results, a simple model is proposed that relates the spectra of instability waves in the boundary layer and turbulent pulsations in free-stream flow. The dependences of the initial amplitude of instability waves and their critical amplification factors (N-factors) on the degree of flow turbulence are also obtained.

Interstellar dust enters the heliosphere due to the relative motion of the Sun and the Local Interstellar Cloud, which contains the Sun. The dynamics of interstellar dust particles is governed mainly by the electromagnetic force. The direction of this force depends on the polarity of the heliospheric magnetic field. In turn, polarity is a function of position and time and depends on the orientation of the solar magnetic dipole axis relative to the solar rotation axis. Previously it was shown that for the case when the magnetic dipole axis coincides with the solar rotation axis, the electromagnetic force acting on dust particles is directed towards the solar equatorial plane in both the northern and southern solar hemispheres. As a result, under the influence of such a force, the distribution of interstellar dust becomes highly inhomogeneous and, in particular, thin regions of increased number density (caustics) are formed. The goal of this work is to study the nature of caustics for a more realistic time-dependent model, when it is assumed that the magnetic dipole axis rotates relative to the solar rotation axis with a period of 22 years in accordance with the 22-year solar cycle. In addition, the magnetic dipole axis rotates due to the rotation of the Sun with a period of 25 days. To calculate the dust number density, the Lagrangian Osiptsov method is used. The shape and evolution of the resulting caustics are examined and the physical mechanisms of their origin are discussed. It is shown that, when taking into account time-dependent effects, caustics appear only in certain phases of the 22-year solar cycle, and then disappear.

The diffraction of plane surface and flexural-gravity waves during their normal incidence at the edge of a floating elastic semi-infinite plate in fluid of finite depth in the presence of a current with velocity shear is studied. The explicit analytical solution to this problem is constructed using the Wiener–Hopf technique. Simple exact formulas for the reflection and transmission coefficients and the energy relations are obtained. The results of numerical calculations using the obtained formulas are presented.

The two-fluid and two-temperature diffusion-drift model of gas-discharge plasma is used to study numerically the structure of the Penning discharge in a cylindrical discharge chamber at the molecular hydrogen pressure of 1 mTorr, the voltage between the electrodes of 500–1000 V, and the axial magnetic field induction of 0.001–0.2 T. Two regimes of existence of the Penning discharge are obtained in the calculations. These regimes differ qualitatively in the electrodynamic structure of the charged-particle flows of gas-discharge plasma, as well as there exist transient and extinction regimes in the weak and strong magnetic fields. The conditions under which the oscillatory motion of electron and ion flows develops in the paraxial regions are found. It is shown that the results of numerical simulation with the use of the diffusion-drift model make it possible to obtain consistent data in comparison with experiment, and at the same time to get an insight about the formation of the structure of flows of electric-discharge plasma particles. This makes it possible to explain the observed experimental data.