Model of Boundary Conditions on Metal Surfaces for Rarefied Gas

EVELINA PROZOROVA

Mathematical-Mechanical Department

St. Petersburg State University

Av. 28 , Peterhof, 198504

RUSSIA

Abstract: Currently, the classical theory discusses issues related to the sliding of liquid and gas along

layer, but adhesion and the formation of a thin stationary layer are possible. Various possible causes

of slipping are discussed. The formation of a dislocation from a point defect near the surface, which is

a vacancy, is considered. An analysis of the causes of pore clogging during water movement near the

surface was carried out. The emphasis is on the change in stress in the metal, taking into account the

influence of the moment that occurs when the position of the molecules changes.

Keywords: boundary conditions, kinetic theory, gas-surface interaction, dislocation, vacancies,

angular momentum

Received: February 22, 2023. Revised: February 24, 2024. Accepted: May 19, 2024. Published: July 4, 2024.

layers of a solid, i.e. it is necessary to solve a

conjugate problem. The great practical

importance of surface and adsorption processes

leads to the need for their detailed study. The

equations for macroparameters proposed by the

theory are applicable inside the region, but near

the boundary, knowledge of the interaction of

flow molecules with the surface is necessary.

Boundary conditions depend on flow regimes,

properties of the surface and medium, and

The boundary conditions for velocity and

temperature (usually at constant density) serve

as the boundary conditions for the Navier-

inside a thin layer do not collide; collisions

occur with surface molecules. The distribution

velocity, but the number of particles does not

change. If we take into account the density

derivative [7,8], we obtain the equations S.V.

Vallander [9]. The process of interaction of a

gas or liquid with a surface is determined by the

interaction potentials of the gas flow and

molecules of the surface a solid body, as well

as the energy of falling particles. In this case,

we studied the process of gas adsorption by a

surface using the Langmuir method. The

experimental Gas-surface interaction data refer

to monobeam interactions. The velocity

distribution qualitatively changes the

interaction process and is largely determined by

the surface structure. In a liquid near the

surface, molecules, such as water, acquire

structure due to the interaction of oxygen with

molecules of the crystal lattice. Water

molecule-dipole. With crystal lattice dipole-

dipole interaction occurs. The position of

surface must occur. It takes time. When water

flows around nanostructures, sliding is

observed in experiments. Experimental studies

show that when flowing around hydrophilic

surfaces, the sliding length is several

nanometers, and over hydrophobic surfaces -

tens of nanometers. The Navier-Stokes

approximation may not work at small scales,

especially near solid-liquid boundaries.

Adhesion conditions may not be correct. The

fluid movement. Size ratio is also an important

factor. Internuclear O–H distances are close to

9.06÷1.22 nm. [12]. Some molecules are in a

free state. It is these molecules that carry out

transport processes in liquids. The size ratio

indicates the possible overlap of the gaps

between surface molecules by a water

molecule. For capillaries with a radius on the

order of the cluster radius, sliding is possible

due to contact with the wall of a small part of

the cluster. If long-range forces are not enough

to destroy the accumulation, then sliding can be

a surface molecule if the surface is stepped

(close interaction approximation). The surface

structure may change during operation. The

most important role in changing the surface

structure and the formation of cracks is played

by defects in the surface and adjacent metal

layers associated with the interaction of

dislocations. This work examines the initial

stage of dislocation formation near a point

defect (vacancy). It is generally accepted that

features of the surface layers of the metal;

therefore, it is necessary to solve the problem

of superposition.

boundary it is necessary to know the interaction

of the flow molecules with the surface. In the

conditions for the Navier-Stokes equations.

Here it is proposed to split the task into two. For

a rarefied gas, at least at low flow rates, it is

proposed to consider a thinner layer equal to

several molecular interaction radii. The mean

free path is too long, interactions of gas

molecules with the wall occur at much shorter

distances. The gas molecules inside the thin

layer do not collide; collisions take place with

surface molecules. The distribution function at

the angular momentum on the structured

surfaces is taken into account.

Molecules moving towards the wall must be

divided into three groups: molecules with low

speed, which subsequently stick to the wall,

molecules with medium speed, which are

reflected from the wall, and molecules with

high speed, which penetrate the wall. The

boundaries of the ranges are determined by the

energy of accommodation for a specific gas and

crystallographic surface. In many cases, the

distance increases, which entails a change in

the interaction potential. In this case, the role of

collective effects is reduced. Having obtained

the distribution function at the layer boundary

it is necessary to solve the Boltzmann equation

in the layer from this boundary to the Knudsen

layer boundary by the small parameter method

using the Chapman-Enskog function. This can

be done by a small change in the distribution

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particle, particle mesh) [5]. These methods are

used to calculate the potentials of metals and

nm, the distance between the nuclei of

hydrogen atoms is 0.15 nm, and the angle

case, the effect of these variables willt be

traced. Using the classical variant leads to a

linear dependence of the moments that can be

realized only under additional conditions.

Interaction with water is determined by the

structure of the molecule and the change in the

the 1s electrons of the H atoms. Four of the six

valence electrons of the O atom that do not

two couples). These allow the oxygen atom of

In this case, the water molecule exhibits the

properties of an electron donor. In the case of

adsorption, unshared electron pairs of

molecules are able to form bonds both with

surface atoms and with other molecules

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Let us consider the relationship between the

forces of the “correct” and distorted lattices.

The usual experimental value is ≈0.1. The

equilibrium position is unstable. Any small

disturbance, such as phonons, or an increase in

load can lead to reverse motion due to repulsive

forces. Under load, due to changes in the

occur. Further propagation requires a

significant increase in voltage. This process

probably requires a relaxation process. The

calculations is performed for all surrounding

points. Due to symmetry, the number of points

are reduced. As the load increases, the

dislocation is determined by the applied energy.

Criteria for the energy state of the energy

balance can be found in [11,12]. In the presence

the surface.

4. Conclusion

The great practical importance of surface and

adsorption processes leads to the need for their

detailed study. The equations for

macroparameters proposed by the theory are

applicable inside the region, but near the