A study of behavior and stability of an advective thermocapillary flow in a weakly rotating liquid layer under microgravity

Knutova, N. S.; Shvarts, K. G.

doi:10.1134/s0015462815030047

Cited by 11 publications

(5 citation statements)

References 8 publications

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“…Стоит отметить, что системы (1) и 2 ; 222 2 2 2 Далее будем рассматривать течения вязкой несжимаемой жидкости, у которых профиль скорости зависит только от одной (поперечной) координаты [35,36]:…”

Section: постановка задачи и методы решенияunclassified

An Exact Solution to the Description of a Unidirectional Marangoni Flow of a Viscous Incompressible Fluid With the Navier Boundary Condition. Velocity Field Investigation

Burmasheva¹,

Prosviryakov²

2019

DREAM

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Section: постановка задачи и методы решенияunclassified

An Exact Solution to the Description of a Unidirectional Marangoni Flow of a Viscous Incompressible Fluid With the Navier Boundary Condition. Velocity Field Investigation

Burmasheva¹,

Prosviryakov²

2019

DREAM

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“…This solution was later published again in [43,44]. The Ostroumov -Birikh family, which describes one-directional fluid flows, turned out to be very useful in solving the problem of convective hydrodynamical stability [45][46][47]. In the scientific works [27,28,[45][46][47][48][49][50][51][52], various modifications and generalizations of the class of exact Ostroumov -Birikh solutions are presented.…”

Section: Introductionmentioning

confidence: 99%

An Inhomogeneous Steady-State Convection of a Vertical Vortex Fluid

Berestova¹,

Prosviryakov²

2023

Nelin. Dinam.

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An exact solution of the Oberbeck – Boussinesq equations for the description of the steady-state Bénard – Rayleigh convection in an infinitely extensive horizontal layer is presented. This exact solution describes the large-scale motion of a vertical vortex flow outside the field of the Coriolis force. The large-scale fluid flow is considered in the approximation of a thin layer with nondeformable (flat) boundaries. This assumption allows us to describe the large-scale fluid motion as shear motion. Two velocity vector components, called horizontal components, are taken into account. Consequently, the third component of the velocity vector (the vertical velocity) is zero. The shear flow of the vertical vortex flow is described by linear forms from the horizontal coordinates for velocity, temperature and pressure fields. The topology of the steady flow of a viscous incompressible fluid is defined by coefficients of linear forms which have a dependence on the vertical (transverse) coordinate. The functions unknown in advance are exactly defined from the system of ordinary differential equations of order fifteen. The coefficients of the forms are polynomials. The spectral properties of the polynomials in the domain of definition of the solution are investigated. The analysis of distribution of the zeroes of hydrodynamical fields has allowed a definition of the stratification of the physical fields. The paper presents a detailed study of the existence of steady reverse flows in the convective fluid flow of Bénard – Rayleigh – Couette type.

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“…The combination ''no-slip condition ? Marangoni condition'' was studied, for example, in the articles [25][26][27][28][29][30][31][32][33][34][35][36]. However, the authors are not aware of a single study in which a comprehensive investigation of all three variants of the Navier condition in combination with the thermocapillary effect is carried out.…”

Section: Introductionmentioning

confidence: 99%

Layered Marangoni convection with the Navier slip condition

2021

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A new exact solution to the problem of Marangoni layered convection is obtained. This solution describes a layered steady-state flow of a viscous incompressible fluid at varying gradients of temperature and pressure. The velocity components depend only on the transverse coordinate; the temperature and pressure fields are three-dimensional. The Marangoni effect is observed on the upper free surface of the fluid layer. On the lower solid surface of the fluid layer, three different cases of defining boundary conditions are considered: the no-slip condition, the perfect slip condition and the Navier slip condition. The obtained exact solution is determined by the interaction of three flows: a flow caused by pressure drop (the Poiseuille flow), a flow caused by heating/cooling and the effect of the gravity force (the thermogravitational flow), and a flow caused by heating/cooling and the fluid surface tension effect (the thermocapillary flow). The obtained exact solutions in the case of each of the three types of boundary conditions specified on the lower surface are analyzed in detail. It has been proved that, when certain ratios of the boundary value problem parameters are fulfilled, the velocity components may acquire stagnation points, this being indicative of the presence of counterflow areas in the fluid layer under consideration. In particular, the presence of up to two stagnation points in each of the two longitudinal velocity components may cause a stratification of the velocity field in more than two regions. The obtained exact solution of the Marangoni layered convection problem can describe flows in thin films through the variation of the geometric anisotropy factor.

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A study of behavior and stability of an advective thermocapillary flow in a weakly rotating liquid layer under microgravity

Cited by 11 publications

References 8 publications

An Exact Solution to the Description of a Unidirectional Marangoni Flow of a Viscous Incompressible Fluid With the Navier Boundary Condition. Velocity Field Investigation

An Exact Solution to the Description of a Unidirectional Marangoni Flow of a Viscous Incompressible Fluid With the Navier Boundary Condition. Velocity Field Investigation

An Inhomogeneous Steady-State Convection of a Vertical Vortex Fluid

Layered Marangoni convection with the Navier slip condition

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