Alexander Mikishev | Sam Houston State University (original) (raw)

Papers by Alexander Mikishev

Bulletin of the American Physical Society, Nov 22, 2021

Fluids, Aug 13, 2021

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Physical Review Fluids, 2021

Three-dimensional (3D) longwave oscillatory Marangoni convection in a heated thin layer with weak... more Three-dimensional (3D) longwave oscillatory Marangoni convection in a heated thin layer with weak heat flux from the free surface is considered. Numerous experiments show that the surface tension is a nonlinear function of temperature. Here we modify the system of nonlinear longwave evolution equations expanding the temperature coefficient of the surface tension into the Taylor series about the surface temperature. Using the weakly nonlinear analysis we explore the patterns formed near the critical value of Marangoni number. Stability of the 3D patterns on square, rhombic, and hexagonal lattices are considered. The nonlinearity of the surface tension's temperature dependence can be a stabilizing factor as well as destabilizing one.

Bulletin of the American Physical Society, 2014

Submitted for the DFD14 Meeting of The American Physical Society Instabilities of evaporating non... more Submitted for the DFD14 Meeting of The American Physical Society Instabilities of evaporating non-isothermal ultra-thin film with insoluble surfactant ALEXANDER MIKISHEV, Sam Houston State Univ, ALEXANDER NEPOMNYASHCHY, Technion-IIT-The stability of an evaporating ultra-thin liquid layer with insoluble surfactant spreading over a free deformable interface is investigated within lubrication theory. The evaporation process is described by 2D one-sided model based on the assumptions of density, viscosity and thermal conductivity of the gaseous phase being small compared to the same properties of the liquid phase. It is assumed that the thermal resistance to the evaporation at the interface is an increasing linear function of surfactant concentration. The evaporation mass flux depends on the interface temperature and vapor pressure. Using the long-wave approach and assumption of slow time evolution, a system of nonlinear equations governing the nonequilibrium evaporation is obtained. The system retains main physical effects which take place in the system. A linear stability analysis is also carried out. Both monotonic instability mode and oscillatory one are found and analyzed. The analysis does not include the Born repulsion force in intermolecular interactions.

Colloids and Interfaces

Marangoni patterns are created by instabilities caused by thermocapillary and solutocapillary str... more Marangoni patterns are created by instabilities caused by thermocapillary and solutocapillary stresses on the deformable free surface of a thin liquid layer. In the present paper, we consider the influence of the insoluble surfactant on the selection and modulational instability of stationary Marangoni patterns near their onset threshold. The basic governing parameters of the problem are the Biot number characterizing the heat-transfer resistances of and at the surface, the Galileo number indicating the role of gravity via viscous forces, and the elasticity number specifying the influence of insoluble surfactant on the interfacial dynamics of the liquid. The paper includes a review of the previous results obtained in that problem as well as new ones.

Bulletin of the American Physical Society, 2017

The large-scale Marangoni convection in a liquid layer heated from below in the presence of an in... more The large-scale Marangoni convection in a liquid layer heated from below in the presence of an insoluble surfactant on its deformable free surface is considered. The layer is subject to vertical vibrations with the frequency 2. Nonlinear amplitude equations governing the evolution of large-scale disturbances of temperature, surfactant concentration and surface deformation are derived in the limit of small Biot number and large capillary number. The system of linearized equations is investigated by means of the Floquet approach. The thresholds of subharmonic, harmonic and quasi-periodic types of instabilities are determined.

Bulletin of the American Physical Society, 2019

Submitted for the DFD19 Meeting of The American Physical Society Influence of nonlinear temperatu... more Submitted for the DFD19 Meeting of The American Physical Society Influence of nonlinear temperature dependence of surface tension on longwave oscillatory Marangoni patterns ALEXANDER MIKISHEV, Sam Houston State University, ALEXANDER NEPOMNYASHCHY, Technion-In most theoretical papers on Marangoni convection the authors assume the linear dependence of the surface tension on temperature. However, according to experiments, that dependence is more complex. In the present work, we consider the influence of nonlinear temperature dependence of surface tension on the nonlinear dynamics of waves created by an oscillatory instability recently discovered in [1] in the limit of small Biot number Bi and wavenumber k, k˜Bi 1/2. Near the critical Marangoni number, that dependence is described by a Taylor series around the reference temperature value. The set of amplitude equations governing the nonlinear interaction of waves has been derived. The stability of different wave patterns and wave pattern selection are investigated. REFERENCE. [1] S. Shklyaev, A. Alabuzhev, and M. Khenner, Phys. Rev. E, 85, 016328 (2012).

Bulletin of the American Physical Society, 2012

Submitted for the TSS12 Meeting of The American Physical Society Onset of Marangoni convection of... more Submitted for the TSS12 Meeting of The American Physical Society Onset of Marangoni convection of a liquid layer with insoluble surfactant in modulated thermal field ALEXANDER MIKISHEV, Strayer University-Katy Campus, Houston, TX-A horizontal layer of an incompressible liquid layer bounded by rigid lower plane and free non-deformable flat upper surface is considered. The layer is heated from below and the heat flux is varying with time around fixed mean value. On the free surface the liquid adsorbs an insoluble surfactant, whose local concentration changes with time due to the advection and diffusion. The linear stability analysis with respect to disturbances of arbitrary finite wave-numbers is performed. Two response modes of the convective system to an external periodic stimulation have been found, the first one with a period of oscillation twice as the period of heat flux modulation (subharmonic mode) and the second one with the same period (synchronous mode). The neutral stability curves are presented for a variety of external conditions. The cellular and long-wave instability thresholds are compared.

Bulletin of the American Physical Society, 2012

A horizontally infinite layer of incompressible Newtonian liquid with insoluble surfactant on the... more A horizontally infinite layer of incompressible Newtonian liquid with insoluble surfactant on the deformable surface is considered. The evaporation process is described by 2D one-side model. Therefore, the assumptions of small density, small viscosity and small thermal conductivity of the gaseous phase compared to the same properties of the liquid phase are accepted. Surface tension of the liquid-vapor surface linearly depends on temperature and concentration of surfactant. Using the long-wave approximation and assumption of slow time evolution the system of nonlinear equations is obtained. That system describes the spatiotemporal behavior of the layer interface and the field of the surfactant concentration. The equations retain all relevant physical effects which take place in the system. Linear stability analysis of the base state in the case of quasi-equilibrium evaporation, when the interfacial temperature equals the saturation one, is performed.

Bulletin of the American Physical Society, 2015

Submitted for the DFD15 Meeting of The American Physical Society Vibrational instabilities of a n... more Submitted for the DFD15 Meeting of The American Physical Society Vibrational instabilities of a nonisothermal liquid layer with insoluble surfactant ALEXANDER MIKISHEV, Sam Houston State Univ, ALEXAN-DER NEPOMNYASHCHY, Technion-We consider an infinite horizontal layer of an incompressible liquid, the deformable upper free surface is covered by insoluble surfactant. The layer is subjected to vertical harmonic oscillations with fixed amplitude and frequency, as well as to a transverse gradient of temperature. We suppose that the surface tension of upper boundary linearly depends on temperature and surfactant concentration. Two types of waves on the surface are possible. The first one is capillary-gravity waves (transverse waves) excited by the usual Faraday instability mechanism, under the influence of the surfactant elasticity. The second type of waves is Marangoni waves (longitudinal waves) related to compressions dilations of the surface. In this work we study the excitation of Marangoni waves by vibration and determine the existence conditions for each type of waves. The results are connected with our previous research on parametric excitation of Marangoni instability when the gradient of temperature is harmonically changed. The instability thresholds are calculated numerically using the Floquet method for disturbances with arbitrary wave numbers.

Bulletin of the American Physical Society, 2016

Submitted for the DFD16 Meeting of The American Physical Society High-frequency vibration of heat... more Submitted for the DFD16 Meeting of The American Physical Society High-frequency vibration of heated liquid layer covered by insoluble surfactant 1 ALEXANDER MIKISHEV, Sam Houston State University, ALEXANDER NEPOMNYASHCHY, Technion-We study the influence of highfrequency vertical vibration on thin liquid layer with insoluble surfactant adsorbed on the free surface. The layer is subjected to a vertical temperature gradient (the layer is heated either from below or from above). We perform the linear analysis of Marangoni instability. The system is characterized by monotonic and oscillatory modes. The characteristic frequency of long surfactant-induced Marangoni waves is O(ε 2), where ε is the scale of wavenumber, hence the frequency of external vibrations of order one can be considered as a high frequency. The threshold of the onset of Marangoni convection is shifted by the vibration. Applying a long-wave approach we obtain a system of weakly nonlinear equations describing dynamics near the threshold. The standard Floquet method helps to investigate the excitation of short scale Marangoni waves.

Microgravity Science and Technology, 2017

The paper presents the analysis of the impact of vertical periodic vibrations on the long-wavelen... more The paper presents the analysis of the impact of vertical periodic vibrations on the long-wavelength Marangoni instability in a liquid layer with poorly conducting boundaries in the presence of insoluble surfactant on the deformable gas-liquid interface. The layer is subject to a uniform transverse temperature gradient. Linear stability analysis is performed in order to find critical values of Marangoni numbers for both monotonic and oscillatory instability modes. Longwave asymptotic expansions are used. At the leading order, the critical values are independent on vibration parameters; at the next order of approximation we obtained the rise of stability thresholds due to vibration.

Physical Review Fluids, 2020

We consider the long-wave Marangoni convection in a horizontally oriented heated thin liquid laye... more We consider the long-wave Marangoni convection in a horizontally oriented heated thin liquid layer with weak heat flux from the free surface. Two modes of instability are possible in this problem: monotonic and oscillatory. The system of nonlinear evolution equations is modified for the case when the surface tension is a nonlinear function of temperature determined by a set of coefficients in the Taylor series expansion about the surface temperature. The coefficients which are used are taken mainly from experimental data. In the case of monotonic instability, we investigate the influence of nonlinear temperature dependence of the surface tension on the stability of roll, square, and hexagonal patterns. In the case of oscillatory instability, we consider the stability of single traveling waves and traveling rectangles.

Fluid Dynamics Research, 2018

View the article online for updates and enhancements. You may also like Stability of a pair of pl... more View the article online for updates and enhancements. You may also like Stability of a pair of planar counter-rotating vortices in a rectangular box Youichi Murakami and Hiroaki Fukuta-Fifth International Symposium on Bifurcations and Instabilities in Fluid Dynamics (BIFD2013) P Z Bar-Yoseph, M Brøns, A Gelfgat et al.-Bifurcations and chaos in a circular Couette system

Fluid Dynamics Research, 2018

Physical Review Fluids, 2019

We consider the long-wave Marangoni instability in a heated liquid layer covered by insoluble sur... more We consider the long-wave Marangoni instability in a heated liquid layer covered by insoluble surfactant. The system of nonlinear equations derived in our previous work is regularized in the limit of strong surface tension. Recent research shows that, without the surfactant, a large-scale oscillatory instability mode exists in the interval of wave numbers k = O(Bi 1/2) (the Biot number Bi 1). Here we study the influence of the surfactant on the Marangoni oscillations. The bifurcation analysis for traveling waves and counterpropagating waves is performed. The types of bifurcation and selected pattern depend on the elasticity number and on the Biot number. Specifically, at small elasticity number, both types of waves are supercritical.

The European physical journal. E, Soft matter, Jan 18, 2017

It is known that the addition of an insoluble surfactant to a Bénard-Marangoni (BM) layer heated ... more It is known that the addition of an insoluble surfactant to a Bénard-Marangoni (BM) layer heated from below or cooled from above can give rise to a supplementary, oscillatory mode of instability. Here the objective is to see how exactly this plays out in the framework of a recently studied and experimentally tested case of a non-long-wavelength BM instability driven by diffusion-limited evaporation into air in isothermal surroundings. Linear stability analysis is accomplished within a now standard reduction to a one-sided model. In the absence of surfactant, we just recover the classical Pearson problem, albeit with an evaporation-specific wavenumber-dependent Biot number potentially attaining large values for strongly volatile liquids. Adding a surfactant not only sharply stabilizes the monotonic Pearson-like mode, but also leads to a more dangerous oscillatory mode, a parametric study of which is here undertaken. Although slanted towards the evaporative case, the present study is ...

Bulletin of the American Physical Society, Nov 22, 2021

Fluids, Aug 13, 2021

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Physical Review Fluids, 2021

Three-dimensional (3D) longwave oscillatory Marangoni convection in a heated thin layer with weak... more Three-dimensional (3D) longwave oscillatory Marangoni convection in a heated thin layer with weak heat flux from the free surface is considered. Numerous experiments show that the surface tension is a nonlinear function of temperature. Here we modify the system of nonlinear longwave evolution equations expanding the temperature coefficient of the surface tension into the Taylor series about the surface temperature. Using the weakly nonlinear analysis we explore the patterns formed near the critical value of Marangoni number. Stability of the 3D patterns on square, rhombic, and hexagonal lattices are considered. The nonlinearity of the surface tension's temperature dependence can be a stabilizing factor as well as destabilizing one.

Bulletin of the American Physical Society, 2014

Submitted for the DFD14 Meeting of The American Physical Society Instabilities of evaporating non... more Submitted for the DFD14 Meeting of The American Physical Society Instabilities of evaporating non-isothermal ultra-thin film with insoluble surfactant ALEXANDER MIKISHEV, Sam Houston State Univ, ALEXANDER NEPOMNYASHCHY, Technion-IIT-The stability of an evaporating ultra-thin liquid layer with insoluble surfactant spreading over a free deformable interface is investigated within lubrication theory. The evaporation process is described by 2D one-sided model based on the assumptions of density, viscosity and thermal conductivity of the gaseous phase being small compared to the same properties of the liquid phase. It is assumed that the thermal resistance to the evaporation at the interface is an increasing linear function of surfactant concentration. The evaporation mass flux depends on the interface temperature and vapor pressure. Using the long-wave approach and assumption of slow time evolution, a system of nonlinear equations governing the nonequilibrium evaporation is obtained. The system retains main physical effects which take place in the system. A linear stability analysis is also carried out. Both monotonic instability mode and oscillatory one are found and analyzed. The analysis does not include the Born repulsion force in intermolecular interactions.

Colloids and Interfaces

Marangoni patterns are created by instabilities caused by thermocapillary and solutocapillary str... more Marangoni patterns are created by instabilities caused by thermocapillary and solutocapillary stresses on the deformable free surface of a thin liquid layer. In the present paper, we consider the influence of the insoluble surfactant on the selection and modulational instability of stationary Marangoni patterns near their onset threshold. The basic governing parameters of the problem are the Biot number characterizing the heat-transfer resistances of and at the surface, the Galileo number indicating the role of gravity via viscous forces, and the elasticity number specifying the influence of insoluble surfactant on the interfacial dynamics of the liquid. The paper includes a review of the previous results obtained in that problem as well as new ones.

Bulletin of the American Physical Society, 2017

The large-scale Marangoni convection in a liquid layer heated from below in the presence of an in... more The large-scale Marangoni convection in a liquid layer heated from below in the presence of an insoluble surfactant on its deformable free surface is considered. The layer is subject to vertical vibrations with the frequency 2. Nonlinear amplitude equations governing the evolution of large-scale disturbances of temperature, surfactant concentration and surface deformation are derived in the limit of small Biot number and large capillary number. The system of linearized equations is investigated by means of the Floquet approach. The thresholds of subharmonic, harmonic and quasi-periodic types of instabilities are determined.

Bulletin of the American Physical Society, 2019

Submitted for the DFD19 Meeting of The American Physical Society Influence of nonlinear temperatu... more Submitted for the DFD19 Meeting of The American Physical Society Influence of nonlinear temperature dependence of surface tension on longwave oscillatory Marangoni patterns ALEXANDER MIKISHEV, Sam Houston State University, ALEXANDER NEPOMNYASHCHY, Technion-In most theoretical papers on Marangoni convection the authors assume the linear dependence of the surface tension on temperature. However, according to experiments, that dependence is more complex. In the present work, we consider the influence of nonlinear temperature dependence of surface tension on the nonlinear dynamics of waves created by an oscillatory instability recently discovered in [1] in the limit of small Biot number Bi and wavenumber k, k˜Bi 1/2. Near the critical Marangoni number, that dependence is described by a Taylor series around the reference temperature value. The set of amplitude equations governing the nonlinear interaction of waves has been derived. The stability of different wave patterns and wave pattern selection are investigated. REFERENCE. [1] S. Shklyaev, A. Alabuzhev, and M. Khenner, Phys. Rev. E, 85, 016328 (2012).

Bulletin of the American Physical Society, 2012

Submitted for the TSS12 Meeting of The American Physical Society Onset of Marangoni convection of... more Submitted for the TSS12 Meeting of The American Physical Society Onset of Marangoni convection of a liquid layer with insoluble surfactant in modulated thermal field ALEXANDER MIKISHEV, Strayer University-Katy Campus, Houston, TX-A horizontal layer of an incompressible liquid layer bounded by rigid lower plane and free non-deformable flat upper surface is considered. The layer is heated from below and the heat flux is varying with time around fixed mean value. On the free surface the liquid adsorbs an insoluble surfactant, whose local concentration changes with time due to the advection and diffusion. The linear stability analysis with respect to disturbances of arbitrary finite wave-numbers is performed. Two response modes of the convective system to an external periodic stimulation have been found, the first one with a period of oscillation twice as the period of heat flux modulation (subharmonic mode) and the second one with the same period (synchronous mode). The neutral stability curves are presented for a variety of external conditions. The cellular and long-wave instability thresholds are compared.

Bulletin of the American Physical Society, 2012

A horizontally infinite layer of incompressible Newtonian liquid with insoluble surfactant on the... more A horizontally infinite layer of incompressible Newtonian liquid with insoluble surfactant on the deformable surface is considered. The evaporation process is described by 2D one-side model. Therefore, the assumptions of small density, small viscosity and small thermal conductivity of the gaseous phase compared to the same properties of the liquid phase are accepted. Surface tension of the liquid-vapor surface linearly depends on temperature and concentration of surfactant. Using the long-wave approximation and assumption of slow time evolution the system of nonlinear equations is obtained. That system describes the spatiotemporal behavior of the layer interface and the field of the surfactant concentration. The equations retain all relevant physical effects which take place in the system. Linear stability analysis of the base state in the case of quasi-equilibrium evaporation, when the interfacial temperature equals the saturation one, is performed.

Bulletin of the American Physical Society, 2015

Submitted for the DFD15 Meeting of The American Physical Society Vibrational instabilities of a n... more Submitted for the DFD15 Meeting of The American Physical Society Vibrational instabilities of a nonisothermal liquid layer with insoluble surfactant ALEXANDER MIKISHEV, Sam Houston State Univ, ALEXAN-DER NEPOMNYASHCHY, Technion-We consider an infinite horizontal layer of an incompressible liquid, the deformable upper free surface is covered by insoluble surfactant. The layer is subjected to vertical harmonic oscillations with fixed amplitude and frequency, as well as to a transverse gradient of temperature. We suppose that the surface tension of upper boundary linearly depends on temperature and surfactant concentration. Two types of waves on the surface are possible. The first one is capillary-gravity waves (transverse waves) excited by the usual Faraday instability mechanism, under the influence of the surfactant elasticity. The second type of waves is Marangoni waves (longitudinal waves) related to compressions dilations of the surface. In this work we study the excitation of Marangoni waves by vibration and determine the existence conditions for each type of waves. The results are connected with our previous research on parametric excitation of Marangoni instability when the gradient of temperature is harmonically changed. The instability thresholds are calculated numerically using the Floquet method for disturbances with arbitrary wave numbers.

Bulletin of the American Physical Society, 2016

Submitted for the DFD16 Meeting of The American Physical Society High-frequency vibration of heat... more Submitted for the DFD16 Meeting of The American Physical Society High-frequency vibration of heated liquid layer covered by insoluble surfactant 1 ALEXANDER MIKISHEV, Sam Houston State University, ALEXANDER NEPOMNYASHCHY, Technion-We study the influence of highfrequency vertical vibration on thin liquid layer with insoluble surfactant adsorbed on the free surface. The layer is subjected to a vertical temperature gradient (the layer is heated either from below or from above). We perform the linear analysis of Marangoni instability. The system is characterized by monotonic and oscillatory modes. The characteristic frequency of long surfactant-induced Marangoni waves is O(ε 2), where ε is the scale of wavenumber, hence the frequency of external vibrations of order one can be considered as a high frequency. The threshold of the onset of Marangoni convection is shifted by the vibration. Applying a long-wave approach we obtain a system of weakly nonlinear equations describing dynamics near the threshold. The standard Floquet method helps to investigate the excitation of short scale Marangoni waves.

Microgravity Science and Technology, 2017

The paper presents the analysis of the impact of vertical periodic vibrations on the long-wavelen... more The paper presents the analysis of the impact of vertical periodic vibrations on the long-wavelength Marangoni instability in a liquid layer with poorly conducting boundaries in the presence of insoluble surfactant on the deformable gas-liquid interface. The layer is subject to a uniform transverse temperature gradient. Linear stability analysis is performed in order to find critical values of Marangoni numbers for both monotonic and oscillatory instability modes. Longwave asymptotic expansions are used. At the leading order, the critical values are independent on vibration parameters; at the next order of approximation we obtained the rise of stability thresholds due to vibration.

Physical Review Fluids, 2020

We consider the long-wave Marangoni convection in a horizontally oriented heated thin liquid laye... more We consider the long-wave Marangoni convection in a horizontally oriented heated thin liquid layer with weak heat flux from the free surface. Two modes of instability are possible in this problem: monotonic and oscillatory. The system of nonlinear evolution equations is modified for the case when the surface tension is a nonlinear function of temperature determined by a set of coefficients in the Taylor series expansion about the surface temperature. The coefficients which are used are taken mainly from experimental data. In the case of monotonic instability, we investigate the influence of nonlinear temperature dependence of the surface tension on the stability of roll, square, and hexagonal patterns. In the case of oscillatory instability, we consider the stability of single traveling waves and traveling rectangles.

Fluid Dynamics Research, 2018

View the article online for updates and enhancements. You may also like Stability of a pair of pl... more View the article online for updates and enhancements. You may also like Stability of a pair of planar counter-rotating vortices in a rectangular box Youichi Murakami and Hiroaki Fukuta-Fifth International Symposium on Bifurcations and Instabilities in Fluid Dynamics (BIFD2013) P Z Bar-Yoseph, M Brøns, A Gelfgat et al.-Bifurcations and chaos in a circular Couette system

Fluid Dynamics Research, 2018

Physical Review Fluids, 2019

We consider the long-wave Marangoni instability in a heated liquid layer covered by insoluble sur... more We consider the long-wave Marangoni instability in a heated liquid layer covered by insoluble surfactant. The system of nonlinear equations derived in our previous work is regularized in the limit of strong surface tension. Recent research shows that, without the surfactant, a large-scale oscillatory instability mode exists in the interval of wave numbers k = O(Bi 1/2) (the Biot number Bi 1). Here we study the influence of the surfactant on the Marangoni oscillations. The bifurcation analysis for traveling waves and counterpropagating waves is performed. The types of bifurcation and selected pattern depend on the elasticity number and on the Biot number. Specifically, at small elasticity number, both types of waves are supercritical.

The European physical journal. E, Soft matter, Jan 18, 2017

It is known that the addition of an insoluble surfactant to a Bénard-Marangoni (BM) layer heated ... more It is known that the addition of an insoluble surfactant to a Bénard-Marangoni (BM) layer heated from below or cooled from above can give rise to a supplementary, oscillatory mode of instability. Here the objective is to see how exactly this plays out in the framework of a recently studied and experimentally tested case of a non-long-wavelength BM instability driven by diffusion-limited evaporation into air in isothermal surroundings. Linear stability analysis is accomplished within a now standard reduction to a one-sided model. In the absence of surfactant, we just recover the classical Pearson problem, albeit with an evaporation-specific wavenumber-dependent Biot number potentially attaining large values for strongly volatile liquids. Adding a surfactant not only sharply stabilizes the monotonic Pearson-like mode, but also leads to a more dangerous oscillatory mode, a parametric study of which is here undertaken. Although slanted towards the evaporative case, the present study is ...