Three-dimensional oscillatory long-wave Marangoni convection in a binary liquid layer with the Soret effect: Bifurcation analysis

In the present study, the onset of thermal convection in a liquid layer overlying a porous layer where the whole system is being laterally heated is investigated. The non-linear two-dimensional Navier Stokes equations, the energy equation, the mass balance equation and the continuity equation are solved for the liquid layer. Instead of the Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. A two-dimensional geometrical model with lateral heating is considered. Two different cases are analyzed in this thesis. In the first case, the gravity driven buoyancy convection and the Marangoni convection are studied. For the Marangoni convection, the microgravity condition is considered and the surface tension is assumed to vary linearly with temperature. Different aspect ratios, as well as thickness ratios, are studies in detail for both the buoyancy and the Marangoni convection. Results revealed that for both the buoyancy and the Marangoni cases, flow penetrates into the porous layer, only when the thickness ratio is more than 0.90. In the case of thermo-solutal convection in the presence of Soret effect, it has been found that the isopropanol component goes either towards the hot or the cold walls depending on the fluid mixtures which has been used in the system.

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Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate

Journal of Fluid Mechanics ◽

10.1017/s0022112007000110 ◽

2008 ◽

Vol 599 ◽

pp. 269-298 ◽

Cited By ~ 10

Author(s):

JUN HU ◽

HAMDA BEN HADID ◽

DANIEL HENRY ◽

ABDELKADER MOJTABI

Keyword(s):

Soret Effect ◽

Short Wave ◽

Heated Plate ◽

Surface Mode ◽

Wave Instability ◽

Binary Liquid ◽

Long Wave ◽

Neutral Curves ◽

Spatio Temporal ◽

Boundary Curves

Temporal and spatio-temporal instabilities of binary liquid films flowing down an inclined uniformly heated plate with Soret effect are investigated by using the Chebyshev collocation method to solve the full system of linear stability equations. Seven dimensionless parameters, i.e. the Kapitza, Galileo, Prandtl, Lewis, Soret, Marangoni, and Biot numbers (Ka,G,Pr,L, χ,M,B), as well as the inclination angle (β) are used to control the flow system. In the case of pure spanwise perturbations, thermocapillary S- and P-modes are obtained. It is found that the most dangerous modes are stationary for positive Soret numbers (χ≥0), and oscillatory for χ<0. Moreover, the P-mode which is short-wave unstable for χ=0 remains so for χ<0, but becomes long-wave unstable for χ>0 and even merges with the long-wave S-mode. In the case of streamwise perturbations, a long-wave surface mode (H-mode) is also obtained. From the neutral curves, it is found that larger Soret numbers make the film flow more unstable as do larger Marangoni numbers. The increase of these parameters leads to the merging of the long-wave H- and S-modes, making the situation long-wave unstable for any Galileo number. It also strongly influences the short-wave P-mode which becomes the most critical for large enough Galileo numbers. Furthermore, from the boundary curves between absolute and convective instabilities (AI/CI) calculated for both the long-wave instability (S- and H-modes) and the short-wave instability (P-mode), it is shown that for small Galileo numbers the AI/CI boundary curves are determined by the long-wave instability, while for large Galileo numbers they are determined by the short-wave instability.

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Thermo-solutal convection with Soret effect

10.32920/ryerson.14664960.v1 ◽

2021 ◽

Author(s):

Md. Abdur Rahman

Keyword(s):

Porous Layer ◽

Liquid Layer ◽

Marangoni Convection ◽

Stokes Equations ◽

Soret Effect ◽

Navier Stokes ◽

Two Dimensional ◽

Navier Stokes Equations ◽

Solutal Convection ◽

Buoyancy Convection

In the present study, the onset of thermal convection in a liquid layer overlying a porous layer where the whole system is being laterally heated is investigated. The non-linear two-dimensional Navier Stokes equations, the energy equation, the mass balance equation and the continuity equation are solved for the liquid layer. Instead of the Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. A two-dimensional geometrical model with lateral heating is considered. Two different cases are analyzed in this thesis. In the first case, the gravity driven buoyancy convection and the Marangoni convection are studied. For the Marangoni convection, the microgravity condition is considered and the surface tension is assumed to vary linearly with temperature. Different aspect ratios, as well as thickness ratios, are studies in detail for both the buoyancy and the Marangoni convection. Results revealed that for both the buoyancy and the Marangoni cases, flow penetrates into the porous layer, only when the thickness ratio is more than 0.90. In the case of thermo-solutal convection in the presence of Soret effect, it has been found that the isopropanol component goes either towards the hot or the cold walls depending on the fluid mixtures which has been used in the system.

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