Analyticity of a free boundary in plane quasi-steady flow of a liquid form subject to variable surface tension

1992 ◽  
pp. 1-16
Author(s):  
Lenoid K. Antanovskii
Keyword(s):  
Surface Tension ◽  
Free Boundary ◽  
Steady Flow ◽  
Liquid Form ◽  
Variable Surface

Shallow three-dimensional flows with variable surface tension

1970 ◽  
Vol 42 (3) ◽  
pp. 549-559 ◽  
Author(s):  
J. Adler ◽  
L. Sowerby
Keyword(s):  
Surface Tension ◽  
Steady Flow ◽  
Viscous Liquid ◽  
Three Dimensional ◽  
Surface Concentration ◽  
Variable Surface ◽  
Chemical Contaminant

The three-dimensional steady flow of a shallow viscous liquid with non-uniform surface tension has been considered when the variation in surface tension results from the presence of an insoluble chemical contaminant on the surface. Similarly solutions for the particular problem of a channel flowing into a semi-infinite lake have been obtained, the depth and surface concentration at infinity being specified.

scholarly journals Marangoni Convection of Dust Particles in the Boundary Layer of Maxwell Nanofluids with Varying Surface Tension and Viscosity

Coatings ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 1072
Author(s):  
Khaled S. AlQdah ◽  
Naseer M. Khan ◽  
Habib Ben Bacha ◽  
Jae-Dong Chung ◽  
Nehad Ali Shah
Keyword(s):  
Surface Tension ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Dust Particles ◽  
Physical Parameters ◽  
Temperature Dependent Viscosity ◽  
Liquid Phases ◽  
Variable Surface ◽  
Basic Equations ◽  
Dependent Viscosity

The flow of nanofluids is very important in industrial refrigeration systems. The operation of nuclear reactors and the cooling of the entire installation to improve safety and economics are entirely dependent on the application of nanofluids in water. Therefore, a model of Maxwell’s dusty nanofluid with temperature-dependent viscosity, surface suction and variable surface tension under the action of solar radiation is established. The basic equations of momentum and temperature of the dust and liquid phases are solved numerically using the MATLAB bvp4c scheme. In the current evaluation, taking into account variable surface tension and varying viscosity, the effect of dust particles is studied by immersing dust particles in a nanofluid. Qualitative and quantitative discussions are provided to focus on the effect of physical parameters on mass and heat transfer. The propagation results show that this mixing effect can significantly increase the thermal conductivity of nanofluids. With small changes in the surface tension parameters, a stronger drop in the temperature distribution is observed. The suction can significantly reduce the temperature distribution of the liquid and dust phases. The stretchability of the sheet is more conducive to temperature rise. The tables are used to explain how physical parameters affect the Nusselt number and mass transfer. The increased interaction of the liquid with nanoparticles or dust particles is intended to improve the Nusselt number. This model contains features that have not been previously studied, which stimulates demand for this model among all walks of life now and in the future.

Stability and bifurcation analysis of a free boundary problem modelling multi-layer tumours with Gibbs–Thomson relation

2015 ◽  
Vol 26 (4) ◽  
pp. 401-425 ◽  
Author(s):  
FUJUN ZHOU ◽  
JUNDE WU
Keyword(s):  
Surface Tension ◽  
Free Boundary ◽  
Boundary Problem ◽  
Stationary Solution ◽  
Free Boundary Problem ◽  
Bifurcation Analysis ◽  
Surface Tension Coefficient ◽  
Stability And Bifurcation ◽  
Stability And Bifurcation Analysis ◽  
A Free Boundary Problem

Of concern is the stability and bifurcation analysis of a free boundary problem modelling the growth of multi-layer tumours. A remarkable feature of this problem lies in that the free boundary is imposed with nonlinear boundary conditions, where a Gibbs–Thomson relation is taken into account. By employing a functional approach, analytic semigroup theory and bifurcation theory, we prove that there exists a positive threshold value γ* of surface tension coefficient γ such that if γ > γ* then the unique flat stationary solution is asymptotically stable under non-flat perturbations, while for γ < γ* this unique flat stationary solution is unstable and there exists a series of non-flat stationary solutions bifurcating from it. The result indicates a significant phenomenon that a smaller value of surface tension coefficient γ may make tumours more aggressive.

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