ON THE COOLING OF A FREE THIN FILM AT THE PRESENCE OF THE VAN DER WAALS FORCES

2004 ◽  
Vol 9 (4) ◽  
pp. 299-312
Author(s):  
G. Gromyko ◽  
S. Tabakova ◽  
L. Popova
Keyword(s):  
Thin Film ◽  
Finite Difference ◽  
Longitudinal Velocity ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
Reynolds Numbers ◽  
Middle Plane ◽  
One Dimensional ◽  
The One ◽  
Hamaker Constants

The cooling of a hot free thin viscous film attached to a rectangular colder frame is considered. The film is under the action of capillary and van der Waals forces and is symmetric with respect to a middle plane. The one@dimensional case of the corresponding non‐stationary nonlinear thermo‐dynamic problem is solved numerically by a finite difference scheme. The numerical results for the film shape, longitudinal velocity and temperature are obtained for different Reynolds numbers, dimensionless Hamaker constants and radiation numbers.

Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

1983 ◽  
Vol 4 ◽  
pp. 297-297
Author(s):  
G. Brugnot
Keyword(s):  
Finite Difference Method ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Momentum Conservation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Modelling Techniques ◽  
Reference Grid ◽  
The One ◽  
Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

scholarly journals One-Dimensional Vacuum Steady Seepage Model of Unsaturated Soil and Finite Difference Solution

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Feng Huang ◽  
Jianguo Lyu ◽  
Guihe Wang ◽  
Hongyan Liu
Keyword(s):  
Finite Difference ◽  
Unsaturated Soil ◽  
Vacuum Pressure ◽  
Vacuum Field ◽  
One Dimensional ◽  
Steady Seepage ◽  
Basic Equations ◽  
The One ◽  
Seepage Law ◽  
Relationship Of

Vacuum tube dewatering method and light well point method have been widely used in engineering dewatering and foundation treatment. However, there is little research on the calculation method of unsaturated seepage under the effect of vacuum pressure which is generated by the vacuum well. In view of this, the one-dimensional (1D) steady seepage law of unsaturated soil in vacuum field has been analyzed based on Darcy’s law, basic equations, and finite difference method. First, the gravity drainage ability is analyzed. The analysis presents that much unsaturated water can not be drained off only by gravity effect because of surface tension. Second, the unsaturated vacuum seepage equations are built up in conditions of flux boundary and waterhead boundary. Finally, two examples are analyzed based on the relationship of matric suction and permeability coefficient after boundary conditions are determined. The results show that vacuum pressure will significantly enhance the drainage ability of unsaturated water by improving the hydraulic gradient of unsaturated water.

The influence of van der waals forces on Tc in thin film of He3

1990 ◽  
Vol 165-166 ◽  
pp. 679-680 ◽  
Author(s):  
G. Haran ◽  
L. Borkowski ◽  
L. Jacak
Keyword(s):  
Thin Film ◽  
Van Der Waals ◽  
Van Der Waals Forces
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