Interfacial wave theory of two-dimensional dendritic growth with anisotropy of surface tension

1991 ◽  
Vol 69 (7) ◽  
pp. 789-800 ◽  
Author(s):  
Jian-Jun Xu
Keyword(s):  
Surface Tension ◽  
Dendritic Growth ◽  
Wave Theory ◽  
Two Dimensional ◽  
Interfacial Wave ◽  
Selection Condition ◽  
Tip Velocity

In this paper, we consider two-dimensional dendritic growth from pure melt with inclusion of the anisotropy of surface tension. The interfacial wave theory previously established for axisymmetric dendritic growth is extended to this case. The results show that the effect of the anisotropy of surface tension on the selection condition of the tip velocity is not significant.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

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