Abstract:
We consider the free-surface flow of liquid of finite depth over a bubble trapped on a plane wall. The flow is assumed to be inviscid and irrotational. The problem is for...Show MoreMetadata
Abstract:
We consider the free-surface flow of liquid of finite depth over a bubble trapped on a plane wall. The flow is assumed to be inviscid and irrotational. The problem is formulated using an integral equation and the solution is obtained numerically using a collocation method. The choices for the two contact angles where the bubble is attached to the wall are shown to depend crucially on the bubble drag. For supercritical flow, the bubble drag is zero and the contact angles are required to be equal. For either subcritical or critical flow, the bubble drag is non-zero. In either case, only one of the contact angles may be chosen freely and the second emerges as part of the solution. The effect of the free surface on the shape of the bubble is demonstrated under a variety of flow conditions.
Published in: IMA Journal of Applied Mathematics ( Volume: 73, Issue: 5, October 2008)
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- Index Terms
- Free Surface ,
- Free Surface Flow ,
- Fluid Flow ,
- Contact Angle ,
- Integral Equation ,
- Part Of The Solution ,
- Collocation Method ,
- Irrotational ,
- Critical Flow ,
- Plane Wall ,
- Bubble Shape ,
- Supercritical Flow ,
- Numerical Methods ,
- Dynamic Conditions ,
- Rigid Body ,
- Drag Force ,
- Newton Method ,
- Trapezoidal Rule ,
- Arc Length ,
- Wave Energy ,
- Wave Train ,
- Bubble Surface ,
- Froude Number ,
- Mesh Points ,
- Wave Period ,
- Nonlinear Algebraic Equations ,
- Solution Branches ,
- Velocity Potential ,
- Circular Arc ,
- Solution Flow
- Author Keywords
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- Index Terms
- Free Surface ,
- Free Surface Flow ,
- Fluid Flow ,
- Contact Angle ,
- Integral Equation ,
- Part Of The Solution ,
- Collocation Method ,
- Irrotational ,
- Critical Flow ,
- Plane Wall ,
- Bubble Shape ,
- Supercritical Flow ,
- Numerical Methods ,
- Dynamic Conditions ,
- Rigid Body ,
- Drag Force ,
- Newton Method ,
- Trapezoidal Rule ,
- Arc Length ,
- Wave Energy ,
- Wave Train ,
- Bubble Surface ,
- Froude Number ,
- Mesh Points ,
- Wave Period ,
- Nonlinear Algebraic Equations ,
- Solution Branches ,
- Velocity Potential ,
- Circular Arc ,
- Solution Flow
- Author Keywords