Define the word surface.
A boundary that separates two domains or one domain from its surroundings.
Denoted by Γ\GammaΓ, with normal vector nnn.
Can state variables be discontinuous at a surface? What would be an example?
es, state variables can be discontinuous at a surface. Example:
Density at a Vapor-Liquid Interface:
Discontinuity occurs because a point is either in vapor, liquid, or at the surface.
No gradual transition; sharp change between phases.
What would be an example where the source term in the boundary ΣΓ is non-zero?
Heterogeneous Catalysis:
Reaction occurring on the surface of a solid catalyst.
Production or consumption of species at the interface.
What is the general differential surface balance? How can it be simplified?
Can you think of an example where the surface velocity uΓ is non-zero?
Moving Membrane in Filtration:
Membrane itself moves, causing a non-zero surface velocity.
Rotating Disk in Liquid:
Disk rotation affects adjacent fluid layers.
In which cases are the velocities at the surface v+ and v− not equal?
Phase Change (e.g., Evaporation):
Different velocities in gas (v+)nd liquid (v−) phases.
Heat Exchange:
Fluid velocities differ on either side of a heat-exchanging surface.
Density Difference:
Different densities lead to varying velocities across the interface.
Last changed4 months ago
