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Generalized Navier Boundary Condition

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Old   December 3, 2013, 00:12
Default Generalized Navier Boundary Condition
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Hello Foamers,

I am trying to implement the Generalized Navier Boundary Condition

beta*U_slip + mu*dU/dn + gamma*(cos(theta_d) - cos(theta_e))*n_a*delta

with

beta: friction coefficient
mu: viscosity
n_w: normal of the wall
gamma: surface tension
theta_d: dynamic contact angle
theta_e: equilibrium contact angle
n_a: normal of fluid interface (alpha)
delta: contact line segment

I thought the partialSlip BC would be a good starting point, but I cannot figure out how to add a constant (surface tension part) to that BC. Has anyone experience writing a mixed/robin BC for a velocity field?

Thanks!

Arnout
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Old   December 4, 2013, 20:58
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Trying to understand the partialSlip BC, so I can figure out how to modify it, but having some trouble. The BC should be equal to:

v dot n = 0
(a*v+(1-a)*(grad(v) dot n)) dot t = 0

with n the surface normal and t a tangential vector. grad has to be dimensionless. This can be discretized as:

(a*v_w + (1-a)*(v_w - v_p)L/d) = 0

with _w the value at the wall, _p in the cell center, d the distance between the wall and the cell center, and L a unit length. Looking at the snGrad function I expect the equation:

snGrad = ((1-a)/(1-a+a*d/L) * (I-n^2) dot v_p - v_p)/d

However, the code reads:

snGrad = ((1-a) * (I-n^2) dot v_p - v_p)/d

and I cannot figure out why.
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generalized navier bc, gnbc, mixed bc, robin bc

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