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Calculating Dynamic Contact Angle with Slip Boundary Condition

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Old   September 7, 2017, 22:57
Exclamation Calculating Dynamic Contact Angle with Slip Boundary Condition
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Faraz
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Hi All,

I need to know exactly how the dynamic contact angle is calculated for 2phase flows. As I know this is the formulation OpenFOAM uses:

θ_d=θ_s+(θ_A-θ_R)∙tanh⁡(U_wall)

Where θ_d, θ_s, θ_A, and θ_R are dynamic, static, advancing, and receding contact angles, respectively, and U_wall is the interface velocity component parallel to the wall (here):

HTML Code:
Foam::dynamicAlphaContactAngleFvPatchScalarField::theta
(
    const fvPatchVectorField& Up,
    const fvsPatchVectorField& nHat
) const
{
    if (uTheta_ < SMALL)
    {
        return tmp<scalarField>(new scalarField(size(), theta0_));
    }

    const vectorField nf(patch().nf());

    // Calculated the component of the velocity parallel to the wall
    vectorField Uwall(Up.patchInternalField() - Up);
    Uwall -= (nf & Uwall)*nf;

    // Find the direction of the interface parallel to the wall
    vectorField nWall(nHat - (nf & nHat)*nf);

    // Normalise nWall
    nWall /= (mag(nWall) + SMALL);

    // Calculate Uwall resolved normal to the interface parallel to
    // the interface
    scalarField uwall(nWall & Uwall);

    return theta0_ + (thetaA_ - thetaR_)*tanh(uwall/uTheta_);
}
My question is about the "uwall", how is it calculated? I think it is the velocity of the wall's neighboring cell, but is it the interface velocity, or the cell velocity (of course I mean the parallel component)? What if there is a slip or partial-slip B.C. applied? How do you interpret this?:

vectorField Uwall(Up.patchInternalField() - Up);

Many thanks in advance,
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Old   September 8, 2017, 03:42
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Anton Kidess
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Up.patchInternalField is the velocity in the cell center next to the boundary face you are looking at. There is no explicit interface velocity. In case of a stationary no-slip wall, Up will be zero and Uwall is the internal field value. In case of a moving no-slip wall, you remove that contribution. In case of perfect slip, your contact angle becomes zero. In case of partial slip, you will have something in between.

Regards to Prof. Bazylak.
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Old   September 8, 2017, 11:41
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Quote:
Originally Posted by akidess View Post
Up.patchInternalField is the velocity in the cell center next to the boundary face you are looking at. There is no explicit interface velocity. In case of a stationary no-slip wall, Up will be zero and Uwall is the internal field value. In case of a moving no-slip wall, you remove that contribution. In case of perfect slip, your contact angle becomes zero. In case of partial slip, you will have something in between.

Regards to Prof. Bazylak.
Hi Anton,

Thanks for your reply. So, in case of no-slip B.C., there is still a Uwall velocity and dynamic contact angle is not equal to the static contact angle, right? Though because Uwall is regularly very small in no-slip case, the dynamic contact angle should be very close to the static contact angle, right?
Therefore, is it correct to say, using dynamic contact angle only makes sense when we use a slip/partial-slip B.C.?
Also, I did not understand why in the fully slip case, the contact angle becomes zero. I can say Uwall can be very large, thus its tanh will be 1, and therefore θ_d=θ_s+(θ_A-θ_R), am I wrong?
Finally, as I know the advancing contact angle must be the maximum, and receding contact angle must be the minimum angle the interface can reach during motion; however, at large Uwalls, θ_d=θ_s+(θ_A-θ_R) will not give θ_A!

Thanks,
Faraz
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Old   September 12, 2017, 03:14
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Uwall is generally not zero, right. I would not dare to say for certain it is generally small. For one, it depends on your mesh resolution. Uwall is zero in static cases (no flow), and then the "dynamic" contact angle becomes the static contact angle (shocking, I know ).

In case of a perfect slip, Uwall is not going to be large, it will be zero parallel to the wall (since a slip boundary condition is defined by zero gradient in parallel and zero normal velocity). Thus your dynamic contact angle should be your static contact angle in this case too (so you are correct about it not being zero).
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