Contact line pinning and incorrect contact angle with Navier slip in high-viscosity / high contact angle at fine mesh Basilisk simulations

[gopal chakka]

Hi everyone,

I am working on two-phase simulations in Basilisk that involve contact-line dynamics with high-viscosity fluids. I am trying to impose a static contact angle of 90°, but the contact line remains effectively pinned, and the apparent contact angle deviates from 90°, especially at high viscosity.

Setup:

• I am using a Navier slip boundary condition at the wall:

u.n[left] = dirichlet(0.0); u.t[left] = dirichlet(u.t[] * lambda / (lambda + mesh));

• Definitions:

#define mesh ((Ldomain)/pow(2,MAXlevel)) #define lambda 5*mesh

• Far-field boundary conditions:

u.n[right] = neumann(0.); p[right] = dirichlet(0.0); u.n[top] = neumann(0.); p[top] = dirichlet(0.0); 

•          CFL condition using in simulations

CFL = 0.1;

Observations:

• The contact line appears pinned (wall-adjacent cells do not move).

• The measured contact angle deviates from the imposed 90°.

• The issue becomes more pronounced as viscosity increases and also at high contact angles ~135 degree at high refinement ~2.5 microns.

Questions:

1. Is the slip length (λ = 5Δ) too small for resolving contact line motion in Basilisk?

2. For high viscosity flows, what is a recommended range of slip length relative to grid size?

3. Could this be primarily a resolution issue near the wall/interface?

4. Are there recommended practices in Basilisk for ensuring accurate contact angle imposition with moving contact lines?

Any suggestions or references would be very helpful.

Thanks in advance!

[Shyam Sunder Yadav]

Dear Gopal

Search for "contact.h" on Basilisk webpage, you will gets lots of examples on how to apply static contact angle.

That may help you...

If you do not apply dirichlet boundary condition for volume fraction f  then the interface should take 90 deg angle...

In the image you attached, I notice that drop is sheared at the contact point...Are you studying drop impact kind of problem or may be you are having high gravity? Why the drop is shearing that way is the question...

Just try with lower drop viscosity once...

Dr. Shyam Sunder Yadav
Associate Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile

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[gopal chakka]

Dear Dr. Yadav,

Thank you for your response. I have already implemented the contact angle using the height function exactly as shown in the Basilisk examples.

vector h[];
h.t[left] = contact_angle(theta_e * pi / 180.);
f.height = h;

There is no Dirichlet BC on f anywhere in the code. The issue persists specifically for high-viscosity fluids (Oh > 0.004) despite correct implementation. My problem is drop impact spreading.

Is there anything additional that needs to be done differently in Basilisk for high-viscosity flows to ensure correct contact angle imposition and contact line motion?

Best regards, 

Gopal Chakka

[Shyam Sunder Yadav]

Dear Gopal

Should not the Navier-Slip condition imply the following?

u.t[left] = u.y[]*( (2.0*lambda - mesh)/(2.0*lambda + mesh) );

We have the definition of Navier slip boundary condition as  u_slip = u_wall = lambda*(d u_t / dn)

Now u_wall = (u.t[left]+u.y[])/2.0     and   d u_t / dn = (u.y[] - u.t[left])/mesh

Putting these, we get the relation 

u.t[left] = u.y[]*( (2.0*lambda - mesh)/(2.0*lambda + mesh) );

You have to enforce the above relation inside an event through a foreach_boundary loop as shown below (It should work I think...)

event navier_slip (i++)

{

foreach_boundary(left) {

u.t[ghost] = u.y[]*( (2.0*lambda - mesh)/(2.0*lambda + mesh) );

//u.t[-1,0] = u.y[]*( (2.0*lambda - mesh)/(2.0*lambda + mesh) );

}

}

Try one of the above forms...

See if it gives better results...

Best wishes

--

Dr. Shyam Sunder Yadav
Associate Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile

[gopal chakka]

Dear Dr. Yadav,

Thank you very much for your suggestion. The Navier-slip formulation you provided is working correctly and the contact line pinning issue has been resolved.

I sincerely appreciate your time and help.

Best regards, 

Ramgopal

[Edoardo Cipriano]

Hello,

Just for reference, the Navier slip boundary condition has recently been added to Basilisk (a couple of weeks ago):

https://www.basilisk.fr/src/?changes=20260316092751

It can be used as follows:

u.t[boundary] = navier (value, sliplength);

Best,

Edoardo

[Shyam Sunder Yadav]

Dear Edoardo

Thanks for pointing out the Navier boundary condition implementation!

It will be useful...

Regards

Dr. Shyam Sunder Yadav
Associate Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile

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