Discussion Forum

Hello!

I am trying to understand the underlying equations of the isothermal case of the following COMSOL model: https://www.comsol.com/model/droplet-evaporation-on-solid-substrate-97071

There are four things I am stuck with for some time now and it would be great if someone can help me out!

To move the droplet interface the model uses: (a) Fluid-fluid interface under the laminar flow physics. (b) Moving Mesh combined with a global ODE for the movement of the contact line. (c) Navier-Slip condition in the laminar flow phsyics such that the contact line can move.

(a) Fluid-fluid interface

When I look at the equations specified under the fluid-fluid interface, my understanding is that the movement of the droplet interface depends on the mass flux over the boundary (Mf). Subsequently, the movement of the boundary results in a certain shape/curvature and thus a certain surface tension. From the top equation:

,

which can be simplified to

,

I understand that this curvature is subsequently used to determine the pressure drop over the interface which can be used in the Navier-stokes equations to calculate the velocity profile. However, I also specify a constant contact angle. But I don't understand how this constant contact angle relates to the equations described above, as it seems that this information is unnecessary if the shape is determined based on the local flux and the pressure is corrected via fluid flow. Can somebody help me out how COMSOL uses this constant contact angle? Is it just a constraint, or is it used to determine the droplet shape/curvature and will the droplet shape thus always be constant (as the model is initially developed for degrees?

(b) Moving Mesh combined with a global ODE for the movement of the contact line

To determine the movement of the contact point, a global ODE is used. This ODE is based on the mesh velocity within the contact point (which is made globally available by a point integral). This mesh velocity depends on the flux which is determined with the use of a lagrange multiplier. From the analytical result we know that the flux is infinite in the contact point. I don't understand how COMSOL manages to get rid of this singularity, as clearly the flux evaluated in the contact point is finite. Is this because the lagrange multiplier is an anverage over the entire boundary? Or is it because of the numerical implimentation where the flux is an integral over one element? Or something else?

(c) Navier-Slip condition such that the contact point can move

I do understand that we need a slip condition at the substrate to overcome the Huh- Scriven paradox. However, I don't understand the physical meaning of the slip length we specify, and how this is used to close the equations.

Phase transition

Finally, I am wondering how COMSOL takes the phase transition from liquid to gas into account within the isothermal model. I believe that the answer lies within the following equation as stated under the fluid-fluid interface node:

,

which can be rewritten to

.

My understanding is thus that the velocity is discontinuous, but COMSOL corrects for this discontinuity by velocity with which either liquid is withdrawn or gas is formed.

If you could provide some insights about any of these questions it would be really helpfull! Make sure that you also look at the isothermal case of the model as I donot take the heat equations into account yet. Thank you so much!!

Best, Imke