# Sessile Droplet Evaporation

Hey All,

I’m a brand new Palabos user, who’s trying to wrap his head around all this. So, please be kind.

My aim is to simulate the evaporation of a droplet of water resting on a surface, at ambient temperatures and pressures, in order to study the liquid velocity fields inside the droplet.

From what I’ve read and understood so far, my problem will need to be set up like this:

• Bottom boundary condition: Bounce-back boundary condition
• Top, left, and right boundary conditions: ambient pressure set by a dirichlet condition
• A multi-phase model: currently looking at Shan/Chen 94
• Geometry of the drop

Am I on the right track?

So, in order to simulate the evaporation, can I somehow define a time constant volume change of the droplet?
Additionally, this volume change condition would need to move with the liquid-has interface.
I’m not sure how to go about accomplishing that…

I hope I’ve laid out my problem clearly.

Thanks,
Jobin

Hello
I cannot clearly understand the process you are going to simulate. Since, as far as I know evaporation occurs due to temperature change but it seems in your case temperature is constant??
Overall, I think your assumptions are true. Be careful that the Shan-Chen 94 model is not appropriate for simulation of high-density ratios problems but is a good choice for the start. I hope you give us more detail about fluids properties to help you.

Best Wishes

Hi,

Interestingly enough, evaporation occurs any time the air directly above the water is not saturated (i.e. 100% RH). In the event that it is fully saturated, the rate of mass transfer of vapour into the liquid and liquid into the vapour is equal, causing no net evaporation. However, diffusion and air currents in the atmosphere ensures that the air directly above the water is essentially never at 100% RH, thus always allowing evaporation to occur. The only case where this can’t happen is inside an enclosed box, where the air will continue to accumulate vapour until 100% RH since the air isn’t replaced with fresh air.

You can think of leaving a glass of water out for a day or two. The water level will have dropped by the end of that period even though the water was never heated; the water will have been at the same temperature as the air. A temperature change (that is, heating the water) can increase the speed of evaporation since the molecules now have a greater amount of kinetic energy to go out of liquid and into vapour form.

I hope that clears it up.

You mention that Shan-Chen 94 is not very well suited for high density ratios. Do you have any alternative suggestions I could pursue?

The fluid properties would be the nominal values for air and water at room temp and ambient pressure:
rho_air = 1.225 kg/m^3, dynamic_viscosity_air = 1.962E-5 kg/m.s
rho_water = 1000 kg/m^3, dynamic_viscosity_water = 1.002E-3 kg/m.s
pressure_air = 101.325 kPa (at boundary conditions specifically)

I look forward to your insight on how to pursue this problem. Like I said previously, I’m most interested in the velocity fields that develop inside a droplet during this sort of evaporation.

Regards,
Jobin

I have worked on the Shan-Chan (Pseudopotential) model. Based on my experience, the Exact difference method proposed by Kupershtokh (On equations of state in a lattice Boltzmann methodI) is the most stable method in the pseudopotential model. It is suitable for high-density ratio (order 1000) problems like your case. In addition, the free energy model is frequently used in most literatures. The pseudopotential model is very easy to implement but it has some disadvantages. For example, some parameters depend on each other. For a complete review about this model, you can read the following article:
A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and applications

Overall, first consider the free-energy model and then think about the exact difference method ( in pseudopotential model). In both models, you have to use an equation of state which means that the parameters are related to each other and it probably makes your problem a bit difficult. Since you have some known values for two phases.

You can send me pm in private.

Regards