Improvement of the surface tension methods

Improvement of the Guntensen method: the correction

The major artefact of this model is the so-called microcurrents, which seems to be a common artefact for any interface using the LBM. These microcurrents drive a small however unwanted flow in the simulation which leads to anisotropy of a drop at rest. It should be noted that these microcurrents are easily overcame by the presence of a flow.

Improvement of the Guntensen method: the correction

The major artefact of this model is the so-called microcurrents, which seems to be a common artefact for any interface using the LBM. These microcurrents drive a small however unwanted flow in the simulation which leads to anisotropy of a drop at rest. It should be noted that these microcurrents are easily overcame by the presence of a flow.

Improvement of the Guntensen method: the correction

The major artefact of this model is the so-called microcurrents, which seems to be a common artefact for any interface using the LBM. These microcurrents drive a small however unwanted flow in the simulation which leads to anisotropy of a drop at rest. It should be noted that these microcurrents are easily overcame by the presence of a flow. We have implemented the RK model by tuning the perturbation to the densities with respect to the lattice. We observed a noticeable diminution of the microcurrents and a significant improvement in the isotropy [see mmdupin for more details].

As Thompson's reported it in his thesis, the surface tension applied by in the RK model is responsible for the microcurrents. He noticed some dependence between the applied perturbation constant and the intensity of the unwanted flow. This has been confirmed by the presence of microcurrents within a monochromatic flow where a surface tension is applied along an imaginary circle

The anisotropy of the microcurrents and the explicit shape of the lattice (here D2Q9) within the microcurrents

suggest that a non-negligeable unbalance of the surface tension between the long (i=1,3,5,7) and short links (i=2,4,6,8). The idea is therefore to modulate one with respect to the other in order to get them balanced and reduce the microcurrents. We define

where short/long refer to the lattice's links. We computed a series of drop supposed to be at rest and calculated the activity of the micro-current (defined as being the lattice-sum of the velocities) and the isotropy of the drop at steady state (defined as being the standard deviation of the distance of the interface to the best fitted circle):

From this graph

• the microcurrents activity can be highly reduced taking ~2.1
• the isotropy of the drop depends highly on the microcurrents activity

We then calculated the interfacial tension for given parameters and and found two expressions for the surface tension (to a first order value in ):

where

The ratio of these two surface tensions gives =2.1213!

This calculation confirmed the results we obtained and validated the improvement. Further measurements using a Fourier fit to fit the interface shown that this model ensures a steady state isotropy of less than a 10th of a node.

It should be noted however that Lishutz et al have implemented a way to put surface tension by having greatly reduced microcurrents. This is by adding a bodyforce perpendicular to the interface and inversely proportional to the radius of curvature (see [sergey] for more details). The main drawback of this method is that it requires non local calculations (i.e. gradients to find the radius of curvature) which annihilates the local property of the RK model.

Improvement to the Lishchuk method

One of the motivation of this project had been to reach micro-fluidic applications. However, being highly interface dominated by definition, any anisotropy or second order overlook show up at this regime. Few improvements to the Lishchuk method had been needed to reach this regime.

Few steps towards the definition of the colorfield, the recolouring step and the velocity definition ensure a net velocity field and stable algorithm even at low Reynolds number (10^-1) and very low capillary number (10^-4).

Taking the walls into consideration: wetting properties for the l and Lishchuk method

Walls interactions are important in many engineering problems. They are crucial at the micro-fluidic regime, where the flow is dominated by its interface and its wetting properties. Neither Guntensen or Lishchuk had considered a method to imbed the walls interactions within their method.

The general idea is based on the same ground for both techniques, that is to say that the same type of forcing can be applied for the walls as for the interface.

a. For the method

The perturbation of the l method is consequently modified as such

b. For the Lishchuk method

The same steps are taken with the Lishchuk method. It consists in imposing an identical bodyforce type perturbation on interfacial node near a wall, acting parallel to the wall and proportional to the targeted wetting of the considered fluid.

c. Droplet shapes for different wetting properties

We obtained the following shapes for different contact angles, for both l and Lishchuk methods

Bigger systems we used to quantify the isotropy of the wetting drop. The shapes obtained were round to a 10th of a node. The following video shows a rectangular drop wetting the surface. Note that the simulation does not reach steady state.

Capillarity has not been fully studied yet. However, rising fluid through a capillary has been observed using this model:

Dynamic contact angle

Very little is known or understood about this controversial phenomena. It is typically observed for moving droplets and two angles can be defined:

This can also be observed when a drop is condensing or evaporating. Two angles can be measures, an advancing (A) and a receding (R). The (static) contact angle lies somewhere between them.

A drop on the surface of a window will drop if the following condition is met

Where the parameters have their usual meanings. The parameters of the following simulation are such that the drop is clamped to the surface because its does not met the latter equation.