LBE Exercise 3: Drop flows


LBE is often referred to as a method that can readily model multiple immiscible fluids and phases. Several LBE-based algorithms exist to model different aspects of multiple fluid systems. The one we will look at for this exercise is that devised by Lishchuk to correctly implement interfacial stresses at the continuum level [Lishchuk2003]: this does not model the kinetics of phase separation (unlike e.g. the Shan/Chen pseudopotential method) but it can model multiple fluid systems dominated by hydrodynamics and easily apply a wide range of specified interfacial tensions.

Please refer to Theory to LBE Exercise 3: Drop flows if you would like more details about the theoretical background to this Exercise.


We are going to use the Lishchuk algorithm implemented in DL_MESO’s LBE code to look at a system of a liquid drop in a bulk immiscible fluid being subjected to linear shear. We can try different flow shear rates and interfacial tensions between the fluids to see what effects these have on the drop.


Copy the lbin.sys, and lbin.init input files from the directory DEMO/LBE/2D_DropShear in your copy of DL_MESO to your working directory.

These simulation input files will model a rectangular box with walls at the top and bottom. While most of the box will be filled with a continuous fluid, an immiscible drop of a different fluid will be placed close to the bottom wall and the simulation will run for a few thousand timesteps without applying the boundary conditions to allow the drop shape to settle. The top wall is then pulled with a constant velocity (in this case to the right), generating a linear shear flow in the continuous fluid. This flow will move the drop both in the direction of the shear and upwards towards the vertical centreline, as well as deform its shape.


  1. Run DL_MESO_LBE in your working directory with the supplied input files. Plot the resulting output files in Paraview and observe how the drop moves when shear is applied.
    • Use the Calculation filter to calculate the phase index (difference in fluid densities divided by their sum) and then the Contour filter to find where the phase index is equal to zero: this should give the effective boundary of the drop.
    • Try calculating the total fluid density with the Calculation filter. Where are the highest and lowest values?
  2. Try replacing the drop given in the lbin.init file with one placed close to the top shearing boundary. (You can use the init.exe utility to create a drop of radius 15 units at, say, y=30.) Does the drop still settle midway between the two solid boundaries?
  3. The shape of the drop (or how much it deforms) will depend on its capillary number (ratio of viscous to interfacial forces). In turn, the capillary number will depend on the shearing velocity of the top wall. Try modifying the top wall velocity and the interfacial tension parameter in the lbin.sys file and see what happens. How high can each of these values be set while ensuring the simulation still makes sense?
  4. You may have spotted that the boundary between the drop and continuous fluid is not sharp. One aspect of the Lishchuk mesophase algorithm is it generates diffuse phase boundaries, but ensures large interfacial tensions can be used. Fluid separation is controlled using a segregation parameter defined in the lbin.sys file: try varying this values to see what effect it has. (Note that you will need to take care to ensure the phase boundary does not interfere with the system’s solid boundaries.)
[Lishchuk2003]SV Lishchuk, CM Care and I Halliday, Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents, Physical Review E, 67, 036701, 2003, doi: 10.1103/PhysRevE.67.036701.