Lagrangian Particle Tracking (WIP)
Microfluidic separation is popular due to the fine control of inertia flow forces as well as the possibility to use external forces such as an electric field. Many applications focus on separating heterogenous biological solutions into separate homogenous sub-populations. One example is the separation of whole blood to obtain circulating tumour cells as explored in Isolation and retrieval of circulating tumor cells using centrifugal forces by Hou et al. 2016 (Problem coming soon!)
The inertia based separation methods uses Dean drag forces where secondary flow perpendicular to the bulk flow lifts and drags particles based on their size and density. The secondary flow often forms vortexes within the channel at the top and bottom of the microfluidic channel but is dependent on the 2D geometry. However, using streamlines of the bulk flow lose the spatial secondary flow and the effects of particle size and density. Streamlines will not model forces acting upon particles.
Lagrangian particles track movement based on forces acting upon a particle such as gravity, buoyancy and drag. Using ParaView, LPT can be implemented using the LagrangianParticleTracker model. This can be enabled through the plugins menu but ParaView will need to be complied from source if using a custom integration model. For this example, we will need a custom integration model for our system.
The easiest method to implement a custom ParaView LPT integrator is to re-use a pre-existing integrator. At the time of writing, ParaView has the vtkLagrangianMatidaIntegrationMode which can be used as an example and edited for a desired application.
I edited the formula to have a relaxation factor, drag force and lift. Additionally, I adjusted the buoyancy / gravity force to be more appropriate for particle microparticle suspension.
Lagrangian Particle Movement
Relax =
Drag =
Net Inertial Lift Force =
Buoyancy / gravity constant =
Where a particles reynolds number is ;
and
are flow and particle density;
is flow dynamic viscosity;
is particle diameter;
is hydrodynamic diameter of the channel
where w is width and h is height;
is the lift force constant which is on average 0.5 for microfluidic channels.