MICRO FLUIDICS | ARTICLE
COMSOL Multiphysics solves these global equations simultaneously with the fluid dynamics equations, which significantly speeds up the solution process. Solution time is also improved via the COMSOL Multiphysics unique capability to automatically evaluate the coupling terms between the fluid variables and the global variables in the Jacobian matrix.
After finding the rotational and translational velocities of the particle that are in equilibrium with the surrounding fluid, the transverse inertial lift forces are calculated. We can then add the effect of the Dean flow, assuming Stokes drag on a particle and the Dean flow velocities obtained in the first model.
It is important to recognise that the solution approach described here is required in order to predict inertial focusing since standard particle tracing is not applicable. In a straight channel, for example, standard particle tracing will predict that a neutrally buoyant particle inserted at a specific location in the channel cross-section will remain at that location. There are no general analytical equations relating the forces and moments that govern inertial focusing to the fluid flow conditions obtained in the absence of the particle. We are, however, developing expressions for the forces and moments acting on particles based on the above CFD solution. We can then use the COMSOL Multiphysics particle tracing capabilities to predict particle motion, including rotation, and inertial focusing by applying the developed expressions as user-defined force and moment equations.
<< Figure 2: Effect of inertial focusing in straight (A) and curved (B) channels. Particles are randomly introduced but become ordered thanks to inertial focusing, as shown in the cross-section images. >>
Validation and Results
The model was first validated against the established solution for straight channel flow in a 50 μm square channel. In this case, the equilibrium particle positions are known to be centred on each face of the square and 10 μm away from the walls for a 10 μm diameter particle at a channel Reynolds number of 20.
We then compared the CFD model predictions to experimental measurements for both straight and curved channels that are 50 μm tall, 100 μm wide and 4 cm long. Figure 3 shows experimental and simulation results for a channel Reynolds number of 100 and three Dean numbers: 0, 6 and 9 (the channel is straight when the Dean number is zero). For each case, we show the particle distribution along the channel length collected using
fluorescent streak microscopy and the force field cross section calculated for that cross section with the equilibrium positions (net force = 0) highlighted. The simulation results are in good agreement with experimental measurements for all three cases, and illustrate the dependence of the equilibrium positions on the channel curvature. Figure 4 shows the velocity in the channel and surface tractions on the particle for one channel/particle configuration where the force is dominated by the wall-particle interaction.
The ability to rapidly iterate through design changes in COMSOL Multiphysics and build a comprehensive theory for the operation of such devices will save experimental time as well as guide the design and optimisation of our lifesaving diagnostic devices.
34 | commercial micro manufacturing international Vol 7 No.1
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