COMSOL Mutltiphyics is a Finite Element Software package that provides numerous options for interconnecting different physics simulations.  This type of simulation is often referred to as a Mutiphyisics Finite Element Analysis.  Using COMSOL, a microfluidic channel was modeled and analyzed under a variety of conditions.  These conditions involved inputting a total volumetric flow rate as a function of time.  Within the channel there were heating elements, elastic structural flanges, a dilute species mixture, and a variable pressure fluid system.  Furthermore, there were also three inlets, two of which contain the heating elements and dilute species mixture.  This simulation was run five times, each with different volumetric flow rates emanating from the different inlets.  However, in each case the total incoming flow rate remained the same.

By varying the percentage of the total flow rate at each inlet, the results related to structural deformation, heat transfer, and mixing a dilute species were widely varied.  For example, the stresses and deformations associated with each inlet percentage were obviously quite different.  In fact, based on this simulation’s results, the steady state stresses on the flanges varied from 9100 Pa to less than 3000 Pa.  The variations in average concentrations at the outlet were even more varied, ranging from .17 to .72 mol/m3. The variations in the average outlet temperature were even more dramatic.  Even though the water in each case began at 280 K, the data at 8 seconds ranged from 280.5 K to 340 K.

Based on these results, the choice of which inlets will receive which percent of the total volumetric flow rate is clearly a critical decision.  It should be stated that this system was capable of generating substantial mixing with the proper inputs.  Furthermore, the amount of heating at the outlet could likewise be controlled through managing the input ratios.

Due to the wide variety of multiphysics interactions, COMSOL was an invaluable resource for running this simulation.  The data acquired from this study was very reasonable, and the simulation itself preformed as expected.

The purpose of this study was to investigate how water flow in a channel would affect a variety of physical quantities in a microfluidic channel, as shown in Figure 1.  The quantities of interest included stress, temperature, and species concentration.  In this COMSOL simulation, the input fluid velocities varied in time, and a parametric sweep was utilized to compute how changing the inlet flow rates would affect the output variables of interest.  More specifically, the 2D volumetric flow rate was kept constant, but the ratios between different inlets were varied.  The total inlet 2D volumetric flow rate is shown in Figure 2.  The importance of relative volumetric flow rates is a consequence of the fact that the side inlets are heated and contain a high concentration of the observed species, in contrast to the central inlet of the channel.  The primary additions in this model are the introduction of the flanges and the heating elements.  As such, the effects these additions will have on the performance of this system will be points of interest in this study.

There were four general output fields of interest in this study.  The first was the fluid flow itself.  Understanding and analyzing the fluid flow in the channel was essential for examining the remaining output parameters.  The core of this study was to vary the ratio of fluid flow at the inlets.  Table 2 details which percentage of the total volumetric flow is represented by each R value.  This understanding is very critical as each plot in the results is represented in term of the R value.  The next field of study involved the structural interactions of the flanges in the channel.  Here, quantifying the stress and deformations was the primary concern.  Although the deformations in the flanges can be described according to classic beam theory, the loading on the surface on the flanges is extremely complex due to the variations across the length and in time.  The next two involved heat and mass transfer, both of which involved advection and diffusion in the moving fluid.  Once again, the calculation involved here are very complex due to the velocity fields being widely varied in both space and time.

It should be noted that the fluid flow and the structural interactions were heavily interdependent on each other.  This is because the deformation of the flanges is calculated based on the fluid flow and vice versa.  Furthermore, the temperature field within the fluid was likewise interdependent on the fluid flow based on the relationship between viscosity and temperature.  Table 1 summarizes the equations utilized by each module in COMSOL.  The interdependence previously mentioned is readily apparent in many of these equations.  Ultimately, the study conducted was an intricate Multi-Physics problem.  This made utilizing COMSOL a very appropriate choice for this study.

The computational procedure for this study was not unlike that for any other FEA simulation.  The model geometry was built, and then each physics module was added with the appropriate boundary conditions.  After an appropriate mesh was added, a parametric sweep was created to vary the inlet flow rates.  Next, the simulation was solved using COMSOL Multiphysics, and finally, the resulting data was post-processed and extracted using tools inside the COMSOL software package.

In Figure 4, the output velocity and stress profiles for three different values of R are shown.  Essentially, the R value corresponds to the fraction of the total flow rate that is entering through center inlet.  The remaining flow rate enters evenly through the side inlets.  As expected, when most of the flow comes from the center inlet, the max velocity is slightly higher.  This is likely due to the increased drag associated with the side channels.

As shown in Figure 5, the species concentration mixes much better when the R value is low.  This result is intuitive, especially since the diffusion constant is quite low.  For low R values, more flow moves through the side inlets, where there is a highest concentration.  This allows the species to mix in the rest of the channel.  It should also be noted that the inlet ratios also affect the deformation of the flanges at t = 8s.  This is due to changes in viscosity.  Here it can be seen that more viscous water (cooler) will produce more drag on the flanges and thus more deformation.

Figures 6 and 7 illustrate the Von Mises stress at the bases of both flanges.  Based on these graphs, both flanges experience similar levels of stress as a function of time.  More interesting, however, is the behavior dependence on R.  Because of the combination of higher viscosity and faster fluid flow associated with high R values, the resulting stresses are higher.  Furthermore, it appears these two factors also increase the time duration before steady state conditions are achieved.

Figures 8 and 9 depict the velocity and displacement in the x-direction of the lower flange tip.  Although the steady state displacements are quite diverse, the velocities demonstrate far less dependence on the R value.  It should be noted that the scaling of this graph does diminish the observable differences at steady state.  Nonetheless, the differences in velocities are far less pronounced than the dramatic differences in the displacement graph.

Figures 10 and 11 display very similar behavior to figures 8 and 9, respectively.  Consequently, it can be concluded that both flanges experience similar velocities and displacements in the x-direction.

Figure 12 illustrates the average concentration at the outlet boundary.  Clearly, the parametric sweep of the R parameter generates very different results for each solution.  This is not surprising since the diffusion constant used in this study is relatively small.  Consequently, the mixing of the dilute species is heavily influenced by the amount of advection.  More specifically, if the higher concentration fluid does not move very quickly through the channel, mixing in the system will be minimal.  In contrast, mixing will be highest when the higher concentration fluid flows throughout the channel.  As such, the solution that COMSOL has provided demonstrates the predicted behavior.  Another important observation is that the time dependence was minimal for all R values, with exception to the initiation of flow near t = 0.

The average temperature at the outlet is plotted against time in Figure 13.  As expected with constant heat flux, the temperature continues to rise for most cases without ever reaching a steady state value.  Clearly, temperature, like all the other output variables of interest, demonstrates dramatic differences based on the R value used.  So much so, that the outlet temperatures vary by approximately 60 Kelvin.  Evidently, more than 10% of the flow rate must occur through the side inlets for a noticeable heating to occur in this simulation.  Notice that all cases begin with an initial temperature of 280 K.

The primary purpose of this exercise was to develop and run a complex COMSOL simulation.  As such, this study was very instructive in teaching a wide variety of topics related to COMSOL.  The first of which was how to utilize a non-constant inlet velocity.  As, seen in Table 3, the input velocity was a very complex expression that quickly rises, and then displays a decaying oscillation.  Additionally, creating this model was very instrumental in teaching how to use physics modules like Fluid-Structure Interaction, Heat Transfer, and Transport of Dilute Species.  On the computational side, it was also useful in generating an effective parametric sweep as well as producing the desired plots.

The focus of this simulation was to determine the effects of varying the ratios of the total flow rate at the different inlets.  More specifically, the structural effects on the flanges, the dilute species behavior, and the temperature were all observed at different R values.  Based on the recorded data, there were significant, if not extraordinary differences in all three.

In conclusion, this study has revealed some fascinating results.  Although it is not surprising that low R values will produce better mixing, they will also result in less maximum stress for the same total flow rate.  However, the heating elements used in this study do appear to be excessive, as heating the channel fluid to 340 K poses safety concerns.  Further iterations of this study would generate and compare different channel geometries and compare the effects on mixing the dilute species.  This said, the current geometry does appear to enhance the mixing that occurs in the channel.