Fig 1.
Using instantaneous simulation of a microfluidic chip to predict the paths followed by fluids and particles flowing through the chip.
A basic “H” channel chip (top) is first separated into nine units (a − i). Units a, c, d, e, f, g, and i are simple channels; the flow of fluid in these channels is akin to the flow of electricity in a network of resistors and therefore can be modeled using principles of electrical circuit analysis (Eqs 1–3 and Kirchhoff’s laws) and models of hydraulic resistance (Eq 4). Units b and h are channel intersections where multiple fluid inlets and outlets come together; the paths followed by particles through these intersections cannot be predicted using analogies with electric circuits. Instead, each unit is described in terms of a prototype intersection (the “Unit Intersection,” bottom left) with different boundary conditions. For example, unit b has two inlets (1 cm/s at North, and 2 cm/s at South), one outlet (3 cm/s at East), and one unused connection (West). By querying a database containing nearly 100,000 pre-simulated unit intersections, suitable simulation results for units b and h are retrieved. Particle trajectories from these unit intersections (red lines in b and h) are then expanded through the rest of the chip using streamline theory [14, 15]. In this manner, the paths followed by fluids and particles through the entire chip are predicted in around one second.
Fig 2.
Graphical overview of the instantaneous microfluidic simulation method.
In Step 1, MATLAB was used to generate 92,934 unit intersections with different random assignments of inlets and outlets and different random flow rates at each of the four connections North, East, South, and West (see also Fig 1). The resulting unit intersections were generated in 10 seconds and saved into a MySQL database. In Step 2, MATLAB was used to control COMSOL Multiphysics to calculate the fluid velocity fields and particle trajectories of each unit intersection and save the simulation results to the MySQL database. A total of 92,934 fluid velocity fields and 5,321,944 particle trajectories were calculated; the entire simulation process took one month to complete, but this step only needs to be performed once. In Step 3, our method is used to predict the path followed by a particle in a given microfluidic chip. First, the fluid velocity profile and particle information of the chip design are imported into MATLAB. Then MATLAB matches each intersection in the chip design with the closest pre-simulated intersection in the MySQL database and returns the corresponding fluid velocity profile and particle trajectory. Finally, the entire path of the particle through the chip is expanded and generated. Simulating a given chip using this approach takes around one second.
Fig 3.
Comparison of results from simulating a simple microfluidic chip design using existing commercial software (COMSOL Multiphysics) and our instantaneous simulation method.
In the COMSOL Multiphysics simulation (A), the fluid velocity field is calculated using finite element analysis (Step 1) and the Particle Tracing for Fluid Flow physics module is used to calculate the paths followed by particles (Step 2). In our instantaneous simulation (B), the flow rates in the channels were calculated using Eqs 1–4 and fluidic analogs of Kirchhoff’s circuit laws, then simulation results for the channel intersections (dashed red boxes) were found by searching for similar intersections in our database of nearly 100,000 pre-simulated intersections (Step 1). The software retrieved the corresponding particle trajectories from these intersection simulations (blue points in Step 2) and expanded them into whole-chip particle trajectories (yellow points in Step 2). Our instantaneous simulation method was 45 times faster than COMSOL Multiphysics, and the predicted locations of each particle at the exit channels agree to within about 1 μm in a 200 μm wide channel. Raw data of these simulations are available for download (S1 File).
Fig 4.
Results from using instantaneous simulation to predict the paths of two 1 μm particles traveling through a randomly-designed microfluidic chip [4], with close-ups of some channel intersections (black circles).
The red lines/circles indicate the particle trajectories obtained from the database of pre-simulated intersections, and the gaps between the red lines are regions where no calculation of particle trajectory is necessary because the channels have no intersections in these regions. This simulation was completed in around one second by our instantaneous simulation method. In contrast, the same simulation failed after five days of computation when using an existing simulation tool (COMSOL Multiphysics). Raw data of these simulations are available for download (S1 File).