(492f) Microfluidic Networks for Sorting of Drops: Design of Network Topology and Entry Times of Drops

Droplet microfluidics involves generation and manipulation of drops in microchannels. Droplet microfluidics offers the inherent features associated with the small length scales of microfluidics, the ability to generate a large number of monodisperse drops in a short time and the ability to encapsulate cells, particles, and microorganisms within the drops. These features of droplet microfluidics allow it to be used for drop-based lab-on-a-chip (LOC) devices. LOC devices aim at performing all the processes and operations in an actual laboratory within a small chip. The automatic functioning of droplet-based LOC devices requires additional functional elements within the chip that can perform operations such as sorting of drops, synchronization of drops, sequencing of drops, etc. These functional units help integrate multiple processes and operations in a droplet-based LOC. Microfluidic networks are potential platforms that can perform these operations when designed appropriately. A general microfluidic network is depicted in Figure 1.

When drops are sent to a microfluidic network, they interact within the network and result in an outlet behaviour. The topology of the network and the entry times of drops affect the interactions. A simple model proposed by Schindler and Ajdari¹ helps simulate the movement of drops in the network. This model views microfluidic networks as equivalent to electrical circuits. The flow in each branch of the network is linearly proportional to the pressure drop across the ends of the branch. Each branch offers resistance to the flow of the continuous phase fluid. The resistance offered by the branch depends on the channel dimensions and the viscosity of the continuous phase. Apart from the resistance offered by the channel, the presence of a drop in a branch imparts additional resistance. When a drop reaches a junction, it moves to the branch with maximum instantaneous velocity away from the junction. Given the network topology and the entry times of drops, with the help of the model, one can simulate the droplet movement in the network and determine the resulting outlet behaviour. This is the forward problem. On the other hand, identifying a suitable network topology and entry times resulting in a desired outlet behaviour is the inverse or design problem. Our previous work² identified that determining the entry times of drops that result in a desired functionality in a given network topology requires solving a linear constraint satisfaction problem. However, solving a combined design problem to determine a network topology and a set of entry times of drops is difficult. The difficulty arises from the nonlinearity in the model constraints and lack of a closed-form expression for the outlet behaviour in terms of the network topology and the entry times of drops. In this work, we formulate and solve a mixed-integer nonlinear optimization problem to determine a network topology and the entry times of drops that result in sorting of two types of drops.

References

1.Schindler M, Ajdari A. Droplet Traffic in Microfluidic Networks: A Simple Model for Understanding and Designing. Phys Rev Lett. 2008;100(4):44501. doi:10.1103/PhysRevLett.100.044501

2.Sankar E. M. A, Rengaswamy R. Droplet microfluidic networks as hybrid dynamical systems: Inlet spacing optimization for sorting of drops. AIChE J. 2022;n/a(n/a):e17633. doi:https://doi.org/10.1002/aic.17633