Design of a model‐based feedback controller for active sorting and synchronization of droplets in a microfluidic loop

Abstract

in Wiley Online Library (wileyonlinelibrary.com).The transport of confined droplets in fluidic networks can lead to complex spatiotemporal dynamics, precluding full control of the position of droplets in the network. Here, we report the design of a model-based feedback controller that can actively regulate droplet positions in a network. We specifically consider droplet dynamics in a microfluidic loop where a main channel splits into two and recombines. Consistent with previous studies, we find that without active control, the dynamics of droplets in the loop can range from periodic to chaotic behaviors. However, by implementing the model-based feedback controller, we show that the droplets can be made to sort alternately into the branches of the loop as well as to synchronize the times at which pairs of droplets exit the loop. In particular, our computations demonstrate that the controller is capable of executing remarkable droplet sort-synchronization tasks in the otherwise chaotic dynamics in the loop. The design of our controller incorporates a hydrodynamic network model, that is, capable of predicting droplet positions and subsequently delivering an actuation to the branches in the loop through elastomeric valves. Efficacy of the controller is discussed in terms of actuation characteristics and constraints imposed by elastomeric valves. The model-based feedback controller framework presented in this study is likely to promote the development of lab-on-chip technologies in which droplet manipulation tasks are executed with active control.The periodic dips in the actuation are shown in the inset. (f) Actuation frequency as a ratio of number of actuations at a particular value to the total number of actuations for synchronizing 35 pairs of droplets. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]The periodic dips in the actuation are seen in the inset. Interestingly in this case the upper branch also gets actuated consistently (f) Actuation frequency as a ratio of number of actuations at a particular value to the total number of actuations for synchronizing 35 pairs of droplets. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Origin of periodic and chaotic dynamics due to drops moving in a microfluidic loop device

“…Confined droplet dynamics is predicted using the network model under the assumption that the droplets do not collide [14]. The network model has been shown to satisfactorily predict the droplet dynamics in microfluidic loop [15] and ladder networks [16,17]. In this model, drops are treated as point objects moving at a velocity v = βQ/S [18][19][20], where β is the slip factor, S is the cross-sectional area, and Q is the flow rate.…”

“…This slight asymmetry ensures that the droplet decisions are deterministic. The resistance of the branch is summation of the resistance of the channel [15] and resistance due to drops (nR d ), where n is the number of drops in the branch and R d is the excess hydrodynamical resistance per drop. Using this network model, we illustrate the QDS principle with two representative scenarios: 3-period and 9-period behaviors, without input fluctuations.…”

Very large scale droplet microfluidic integration (VLDMI) using genetic algorithm

“…The network model has been validated in a number of studies. In our prior work (Maddala et al, 2011), we have shown that the model can predict complex behavior that are experimentally observed in simple loop devices. Further, we have shown that the network model can also be used in ladder devices (Maddala & Rengaswamy, 2014).…”

“…In this work, the continuous variables are taken from literature (Maddala et al, 2011;Maddala & Rengaswamy, 2014) and the discrete variables are optimized using genetic algorithm.…”

“…In most of the aforementioned applications, microfluidic devices are often restricted to being droplet generators (Maddala et al, 2011). To extend the use of these devices to more complex biological analysis, additional functionality needs to be incorporated beyond the role of droplet generation.…”