(469a) Experimental and Simulation Studies of Nonlinear Dynamics of Droplets in a Microfluidic Loop Device

Srinivasan, B., Columbia University
Maddala, J., Texas Tech University
Bithi, S. S., Texas Tech University
Vanapalli, S. A., Texas Tech University
Rengaswamy, R., Texas Tech University

Droplets moving even in simple microfluidic devices have been reported to exhibit rich nonlinear dynamic behavior such as period doubling, bifurcations, and chaos. There is growing interest among researchers to understand this complex nonlinear behavior in microfluidic systems. Mathematical and numerical models are being developed to understand these phenomena. Recently, Schindler et al. (2008) proposed a simple circuit model for studying the droplet dynamics in a microfludic loop device. Remarkably, this simple circuit model was able to predict the complex behaviors in loop devices.

In this work, experimental evaluation of the predictive capability of the network model will be reported. Microfluidic devices containing a loop are fabricated in polydimethylsiloxane (PDMS) using accepted methods of soft lithography. The experiments are conducted with aqueous drops in an oil phase (hexadecane) stabilized with 2 wt% span80 as a surfactant. Experiments are conducted at constant flow rate conditions. Images are analyzed to obtain droplet entry and exit times in the loop. The network model has two free parameters, the hydrodynamic resistance of droplets (Rd), and the ratio of droplet to bulk velocity (β). The predictive capability of the model is evaluated by experimentally measuring Rd and β. The hydrodynamic resistance of the droplet is obtained by conducting experiments similar to that proposed by Vanapalli et al. (2009) and β is determined by analyzing droplet motion in rectilinear channels.

Poincare maps, residence times (time spent by the droplets in the loop) and sequence of the droplets exiting the loop are computed using the data obtained from experiments and simulations. Results obtained indicate that the network model reproduces the periodic and aperiodic behavior observed in experimental Poincare maps fairly well with a few exceptions. However, in terms of predicting the residence times and sequence of the droplets in the loop, the model needs to be improved to include: (i) the entrance effects of the droplets, (ii) the complex relation governing the velocity of the droplets as a function of flow rate, (iii) the nonlinear hydrodynamic interaction among droplets as a function of input flow rate, and (iv) finite size of the droplets.

References 1. Schindler. M and Ajdari. A ?Droplet Traffic in Microfluidic Networks: A Simple Model for Understanding and Designing?. Physical Review Letters, 100, February 2008. 2. Vanapalli, S. A., Banpurkar, A. G., van den Ende, D., Duits, M. H. G. and Mugele, F., ?Hydrodynamic resistance of single confined moving droplets in rectangular microchannels? . Lab on a Chip, 9, 982-990, 2009.