(550c) Particle Manipulation and Active Mixing of Trapped Droplets

The problem of particle trapping and manipulation has a wide range of applications in biotechnology and engineering. Recently, a flow-based, particle-trapping mechanism called the Stokes trap was developed to allow for trapping and control of small particles in microchannels [1]. This mechanism consists of trapping particles in the intersection of multiple branches in a microfluidic channel. The motion of such particles can then be controlled by changing the flow rates in the branches. For deformable particles, droplets and vesicles, this mechanism can also be used to perform rheological experiments to determine the viscoelastic response of an emulsion or cell suspension [2]. Besides these applications, the various flow modes produced by the Stokes trap can also be used to manipulate the shape and even induce internal mixing in droplets. In this work, we analyze the dynamics of a droplet in a Stokes trap through boundary-integral simulations [3]. We also explore the response of drop shape with respect to distinct external flow modes, which allow us to perform numerical relaxation experiments such as step strain and oscillatory extension. A linear controller is also used to manipulate drop position, and the drop deformation is characterized by a decomposition of the shape into spherical harmonics. For droplets with small deformation (e.g., small radii and/or capillary number), we observe a linear superposition of harmonics that can be used to manipulate drop shape. We also investigate how the different flow modes may be combined to induce mixing inside the droplets by performing a mixing-number analysis [4]. The transient combination of modes produces an effective chaotic mixing inside the droplet, which can be further enhanced by changing parameters such as viscosity ratio and flow frequency.

[1] Shenoy A., Rao C. V., Schroeder C. M. Stokes Trap for Multiplexed Particle Manipulation and Assembly Using Fluidics. Proc. Natl. Acad. Sci. U.S.A. , 113 (15), 3976–3981, 2016.

[2] Lin C., Kumar D., Richter C. M., Wang S., Schroeder C. M., Narsimhan V. Vesicle Dynamics in Large Amplitude Oscillatory Extensional Flow. J. Fluid Mech., 929, A43, 2021.

[3] Roure G., Zinchenko A. Z., Davis R. H. Numerical Simulation of Deformable Droplets in Complex-Shaped Microchannels. Phys. Rev. Fluids (under review), 2023.

[4] Stone Z. B., Stone H. A. Imaging and Quantifying Mixing in a Model Droplet Micromixer. Physics of Fluids 17 (6), 063103, 2005.