The dynamics and ordering of droplet monolayers in strongly confined suspensions

The dynamics of droplet suspensions is strongly affected by confinement in Hele–Shaw flows. In particular, in a strongly confined Couette flow the veloc- ity field scattered from the particles promotes the spontaneous formation of or- dered drop microstructures. This phenomenon has been experimentally observed in Stokes flow regime by several research groups. To explain the experimental observations, I have worked on developing a reduced hydrodynamic model uti- lizing a combination of Hele–Shaw multipoles and the swapping-trajectory effect to numerically predict the droplet motion. According to my simulations, the Hele– Shaw quadrupolar interactions are the main governing hydrodynamic mechanism responsible for the self-assembly and further rich dynamics of the droplet mi- crostructures. A comparison between the simulation results from the reduced model and direct simulation data provided by our collaborators at the George Washington University shows that the model correctly captures the droplet chain formation and subsequent dynamics [Singha et al. Soft Matter, 2019,15, 4873-4889]. Driven by incident Couette or Poiseuille flow, droplets already arranged in linear chains exhibit diffusive or wave-propagation dynamics. According to my calcu- lations, the symmetry of the interparticle interactions (which depends on the type of the incoming flow) determines the type of the chain dynamics. Experiments conducted by our collaborators in the Chemical Engineering Department at Texas Tech University show that in a strongly confined Poiseuille flow emulsion droplets exhibit large velocity fluctuations. We used a modified version of our Hele–Shaw model to investigate the system and found that dipolar interactions are the pri- mary mechanism governing the droplet dynamics. We determined that the ob- served velocity fluctuations originate from the variation in the mobility of elon- gated droplet clusters [Darabad et al. arXiv:2102.02774v1].

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