Extracting the hydrodynamic resistance of droplets from their behavior microchannel networks

The overall traffic of droplets in a network of microfluidic channels is strongly influenced by the liquid properties of the moving droplets. In particular, the effective hydrodynamic resistance of individual droplets plays a key role in their global behavior. We here propose two simple and low-cost experimental methods for measuring this parameter by analyzing the dynamics of a regular sequence of droplets injected into an « asymmetric loop » network. The choice of a droplet taking either route through the loop is influenced by the presence of previous droplets which modulate the hydrodynamic resistance of the branches they are sitting in. We propose to extract the effective resistance of a droplet from easily observable times series, namely from the choices the droplets make at junctions and from the inter-droplet distances. This becomes possible when utilizing a recently proposed theoretical model, based on a number of simplifying assumptions. We here present several sets of measurements of the hydrodynamic resistance of droplets, expressed in terms of a « resistance length ». The aim is twofold, (1) to reveal its dependence on a number of parameters, such as the viscosity, droplet volume, their velocity as well as the spacing between them. At the same time, by using a standard measurement technique, we compare the limitations of the proposed methods. As an important result of this comparison we obtain the range of validity of the simplifying assumptions made in the theoretical model.

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