(300j) Highly Parallelized Microfluidic Manometry to Quantify Fluid Resistance in Complex Geometries

Measurement of pressure drop versus flow rate relations in microfluidic geometries is of broad interest in a variety of applications including particle separations, oil recovery, drag reduction and rheology of complex fluids. Demanded by the needs of these applications together with the advent of simple lithography methods has led to new capabilities to fabricate microfluidic conduits where not only the shape of the bounding walls can be arbitrarily varied (e.g., linear, sinusoidal) but also the internal space of the conduit can be laden with a variety of microstructures (e.g. pillars). As a result, the conduit design space is virtually infinite bringing in the challenge of how to quantify fluid resistance in a large number of microfluidic conduits, while maintaining operational simplicity.

Currently, computational fluid dynamics (CFD) is the main workhorse to determine fluid resistance in complex geometries. However, CFD approaches are rather cumbersome when a wide range of conduit geometries needs to be investigated, because mesh generation needs to be carried out every time the geometry is tweaked. Experimental approaches to determine fluid resistance in microscale geometries are also limited; most require either expensive precision sensors or complicated setups involving lasers, deformable membranes and multi-layer devices. These methods are inherently low throughput and are not scalable to quantify fluid resistance in a parallelized fashion. With such a large design space, it is advantageous to have a technique that is not only simple and easy to fabricate but can also test multiple designs in one device.

We have developed a new method for parallelized measurement of pressure drop verses flow rate relations for microfluidic conduits of arbitrary shape and complexity – that is only limited by the fidelity of fabrication. Our method involves integrating co-flowing laminar streams with microfluidic networks. We derive analytical expressions relating pressure drop as a function of system parameters. We quantify fluid resistance in a variety of rectangular ducts and find the results agree with theories of single-phase laminar flows.  We also measure pressure drop across many serially connected microfluidic conduits laden with microstructures and compare the results with literature values for porous media. Finally, we highlight the potential of this highly parallelized microfluidic manometry method for probing the rheology of complex fluids and mechanics of deformable particles.