Reconstruction of the Interface between two Fluids in Microfluidic Devices using Astigmatic Particle Imaging.

In many microfluidic applications, two or more liquid species are present and interact with each other. In many cases, information about the contact surfaces between the species is required to characterize fluid phenomena or the perfor- mance of the device. One example is given by micro-mixers, in which the low Reynolds numbers applied cause convective mixing to be limited and diffusion becomes the primary mechanism of interaction between two species. For this reason, passive micro-mixers use particular channel geometries at these Reynolds numbers, to establish secondary flow patterns, increasing the contact area between the two mixing species, functional for diffusion, thus increasing the mixing potential. The measurement of the contact surface between the two fluids is critical to properly characterize the mixing efficiency at these scales. At present, to experimentally characterize the convective interaction between two fluids, in a microfluidic mixer for instance, dye visualizations are used. However, these methods generally give an averaged concentration value over the optical axis, and do not provide adequate information about complex topologies of the contact areas between the two fluids. In this work, a novel technique that reconstructs the contact area between two fluids in a microfluidic device is presented. A homogeneous dispersion of tracer particles is introduced in the flow of one of the two inlets of the micro-mixer. Since the tracer particles only belong to that flow, and the diffusion of the tracers is negligible, as proven experimentally, the stream of tracer particles can give an insight on the spatial distribution of the two flows. The 3D position of each particle in the measurement volume is obtained using an imaging method based on an optical aberration called astigmatism to code the depth position of the particle. Spatial concentration of particles in the measurement volume is therefore computed on a Cartesian lattice. To control the uncertainty due to undersampling, smearing out small fluctuation, the computed concentration undergoes a simulated time-diffusion process in the Matlab environment (3D explicit finite difference with free boundary condition). The contact area between the two species is visualized by the iso-surface of the particle con- centration, with the concentration equal to 0 in one fluid, and larger than 0 in the other. The technique is demonstrated for different Reynolds numbers on a passive micro-mixer.