Computational modeling of the driven flow of multi-component fluids past chemically, physically and thermally heterogeneous substrates can provide insight into a variety of processes, from flow in microfluidic devices to polymer processing in reaction chambers. One of the challenges in modeling these systems is capturing the close interplay between hydrodynamics and thermodynamics. The lattice Boltzmann method (LBM) provides a computationally efficient method for carrying out such investigations. We review recent studies using the LBM to examine the flow of partially miscible binary fluids through channels that contain chemically, topographically or thermally patterned substrates. The findings highlight how the substrates can be modified to yield the required behavior at fluid/surface and fluid/fluid interfaces and consequently, the desired macroscopic properties. Specifically, the results provide guidelines for optimizing processes in microfluidic devices and in creating microemulsions with well-controlled morphologies. The studies also reveal new phenomena that arise from the interplay between flowing complex fluids and chemically, physically and thermally patterned confining walls.
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