Numerical Simulation Of Droplet Rheology In Microfluidic Devices

Microfluidics is the science and technology of systems that process or manipulatesmall (10-9to10-18litres) amounts of fluids, using channels with dimensions of tens tohundreds of micrometres. Due to the microscale, precise control of laminar flow andmany other attractive features, microfluidics has received a good deal of attention inrecent years. Various droplet-based microfluidic devices have been designed andwidely applied in many research areas such as biology, material and medicine.In this paper, we employ a two-dimensional spectral boundary element methodwhich exploits all the benefits of the spectral methods and boundary element methodsto numerical simulate the microfluidic rheology. Besides, we employ the self-adaptmesh restructuring algorithm to enhance the numerical instability, through an explicittime-integration algorithm (fourth-order Runge-Kutta method) to solve the kinematiccondition at the interface, and use mesh splicing to simulate the process of dropletbreakup.In this paper, our numerical methods were translated into Fortran program. Theprogram was debugged and executed in the Compaq Visual Fortran6. Employing thecompiled program, we can obtain the computational results of droplet rheology in thecross-slot, MFRM and T-juction micro devices.The deformation and breakup of droplets in cross-slot are similar to those inT-junction. Flow stagnation point exists in both case, and the location of the pointrelates to the geometry of the micro channels and various flow rates of the outlets.However, the restriction effect of geometry on droplet deformation in T-junction ismore significant. Through controlling the flow stagnation point and the initial locationof the droplet centroid, we can operate the deformation and breakup of dropletssymmetrically or asymmetrically with precise control and reproducibility. Besides, wehave investigated the effects of physical parameters and geometry on the interfacedynamic.Comparing to simple microfluidic devices like the cross-slot and T-junctionwhich can only generate a single fixed flow type, MFRM can produce the entirespectrum of flow patterns by adjusting the ratio of volume flow rates. Thus, a continuous manipulation of droplets can be done through the variation of flow fields.Behaviors of deforming or rotating droplets trapped in a MFRM are determined bythe size of orifices connecting the channels (inlets and outlets) and the central cavity,and the volume flow rate of the continuous phases (CP) pumped into and out of thedevice, especially for the rotation of droplets. In this paper, through numericalcomputation and an approximate analysis of order of magnitude, a simple conclusionthat the average angular velocity of the rotation is proportional to the volume flowrate CP at inlets and the radius of the central cavity is presented. Besides, theappropriate radius of the central cavity which directly determines the size of theorifices is specified through the analysis of the flow fields. These results are helpful indesigning a MFRM with a much larger depth than the width of the micro-channel forthe purpose of microfluidic rheometry.