The dynamics of micro-capsules has attracted a lot of attention in the last decade due to their vast applications in different industrial sectors such as cosmetic products, food industry, chemical processes, reaction systems, cell modeling, drug delivery, and medical processes. Additionally, biological cells such as red blood cells can be modeled as capsules. Understanding the rheological behavior of these cells provides great physical insight for early diagnosis of relevant diseases. The main objective of this research is to investigate the effects of physical and geometrical parameters on the hydrodynamics of simple and multiple capsules in complex mi- crofluidic devices.

For this purpose, we have developed the mathematical formulation needed for modeling multiple capsules with or without complex internal structures. The developed framework provides an enormous flexibility in problem definition, and facilitates the investigation of the hydrodynamics of a wide class of capsules in microfluidic channels and vascular capillaries.

We first study the deformation of a spherical capsule in a T-junction channel. It is shown that an initially spherical capsule develops a bean shape at low flow rates and an inverse kayak shape at high flow rates. Based on the non-trivial deformation of the capsule, a new methodology for the determination of membrane moduli is proposed. For an accurate determination of the membrane moduli, it is paramount to measure the capsule dimensions precisely, which is easier in the proposed device owning to the stagnation-point flow of the T-junction. To determine the membrane moduli, one needs to do a single experiment for different flow rates, and compare the experimental measurements of the capsule steady-state dimensions with the provided computational data.

We then consider the flow dynamics of non-spherical capsules and investi- gate the effects spheroidity and initial orientation on the steady-state shape. It is found that a non-spherical capsule, placed with a non-zero initial orientation angle along the centerline of a microchannel, does not practically rotate during deforma- tion. Thus, precise instrumentation is required for proper alignment of the capsule which influences the deformation and steady-state shape. This behavior may explain possible inconsistencies between measured (experimental) and calculated (compu- tational) shapes.

We then study the lateral migration of capsules with different size in a mi- crofluidic channel with a trapezoidal cross-section. Owing to the emergence of 3D printing technology, fabrication of a channel with trapezoidal cross-section is fea- sible. Based on our computational data, we proposed an optimized geometry that could be utilized for separation of capsules or cells with different size. The main

advantage of the proposed geometry is its inexpensive fabrication cost without the need for incorporating complicated inner structures, which automatically eliminates the risk of channel clogging. Moreover, the simple structure of the trapezoidal mi- crochannel allows an easy scale out through parallelization and reduction of the cell sorting time.

In addition, we investigate the complex behavior of two (equal or unequal sized) capsules flowing in a square microfluidic channel. Capsules merging process controls the on-demand drug release and reaction. Thus, we identified the hydro- dynamic conditions that facilitates or hinders the merging of the capsules. The merging process is commonly accompanied by the drainage of existing liquid film between two particles. We observed that the capsules merging in most cases is ac- companied by the formation of dimple surfaces, and thus a simplified flat lubrication surface assumption which is widely-used in the theoretical studies might not be an ideal choice for modeling the film drainage time in merging process.