## 1 Introduction  
### Microfluidic Systems for Cellular Flow Manipulation  
Most of the in vivo and in vitro studies have been carried out at a bulk-level. Although these techniques bring invaluable critical insights into various fields, including biology and medicine, they usually lack single-cell resolution features to recognize cell heterogeneities associated with diseases. For studying rare cell events and the intermediate extracellular signaling, through which cells communicate, analysis tools with the micro-level resolution are of significant importance. Microfluidics chips offer new approaches for cell assays and have also been used for studying of cell biology by providing platforms for manipulating, separating, sorting, filtering, trapping, and detecting tiny biological particles based on cellular heterogeneity. They can simulate small-scale fluid flow and chemical gradients and offer full manual control over the particles to study the desired details, e.g., for food market, clinical, pharmaceutical, and other applications [1; 2; 3; 4; 5; 6; 7]. Precise manipulations such as focusing, separation, and fractionation of cells is a vital capability of microfluidics which can be achieved by engineering hydrodynamics forces based on unique physical attributes of cells such as size [8; 9], density [9; 10], deformability [11; 12; 13], and morphology [14] using variety of methods such as crossflow filtration [15], electrode arrays [16], optical force switching [17] and other methods, some of which can be found in detail in the review presented in [18]. In this spirit, hydrodynamic phenomena, which carry microenvironmental physical impacts on cells, are critical in almost all physiological functions and bodily systems. Generally, microfluidic devices can sort/isolate or partition cells by active approaches with external forces from acoustics [19; 20], magnetics [21; 22], and electrokinetics [23], as examples, as well as by passive approaches such as cellular immobilization [24], deterministic lateral displacement [25], and hydrodynamic filtration [26]. These devices have also been extensively used and proposed to study mechanical shear stress, and cell deformability and the recent advances of these applications can be found in [27; 28; 29; 30]. This is extremely helpful since deformability of RBCs (red blood cells) can represent a potential sign of several sicknesses [28]. Moreover, microfluidic devices have been proposed to study the possible effects of microbubbles in microvessels [28] to represent the effects of these bubbles, which can form in the blood vessels occasionally and cause possible pathological events, such as preventing the food to reach to the cells in specific regions. Also, targeted drug delivery via nanomaterials, such as carbon nanotubes, was introduced recently and significantly increased the efficacy of the drugs [31; 32; 33; 34]. As evaluation of these particles are highly dependent on their microenvironments, finding the optimum design point is facing some difficulties [35] and microfluidic systems can offer exceptional abilities to screen the nanoparticles to resolve these difficulties [1]. [PERSON] et al. [36] presented an in-dept review of nanoparticle delivery steps in cellular flows and summarized several microfluidic models specialized in nanoparticle evaluations related to such investigations. Particle sorting mechanisms are required to direct the drugs to the targeted cells, and numerical methods have proved themselves to be efficient in conducting such simulations [37; 38]. Microfluidic devices, generally, implement any one of the two different approaches; active approaches and passive approaches. In the latter, as opposed to former which relies on fluorescent labels or beads, a variety of techniques based on inherent differences in cellular morphology among cell groups (e.g., size, shape, compressibility, and density) are employed to sort cells.