## 1 Introduction  
Flows in microsystems, to a large degree, are influenced by boundaries, much more than macro-flows. It is not only because of a large surface-to-volume ratio, but also due to high-velocity gradients that can be easily achieved through microchannels, even in the Stokes flow regime (\(\mathrm{Re}\ll 1\)) at low mean fluid velocities (\(u<1\cdot 10^{-3}\) m/s) [1]. The phenomena are the basis of inertial microfluidic platforms. Additionally, in the intermediate range of laminar flow (\(\sim\)1 \(<\) Re \(<\) -100), nonlinear and irreversible motions of fluid and particles [2, 3] are observed. Moreover, in the laminar flow regime, geometry-induced flow patterns are commonly observed and employed, e.g., secondary flow in curved channels (Dean flow) for fluid mixing [4] and particle separation [5], or lateral flow, serpentine flow, pinched flow, multi-orifice flow, etc., for cell sorting [6]. The channels' inlets and outlets can also play a significant role in forming the flow structure, especially in short and wide channels such as cell culture chambers (CC), but there is a lack of analysis in the literature of such effects. As in our invented microdevice, the advective flow of medium in CC is responsible for gradient generation and can influence cytotoxicity, mortality, and morphology cells [7], we will precisely analyze the hydrodynamics of fluid flow in CC using our computational fluid dynamics (CFD) tool Microflow 3D, that is a lattice-Boltzmann method (LBM) solver designed for flow simulations in microsystems and circulatory systems. Recently, the LBM method has been successfully applied for analysis of the transport of particles and fluids through multichannel microfluidic networks [8] or droplets' formation and manipulation in lab-on-a-chip microfluidic systems [9; 10], and also to analyze the particle inertia and volume fraction effects on colliding particle-pairs in turbulent microflows [11]. The superiority of LBM over other CFD methods lies in the locality of the algorithm. Interactions between nodes are entirely linear, while the method's non-linearity enters a local collision process within each node [12]. This property makes the LBM very amenable to high-performance computing on parallel architectures, including GPUs [13; 14]. The key advantage of LBM from the viewpoint of microfluidics is the adequacy for simulation of mesoscopic physics and multi-scale effects, which are hard to describe macroscopically. Lab-on-a-chip devices, in particular biochips, have become a powerful analytical tool that brings together multiple disciplines for biomedical research and has the advantages of miniaturization, automation, integration, and portability [15]. They are natural candidates for a future replacement of standard laboratory equipment and protocols in drug development pipelines. Currently, in vivo animal models are commonly used for preclinical drug validation, but only 8% of successful animal trials for cancer drugs translate to successful human clinical trials due to specific differences in physiology and cell biology [16]. Due to ethical issues, high costs, and inconvenience of animals' breeding, there has been increasing research in mimicking in vivo conditions with micro-physiological systems (MPS), such as tissue-on-a-chip and organ-on-a-chip [17; 18]. MPS models are able to recapitulate the function of human organs and tissues with so far unreachable accuracy, which offers a chance of reduction of present high failure rates in drug development pipelines [19]. Recently, we have developed a simple construction biochip for high-throughput drug screening (HTS). The chip mimics a complex microenvironment of tumor tissue with greater accuracy than standard multi-well-plate cultures, offering at the same time even higher throughput with the same ease of use. The biochip with a developed gradient of dyes is presented in Figure 1. The main structural elements of the microsystem are three identical cell culture chambers with dimensions of 59/4.1/0.13 mm (L/W/H).