## 3 Results and Discussion  
### Model Validation  
We have analyzed the liquid flow hydrodynamics in the device's CC, performing numerical simulations of the LBM/CFD method for the same geometry and conditions as present in the device's standard operation protocols [20]. The simulation results were compared with the experimentally determined overall volumetric flow rates of the fluid in CC. The average value of predicted velocity magnitude for the cross-section A (Figure 2)was \(5.79\times 10^{-3}\) m/s, and its maximal value was observed in the channels' axis as \(8.93\times 10^{-3}\) m/s, which gives the value of mean volumetric flow rate in CC as \(2.85\times 10^{-9}\) m\({}^{3}\)/s. This value is in good agreement with the experimentally determined volumetric flow rate, \(V\), of cell culture medium in the microdevice's CC, sloped at an angle of 30\({}^{\circ}\). The median value of \(V\) for three different microsystems (CI-CIII), and the three repeats of experiments (1-3) for each device with five repetitions of measurement (45 points), was slightly higher, at 3.036 \(\times\) 10\({}^{-9}\) m\({}^{3}\)/s, with the standard deviation (SD) of 3.8% (Figure 3). Thus, the relative error of volumetric flow rate prediction was 6.1%, and it does not go beyond the acceptable ranges for engineering calculations. Looking at Figure 3, we can see that the determined values of flow fluctuations in CC are quite large (2.8-3.3 \(\times\) 10\({}^{-9}\) m\({}^{3}\)/s). The flow fluctuations are a well-known issue and source of errors in continuous-flow microsystems, where the very small flow rates have to be controlled and stabilized in time (at the level of microliters per second). Fortunately, this is not a problem for the proper operation of our solution, because the volumetric flow rate deviations do not affect changes of the shape of the velocity profile in CC as long as flows are laminar, and consequently do not have an impact on the proper development of a gradient. The median value of the Reynolds number calculated from experimentally determined flow rates is Re = 1.44, which confirms the deep laminar regime of the chip operation. In Figure 4, simulated velocity profiles are compared with an algebraic solution of the NSE for the rectangular duct (Equation (7)). The Poiseuille number, Po = 23.09, for the rectangular duct was calculated according to the formula provided by [PERSON] and [PERSON] [PERSON] and [PERSON] (2018). The mean and median values of the relative velocity prediction error for the CC cross-section A (Figure 2) were 1.0% and 0.93%, respectively. Its maximal value reached 16.8%, but the minimal observed fluid velocity prediction error was only about 0.03%. The distribution of the relative error of the simulation is presented in Figure 5.  
Figure 3: The experimentally determined values of volumetric flow rates in CC for a device sloped at an angle of 30\({}^{\circ}\). The largest difference between the simulation results and the algebraic solution of the NSE is noticed in the first row of nodes adjacent to the shortest edge of the duct (the height of the channel). For the axial lines C and D (Figure 2), the mean relative velocity prediction errors were 0.85% and 0.95%, respectively. The obtained fluid velocity profiles in CC are parabolic in the Z direction (C axial line) (Figure 6a), while in the Y direction (D axial line), they are nearly flat and correspond to the plug-flow profile (Figure 6b). The plug-flow-like profile is responsible for the even distribution of species across the CC, while the parabolic profile allows the development of the linear gradients along the CC during fluid reciprocating flow. The lattice-Boltzmann model of liquid flow in culture chambers of the microdevice predicts fluid velocity distributions with high accuracy. In regions where we could expect the almost fully developed velocity profile, the prediction error is less than 1%, compared to the analytical solution of NSE.