The blood circulation carries valuable information about the human body's functioning. Thus, there is a continuous need for novel, accurate, and fast techniques to analyse blood samples. The objective of this research is to design, numerically simulate and optimize a low-cost microfluidic lab-on-a-chip device, which, in the future, can be used to quickly help the diagnosis of different diseases, by using a single drop of blood from a patient. The designed microdevice includes two fluid inlets, an outlet, a serpentine area for achieving a fully developed continuous flow, as well as a detection chamber able for optical measurements. The numerical model of the designed microdevice was computed in COMSOL Multiphysics, taking into account the flow and tracing of microparticles that mimic blood cells. In order to reach the optimal lab-on-a-chip geometry, i.e., achieving a high and stable number of particles in the detection chamber during the entire microfluidic assay, the inlet velocities, the channel width, and the diameter of the detection chamber were individually optimized. A mesh study was also performed to improve the accuracy of the results, aiming the lowest computational effort. From the obtained results, it was observed that a lab-on-a-chip geometry with a 1 mm channel width and a 3 mm detection chamber radius, with fluid inlet velocities, for both particles and buffer fluid, of 1 mm/s, was the one with the most interesting results for the intended application, with a relatively constant number of particles flowing through the detection chamber (more than 2000 particles, on average, for the selected inlet conditions).