As inertial microfluidics is a proven technique for manipulating particles within microchannels, a deep understanding of hydrodynamics forces acting on particles in these systems is crucial for optimal manipulation. However, existing numerical techniques for examining particle equilibrium positions are often time-intensive and require high-memory systems, limiting accessibility due to complexity and cost. To address this issue, this study proposes a method to develop a correlation for fast estimation of particle equilibrium positions. An algorithm is devised to develop the correlation in three main steps: first, a dataset is created by conducting simulations using the finite element method, considering width, height, flow rate, particle size, and curvature radius. The computed distance between the equilibrium position of the particle and the inner channel wall serves as input for the next step where a general form of the correlation is established using Buckingham's Pi-theorem. The unknown coefficients of the correlation are calculated using 80 percent of the dataset from the first step and the least sum squares errors method. Finally, the obtained correlation is validated using the remaining data and previous experimental studies. The proposed correlation reduces the computational burden associated with predicting particle focus positions, with a 3.7 percent mean absolute error.
