Mixed-phase clouds, which consist of ice particles, supercooled liquid droplets and water vapor, play a significant role in global precipitation and energy budget. This thesis explores the mixed- phase processes in a cloud chamber using the University of Warsaw Lagrangian Cloud Model. The study explores the Wegener-Bergeron-Findeisen (WBF) process, in which ice particles grow at the expense of liquid droplets due to the difference in saturation vapor pressures. Numerical simulations of mixed-phase clouds are performed. The simulation setup is based on experiments performed in the Pi Chamber at the Michigan Technological University. The Super-Droplet Method is used to assess the evolution of size distributions and concentrations of supercooled droplets and ice particles. The results are compared with laboratory measurements from the Pi Chamber. It is found that mixed-phase clouds in the Pi Chamber are stable. The liquid water is not fully depleted by the WBF process because new CCN are constantly injected and cloud droplets form in regions of supersaturation. The clouds are in a steady state, because the injection of particles is balanced by their removal by gravitational settling. In clouds with a fixed forcing of supersaturation and a constant injection of CCN, the cloud properties are controlled by the ice injection rate. The probability distribution functions of particle diameter obtained in this study are in agreement with those measured in the Pi Chamber by Desai et al. (2019).