Mesospheric CO₂ ice clouds on Mars are simulated with a 1D microphysical model, which includes a crystal growth rate adapted to high supersaturations encountered in the martian mesosphere. Observational constraints (crystal radius and opacity) exist for these clouds observed during the day around the equator at ∼ 60-80 km altitude. Nighttime mesospheric clouds interpreted as CO₂ ice clouds have also been characterized at low southern latitudes, at ∼ 90-100 km altitude. From modeling and observational evidence, it is believed that mesospheric clouds are formed within temperature minima created by thermal tides, where gravity wave propagation allows for the creation of supersaturated layers (cold pockets). Thus, temperature profiles perturbed by gravity waves are used in the model to initiate nucleation and maintain growth of CO₂ ice crystals. We show that it is possible to reproduce the observed effective radii for daytime and nighttime clouds. Crystal sizes are mainly governed by the altitude where the cloud forms, and by the amplitude of supersaturation. The temporal and spatial behavior of the cloud is controlled by the extent and lifetime of the cold pocket. The cloud evaporates fast after the cold pocket has vanished, implying a strong correlation between gravity wave activity and COv cloud formation. Simulated opacities remain far below the observed ones as long as typical dust conditions are used. In the case of the lower daytime clouds, the enhanced mesospheric dust loading typically reached during dust storm conditions, allows for greater cloud opacities, close to observed values, by supplying the atmosphere with condensation nuclei. However, CO₂ ice clouds are not detected during the dust storm season, and, because of fast sedimentation of dust particles, an exogenous supply (meteoritic flux) appears necessary to explain opacities of both daytime and nighttime mesospheric CO₂ ice clouds along their whole period of observation.