We present the first computational study of the dynamics of inertial particles in a shearless turbulence mixing layer. We parametrize our direct numerical simulations to isolate the effects of turbulence, Reynolds number, particle inertia, and gravity on the entrainment process. By analysing particle concentrations, particle and fluid velocities, particle size distributions, and higher-order velocity moments, we explore the impact of particle inertia and gravity on the mechanism of turbulent mixing. We neglect thermodynamic processes, including phase changes between the drops and surrounding air, which is equivalent to assuming the air is saturated (i.e. 100 % humidity). Entrainment is found to be governed by the large scales of the flow and is relatively insensitive to the Reynolds number over the range considered. Our results show that both fluid and particle velocities exhibit intermittency and that gravity and turbulent diffusion interact in unexpected ways to dictate particle dynamics. An analysis of the temporal evolution of fluid and particle statistics suggests that particle concentration profiles and velocities are self-similar under certain circumstances. We also observe large fluctuations in particle concentrations resulting from entrainment and introduce a model to estimate the impact these fluctuations have on the radial distribution function, a statistic that is often used to quantify inertial particle clustering. Our study is both a computational counterpart to and an extension of the wind tunnel experiments by Gerashchenko, Good & Warhaft (J. Fluid Mech., vol. 668, 2011, pp. 293–303) and Good, Gerashchenko, & Warhaft (J. Fluid Mech., vol. 694, 2012, pp. 371–398). We find good agreement between these experimental studies and our computational results. We anticipate that a better understanding of the role of gravity and turbulence in inertial particle entrainment will lead to improved cloud evolution predictions.