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Most simulations of atmospheric phenomena – including both large-eddy simulations (LES) and direct numerical simulations (DNS) – assume phase equilibrium between the liquid and the vapor phases of water. This assumption, however, implies that the relaxation processes for supersaturation fluctuations act on by far shorter time scales than the fastest convective scales, which is debatable for realistic atmospheric conditions. Stratocumulus clouds play an important two-fold role in the Earth's climate as they can have a cooling effect by reflecting large portions of solar radiation to space on the one hand, but insulating the Earth's surface at night on the other hand. An accurate representation of their formation and lifetime in climate projections, calls for a better understanding of the role of supersaturation fluctuations. Here, we investigate the influence of "slow" saturation adjustment on cloud entrainment and desiccation for stratocumulus clouds.The relative importance of supersaturation fluctuations can be quantified in terms of a Damköhler number Da=τfl/τph defined as the ratio of the flow's mixing time scale τfl over the phase relaxation time scale of supersaturation τph. While the assumption of phase equilibrium corresponds to Da→∞, estimates of realistic atmospheric conditions rather suggest an effective Daη=O(10-2–10-1) with respect to the smallest flow scales, i.e., the Kolmogorov time scale. This indicates that supersaturation fluctuations begin to play a more prominent role.We perform 3D DNSs of a (stratocumulus) cloud-topped convective boundary layer at Re=5000 and analyze the influence of "slow" supersaturation relaxation for 10-2≤Daη≤101 compared to the case with phase equilibrium assumption Daη=∞. The supersaturation in our simulations is limited to the cloud layer and therein mostly correlating with ascending flow. The largest values of supersaturation up to 4% are found at the cloud base, while within and at the top of the cloud layer, supersaturation is mostly limited to a few tenths of percent. In contrast to these local extreme values, we find that, spatially, cloud bulk and top are (super)saturated to a greater extent than the cloud base. Most crucially, we find that the clouds liquid water content is decreasing for Daη>1, while it is stable for Daη≈1 and even increasing for Daη