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The dynamics of an evaporating droplet in an unsteady flow is of practical interest in many industrial applications and natural processes. To investigate the transport and evaporation dynamics of such droplets, we present a numerical study of an isolated droplet in an oscillating gas-phase flow. The study uses a one-way coupled two-phase flow model to assess the effect of the amplitude and the frequency of a sinusoidal external flow field on the lifetime of a multicomponent droplet containing a non-volatile solute dissolved in a volatile solvent. The results show that the evaporation process becomes faster with an increase in the amplitude or the frequency of the gas-phase oscillation. The liquid-phase transport inside the droplet also is influenced by the unsteadiness of the external gas-phase flow. A scaling analysis based on the response of the droplet under the oscillating drag force is subsequently carried out to unify the observed evaporation dynamics in the simulations under various conditions. The analysis quantifies the enhancement in the droplet velocity and Reynolds number as a function of the gas-phase oscillation parameters and predicts the effects on the evaporation rate.