Amid escalating water scarcity and rising energy prices, the scientific community strives to propose innovative and efficient water treatment solutions. In this context, solar passive technologies have attracted much attention. Furthermore, recent studies have experimentally revealed that the Marangoni effect, when leveraged in well-designed passive devices, may be a promising pathway towards long-term stable performance. This study presents a comprehensive numerical exploration of applying the Marangoni effect to mitigate salt accumulation, a challenge in long-term system operation. Through an extensive sensitivity analysis, we evaluate the solute molar outflow induced by the Marangoni effect, as different parameters vary. Specifically, the Marangoni effect induces enhanced mass transport, outperforming pure diffusive flow by over three orders of magnitude, under nighttime isothermal conditions. Furthermore, we provide a semi-empirical equation describing accurately the mass transfer versus the Marangoni number. Hence, nighttime brine discharge simulations show rapid salt reduction from the evaporator, reaching seawater-like salinity levels within two hours, setting stage for optimal daytime performance. To the best of our knowledge, this discharge time is the lowest reported in the literature under equivalent conditions. In conclusion we believe that the still poorly explored Marangoni effect may offer a durable mean of providing freshwater, particularly in emergencies.