Ceramic dissolution within silicate melts is often caused by Marangoni convection arising from surface tension gradients, unless it is counteracted by forced convection, which typically occurs beyond a specific critical Reynolds number (〖Re〗_c). This study presents a method for determining the 〖Re〗_c required to suppress Marangoni convection at the alumina (Al2O3)/slag/air triple point. This approach utilizes a modified finger test device equipped with a high-resolution laser for dimensional measurement, allowing accurate determination of mass flux densities from the grove and mantle separately. Subsequently, we examined the dissolution of Al2O3 fine ceramics in a quaternary silicate melt of calcium oxide (CaO)–Al2O3–silicon dioxide (SiO2)–MgO (or magnesium oxide), featuring a CaO/SiO2 weight ratio of 0.65. The experiments were conducted at 1550 °C for speeds of 0, 50, 100, and 200 rpm. The findings revealed a critical rotational speed of 127 rpm for Al2O3-dissolution in this silicate slag at 1550 °C using the aforementioned device, corresponding to an 〖Re〗_c of 6.46. These results contribute to a deeper understanding of the factors influencing ceramic dissolution in silicate melts and offer valuable insights for materials and process engineering applications.