Modeling the growth of large, single crystals from liquids is significantly complicated by free or moving boundaries, which are defined by thermodynamic phase transitions between liquid and solid. Their presence makes domain shapes part of the solution and introduces strong nonlinearities. Effective algorithms for such problems are now well established, and modeling has advanced the understanding of many crystal growth processes [1]. We have recently developed a quasi-steady-state (QSS), finite-element model for the high pressure, high temperature (HPHT) growth of diamond single crystals [2]. These processes are able to produce high- quality, centimeter-size diamonds from a metallic liquid flux at pressures of 50,000 atmospheres and temperatures of 1,500 K, mimicking the conditions under which diamonds grow in the earth's crust. An important feature of the HPHT crystal growth process is a dissolving carbon source that is placed in the growth cell to feed the growing diamond crystal. In [2] and all other prior models, the location of this dissolution interface is simply prescribed at a fixed location for every stage of growth. Here, we present a rigorous QSS formulation to solve for the location of the carbon-liquid dissolution free boundary. This interface is in local thermodynamic equilibrium, and carbon fluxes across the interface must balance. These two conditions are simultaneously satisfied via solution of species transport through the liquid and the location of the free boundary. However, well-posedness also dictates a global species constraint to determine the QSS velocity of the dissolving interface. To our knowledge, this formulation has never before been applied to this or similar problems in which a dissolution boundary is present, such a physical and chemical vapor transport (PVT and CVT) growth processes. New simulations demonstrate how the shape of the dissolution interface affects liquid flows, carbon transport, and crystal growth. REFERENCES [1] J.J. Derby, "Modeling the growth of bulk, single crystals: Seeing what is hidden," Annu. Rev. Chem. Biomol. Eng. 16, 217–48 (2025). doi:10.1146/annurev-chembioeng-082223-110559 [2] S.S. Dossa, I. Ponomarev, B. Feigelson, M. Hainke, C. Kranert, J. Friedrich, and J.J. Derby, "Analysis of the High-Pressure High-Temperature (HPHT) growth of single crystal diamond," J. Crystal Growth 609, 127150 (2023). doi:10.1016/j.jcrysgro.2023.127150