Modeling of Fluid Flow and Heat Transfer in a Hydrothermal Crystal Growth System: Use of Fluid-Superposed Porous Layer Theory

Abstract

Hydrothermal synthesis, which uses aqueous solvents under high pressure and relatively low temperature, is an important technique for difficult to grow crystalline materials. It is a replica of crystal growth under geological conditions. A hydrothermal growth system usually consists of finely divided particles of the nutrient, predetermined volume of a solvent and a suitably oriented crystal seed (Fig. 1) under very high pressures, generally several thousand bar. The nutrient dissolves at a higher temperature in the lower region, moves to the upper region due to buoyancy-induced convective flows, and deposits on the seed due to lower solubility if the seed region is maintained at a lower temperature. The system can be modeled as a composite fluid and porous layer using the Darcy-Brinkman-Forchheimer flow model in the porous bed. Since the growth process is very slow, the process is considered quasi-steady and the effect of dissolution and growth is neglected. This first study on transport phenomena in a hydrothermal system therefore focuses on the flow and temperature fields without the presence of the seed and mass transfer. A three-dimensional algorithm is used to simulate the flow and heat transfer in a typical autoclave system. An axisymmetric flow pattern at low Grashof numbers becomes three-dimensional at high Grashof numbers. A reduction in the porous bed height for fixed heated and cooled regions can result in oscillatory flows. These results, for the first time, depict the possible flow patterns in a hydrothermal system, that can have far reaching consequences on the growth process and crystal quality.