Crystal growth in flowing solution, observations and modelling.
Résumé
Numerous studies and observation have been made on the influence of flow to crystal growth in solution. Previous observations of growth bands in natural galena suggests that upstream crystal faces possess a higher growth rate (Kessler et al. 1972). Flow control on crystal growth is complex and different approaches have therefore been considered. Studying at very thin scale focuses on crystal face behaviour with effect of flow on crystals defects (e.g. step bunching; Chernov 1992 and 2004). At crystal scale several observations and models propose to link crystal shape and growth kinetics to fluid flow. Experiments showed that in case of volumic diffusion, the bulk crystal growth rate is proportional to the inverse of the square root of the flow kinetics (Garside et al. 1975). By experiments on ammonium-dihydrogen phosphate (ATP) (Prieto & Amoros 1981) and This work concerns a very simple and well-defined geological situation: calcite-rich precipitate formed in a horizontal pipe channelling hot water (82°C) of hydrothermal spring in Chaudes-Aigues city (French Massif Central). Shape preferred orientation statistics were performed on 563 calcite sections in the (0001) calcite plane, shows elongated shapes with a general orientation parallel to the pipe axis. The mean shape orientation is the average of two distinct sub-populations that deviated slightly from the pipe axis. Observation on calcite shapes and the direction of the magnetic lineation are coherent, and suggest that it is possible to track hydrothermal paleo-circultion using magnetic lineations and petrographic fabrics. The proposed crystal growth model is based on the work of Gilmer et al. (1971). These authors consider two kinds of processes: diffusion of solute through a volume of unstirred liquid (i.e. boundary layer) to the crystal surface and reactions at the surface leading to the incorporation of molecules in the lattice. When the boundary layer is thicker, the diffusion process becomes slower and controls the crystal growth rate. Thus, it is possible to establish a quantitative link between growth rate and fluid velocity. Such equation has been only demonstrated in the case of crystal face parallel to fluid flow (Carlson 1958; Gilmer et al. 1971). This work proposes to estimate crystal growth rate in flowing solution based on diffusion through the boundary layer thickness. This latter is defined by a combination of diffusion law with fluid dynamical equation simplified for high Reynolds number and for crystal faces orientated from 90° to –18° as function of the flow. The proposed growth rate equation depends on two main parameters: (a) the position along the face and (b) the angle made by flow with the crystal face. The growth rate equation is proportional to the square root velocity and is in agreement with the Garside et al. experiments (1975). More over, this model is applied to calcite growth rate in 2D section perpendicular to the axis. The calcite shape reconstruction is similar to the texture observed at Chaudes Aigues. The differential growth rate with exposition allows to explain the elongated shape of the calcite crystal observed in the pipe. This approach may be applied for various geological setting, from deep metasomatism to flowing on the earth surface.