Model equations for the calculation of the volume and surface of a sucrose crystal: a tool for accurate crystal growth rate determination

Abstract

Usually, crystal growth rate is expressed as a linear velocity deduced from the direct observation of the growth of individual crystals. In the general case of crystals grown in a pilot crystallizer or in an industrial pan, it is more convenient to express the overall growth rate in unit mass per unit time per unit crystal surface area. In the absence of direct measurement of crystal dimensions, such an expression necessitates the use of a shape factor relating the crystal surface to the volume (or mass).

We have used a model of a sucrose crystal with a simplified geometric shape to approach the practical problem of determination of crystal growth rates without the need to adopt empirical shape factors from the literature. The geometric model allowed establishing of model equations for the calculation of a sucrose crystal surface and volume and applying these equations to the determination of crystal growth expressed as mass unit per unit time and unit surface area of the growing crystal. The proposed model was validated by direct measurement of the dimensions of hundreds of crystals of different origins.

Comparison of the experimental sucrose crystal growth rates obtained by the end-to-end method and the rates calculated with the proposed model show a good fit. This work aims at making crystal growth rate determination less dependent on empirical shape factors and more accurate.