Abstract
We describe the design and operation of a Poiseuille Flow Crystalliser (PFC) that allows direct exploration of the effect of hydrodynamic and physico-chemical conditions on the aggregation of crystals growing in suspension. The PFC operates as a differential reactor where changes between inlet and outlet are small enough not to change the rate, but large enough to be measureable. Automatically measured changes in size distribution yield very clear quantitative evidence of aggregation. We use these data to explore the three open questions of Hounslow et al. (2013) and show how to average underlying point aggregation kinetics over a whole vessel and how to extract point data from average data. We introduce the critical aggregate size, D, as the particle size that at the average shear rate has a Mumtaz number, M=1, and so disruptive forces are in balance with the strength of growing bridges. In a study of rounded calcium oxalate monohydrate particles we show that values of D can readily be determined by fitting the change in size distribution in the PFC. We are able to discriminate among candidate models relating aggregation efficiency to M by means of an empirical fitting investigation and by directly determining the aggregation efficiency – both averaged and un-averaged for the vessel. We conclude that aggregate rupture happens under simple tension and that the effective average size of two colliding particles is their geometric mean. D2 is predicted and observed to be directly proportional to the ratio of crystal growth rate to flow rate squared. We demonstrate that no attractive or repulsive inter-particle forces are active in aiding or retarding aggregation in this system. The constant of proportionality from these results allows the material property controlling aggregation – the product of yield strength and a geometric factor with dimensions of length – to be determined as L⁎σY=1.35±0.01 Nm−1.
Highlights
In the first paper of this series (Hounslow et al, 2013) – to be referred to as Part I – we developed Mumtaz's theory (Hounslow et al, 2001) for the rate of aggregation of growing crystals in suspension in the context of a thorough literature survey
We describe the design and operation of a Poiseuille Flow Crystalliser (PFC) that allows direct exploration of the effect of hydrodynamic and physico-chemical conditions on the aggregation of crystals growing in suspension
In a study of rounded calcium oxalate monohydrate particles we show that values of D can readily be determined by fitting the change in size distribution in the PFC
Summary
In the first paper of this series (Hounslow et al, 2013) – to be referred to as Part I – we developed Mumtaz's theory (Hounslow et al, 2001) for the rate of aggregation of growing crystals in suspension in the context of a thorough literature survey. It is well established that when crystals are present in a supersaturated solution, relative motion will induce collisions and that some of those collisions will result in permanent attachment of the colliding crystalto each other. It is further well established that over a range of sizes and operating conditions the relative motion is induced by fluid shear so the collision rate can be described by rC 1⁄4 C0NINII ð1Þ where N is the number of particles per unit volume in suspension of “type” (e.g. size) I or II involved in a collision. We refer to particles in this work to mean any single, separate crystal or aggregate of crystals
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