(378f) Crystal Wet Milling and Particle Attrition in High Shear Mixers
Based on the literature, it was reasoned that along with size and shape, stress intensity factor (or fracture toughness) and hardness are the important physical properties affecting breakage rate. To vary these properties, several crystalline materials were milled in anti-solvents (e.g. sugar in isopropyl alcohol) to allow discrimination between mechanical size reduction and solubility effects. Collision rates were varied by changing particle concentration; and coatings and small geometric changes were used to consider interactions with solid surfaces. Rotor speed and volumetric throughput were adjusted to independently vary energy input and mill head residence time. By varying operating conditions, mill head geometry and crystal mechanical properties, it is possible to discriminate among various crystal fracture (e.g., plastic vs. elastic deformation) and particle breakage mechanisms (e.g., fluid shear, particle-particle collisions, particle-blade collisions) to develop mechanistic relationships which aid in process scale up and serve as inputs to population balance models and other models for the evolution of the crystal size distribution.
Crystal mechanical properties were measured with a Hysitron TriboIndenter. Particle size distributions were measured by several methods. A Lasentec focused beam reflectance measurement (FBRM) probe and Particle View Microscope (PVM) were placed in the holding tank to continuously monitor particle size and suspension uniformity. Grab samples, acquired in the holding tank at well-defined time intervals, were analysed using a Horiba laser diffraction instrument and by microscopy with an automated image analysis technique. Based on the results appropriate diameters were defined to track the milling rate and ultimate size of the largest surviving particles as well as the characteristics of the fines produced via attrition from the parent crystals. CFD simulations were conducted to estimate the power draw for different rotor speed and rotor and stator gap clearance.
Classical grinding relations show a different dependency on particle size (e.g. proportional to size, surface area, volume, etc.) for the impact energy needed to fracture a particle. For particles colliding with a solid surface, Gahn and Mersmann (1997) and Ghadiri and Zhang (2002) have developed mechanistic models for fracture based on elastic and plastic deformation of the crystal, respectively. In this study, we also consider the case where both elastic and plastic response is important. This gives rise to a series of models that have their roots in the classical grinding relations, where the cohesive force resisting breakage can be identified and employed to construct and contrast correlations of practical utility. To this end, it is proposed that both macroscale (related to tip speed) and turbulent inertial subrange scale (related to power per mass) collision velocities can be responsible for breakage. This leads to a class of mechanistic models for the maximum stable crystal size and well as the breakage rate and production rate of fines. Model discrimination is based on comparison to the data.
The mechanistic theory is further exploited to provide breakage kernels based on probability of collision and collision rate theories. Application of the breakage functions to predict the attrition rate as well as their implementation within a Population Balance framework is discussed. The results of this study are not restricted to rotor-stator mixers; the scaling laws, non-dimensional correlations, and breakage functions developed here can be applied to mixing processes in which particle breakage occurs according to the same mechanism(s).