(164f) Sonofragmentation: Experimental Observations and Population-Balance Modeling

The application of high-intensity ultrasound to the crystallization of active pharmaceutical ingredients (APIs) has been a topic of recent interest; judicious application of ultrasound can induce crystallization with relatively short induction times and improve reproducibility and has the potential to improve the control of polymorphism, particle shape, and crystal size distribution. A variety of empirical work has been performed in this field, but the understanding of the underlying principles remains largely undeveloped.

The effects of high-intensity ultrasound arise primarily from acoustic cavitation, that is, the formation, growth, and implosive collapse of bubbles. The conditions in the bubble can reach thousands of degrees Kelvin and hundreds of atmospheres. These extreme conditions have been exploited to drive high-energy chemical reactions. Acoustic cavitation can generate shockwaves into the liquid (which can induce high-velocity inter-particle collisions) and can create microjets at liquid-solid interfaces (which can pit surfaces or break particles). The chemical and physical effects of ultrasound have been catalogued in detail for homogenous systems and heterogeneous mixtures involving inorganic solids such as metal powders.

The physical effects of ultrasound on friable organic crystals, such as APIs, are less well developed. An understanding of these effects is needed to be able to predict and control the effects of sonication on particle size and morphology post-crystallization, and to possibly extract the contribution of secondary nucleation via particle breakage during ultrasonically-induced crystallization (sonocrystallization). We present here a systematic study of the effects of experimental parameters on particle attrition, using aspirin (acetylsalicylic acid) as a model material. Specifically, the effects of sonication time and intensity have been explored, as well as solvent properties such as vapor pressure and viscosity. The effects of particle loading have also been examined. Some sample results are reported in Figure 1, which show the nonlinear dependency of the particle breakage with ultrasonic intensity. A factor of two change in the ultrasonic intensity is observed to typically result in about a factor of two change in the average particle volume.

Figure 1. Left: optical micrographs of aspirin crystals broken by ultrasonic irradiation. Right: average size of aspirin crystals after sonication as a function of ultrasonic intensity. All experiments correspond to the exact same initial conditions followed by one minute of total ultrasonic irradiation using a 20% on/off pulse cycle. The average particle volumes at the right were determined by image analysis of optical micrographs of the product crystals.

Additional experiments were designed and performed to elucidate the mechanism of particle breakage. Based on the literature it was not immediately evident whether particle-particle collisions, particle-horn collisions, particle-cell collisions, or particle-shockwave interactions were primarily responsible for the observed effects. Experiments that were carefully designed to decouple these effects will be described that implicate direct particle-shockwave interactions as the dominate mechanism of particle breakage. The presentation will also include a real-time movie taken by in-situ optimal video microscopy that allows a visual observation of the fluctuations of a cavitating bubble and its interaction with an aspirin crystal.

The effects of ultrasound on the crystal size distribution were modeled by a population balance equation, which is a commonly used model for the dynamics of particulate processes (Hulbert and Katz, 1964). The experiments were designed to have zero supersaturation so that nucleation, growth, and aggregation/coalescence do not occur, which results in a simplified population balance that includes only the breakage phenomena:

where S is the breakage selection rate constant, b is the breakage function, n is the number density function, and m is a measure of the particle size (mass, in this case). The common assumption was made that a breakage event results in two equally sized particles. As commonly used in the literature (Tan et al., 2004), the breakage selection rate constant was assumed to be a power law function of the crystal geometry:

The values for the prefactor and exponent in the power law model were determined by least-squares parameter estimation that minimized the difference between the model and experimental number density functions, for experimental data sets in which one experimental parameter changes at a time, and for experimental data sets in which multiple parameters changed in the experiments. This approach enabled an examination of the relationships between the fitted model parameters to the total sonication time, ultrasonic intensity and fluid viscosity. The results are compared to a first-principles model for the breakage selection rate developed from expressions for the cavitating bubble dynamics from the sonochemistry literature and assumed interactions between the bubbles and the crystals. To our knowledge, these are the first population balance models for the effects of ultrasonic irradiation on second nucleation or crystal breakage that incorporate first-principles models for the cavitating bubble dynamics.

References:

H.M. Hulbert and S. Katz. Some problems in particle technology. A statistical mechanical formulation. Chemical Engineering Science, 19, 555-574 (1964).

H.S. Tan, A.D. Salman, and M.J. Hounslow. Kinetics of fluidized bed melt granulation IV. Selecting the breakage model. Powder Technology, 143-144, 65-83 (2004).