Model-based design and control of directed self-assembly of colloidal particles and protein crystallization

Abstract

Self-assembly is a promising route for the fabrication of advanced materials with novel properties. Applications of self-assembly include colloids, lipid bilayers, and the assembly of proteins into crystals. Despite the promising applications of self-assembly, external controls employing electric and magnetic fields, or fluid flows are often necessary to reliably guide self-assembly processes. Dynamic models can determine optimal input trajectories of manipulated variables during directed self-assembly. The second chapter of this thesis presents a dynamic model for the simulation of particle trajectories in the presence of an electric field with time-varying properties. The model is based on first principles and has been experimentally validated under different conditions. The model is used to predict the dynamic trajectories of particles when considering electrokinetic forces and fluid drag with the assumption of negligible Brownian motion for a system with low spatial particle density. The importance of Brownian motion and particle-particle interactions are then considered. The model can be used to predict the dynamic development of the spatial particle density distribution and the probability density associated with particle positions. The dynamic model has been utilized in a novel open-loop control scheme for shaping local particle densities. The dynamic model has great promise to be used for model-based control of directed self-assembly of colloidal particles. Mixing or agitation is essential for the reliable self-assembly of proteins into crystals. Mixing of protein solutions requires a balance between fast mixing and low shear under laminar flow conditions to minimize supersaturation gradients. The third chapter of this thesis addresses the problem of obtaining homogeneous supersaturated solutions in protein crystallization in the laminar flow regime with a novel Kenics mixer. The novel mixer design features gaps between the mixing elements, which can achieve the same level of mixing as the conventional design but with fewer mixing elements and a substantially lower pressure drop and shear rate. The mixing effects at the entrances and exits of the mixing elements are enhanced by the introduction of gaps between the elements. The performances of Kenics mixers based on the right-left and right-right configurations with different gap lengths are characterized in terms of pressure drop, coefficient of variance of concentration, residence time distribution, and extensional efficiency with computational fluid dynamics simulations. Furthermore, the coefficient of variance of concentration is measured experimentally with several 3-D printed devices. The gaps reduce the mixing length when the design is based on the right-right configurations and the gap-to-diameter ratio is 0.5 or 1.0 compared to the corresponding conventional design. Additionally, Taylor dispersion is suppressed with the introduction of gaps, which enables a narrower residence time distribution. The presence of gaps between mixing elements introduces an additional degree of freedom, which can be utilized to strike a compromise between the required mixing length and pressure drop. Seeding is often used in the fine chemicals and the pharmaceutical industries to reliably control the quality of crystalline products with a narrow crystal size distribution (CSD) by suppressing nucleation. However, the generation of small, non-agglomerated crystals with narrow crystal size distributions can be laborious. The conventional approach to seed generation which generally involves milling, sieving, and ripening to obtain seed crystals is challenging for applications involving proteins due to the susceptibility of proteins to denaturation. The challenge of generating small protein seed crystals with narrow crystal size distributions is addressed in the fourth chapter of this thesis using a gapped Kenics tubular crystallizer (gKTC) as a seed generation device. The gapped Kenics tubular crystallizer is based on the R-R Kenics mixer with a gap-to-diameter ratio of 1.0. Compared with a stirred tank crystallizer, smaller non-agglomerated protein crystals are consistently generated in the gKTC at shorter residence times. The higher nucleation rates in the gapped Kenics tubular crystallizer may be attributed to the promotion of heterogeneous nucleation by the mixing elements or differences in hydrodynamics between the gapped Kenics tubular crystallizer and the stirred tank crystallizer. Different seeding policies can be implemented by adjusting the transfer of crystals from the gKTC to a batch crystallizer, which offers flexible control over the CSD of the batch product. This flexibility is demonstrated through an open-loop control strategy in which an optimal seeding policy to obtain a flat-top CSD is derived from a population balance model, which is then implemented experimentally. The obtained CSD is close to the specified one, which cannot be achieved well with conventional batch crystallization. Finally, a novel data-driven methodology is presented for developing mathematical models for crystallization processes. The data-driven approach iterates between a partial least-squares fit and a sparsity-promoting step leading to the discovery of sparse interpretable models. The data-driven method is robust against noise. The performance of the data-driven methodology is characterized for the identification of crystallization kinetics in an MSMPR as well as the crystallization of lysozyme in a batch stirred tank. Remarkable agreement is obtained between the data-driven model and the data obtained from seeded batch protein crystallization experiments. The presented data-driven approach can be attractive for industrial crystallization processes where process analytical technology (PAT) tools are available for the measurement of process variables. The work presented in this thesis can provide the basis for modelling, design, and control of chemical engineering processes. For instance, the first-principle model presented in Chapter 2 can be employed in the design of closed-loop model-based controllers for colloidal particle self-assembly. The novel mixer that has been characterized here, may also be interesting for continuous crystallization applications in the pharmaceutical industry. Furthermore, the CFD model presented for the simulation of the Kenics static mixers can be utilized for the design and optimization of other static mixers. Additionally, the seeding approach introduced in this thesis may be exploited for the generation of seed crystals for other model compounds while the data-driven approach presented in Chapter 5 may be further investigated for crystallization processes involving complicated secondary phenomena such as agglomeration and the breakage of crystals.

Date of Award	2022
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Richard LAKERVELD (Supervisor)