Research Projects

Twin-screw granulation (TSG) is a continuous wet granulation method widely used in the pharmaceutical industry to produce solid dosage forms such as tablets and capsules. It involves the mixing of powders with a liquid binder using intermeshing co-rotating screws, enabling efficient simultaneous mixing, wetting and granule formation. TSG offers advantages such as improved product consistency, scalability, real-time quality monitoring and suitability for continuous manufacturing. To understand and predict granulation dynamics in TSG, researchers use compartmental population balance models (CPBMs). These models divide the granulator into spatial compartments (e.g., wetting and kneading zones), where key processes like coagulation and fragmentation dominate. Recent developments include novel breakage kernels that incorporate screw design and material properties, as well as multi-dimensional CPBMs that track granule attributes such as size, porosity and moisture content. Mathematically, CPBMs are governed by nonlinear integro-differential equations that describe the evolution of particle size distributions under simultaneous coagulation and breakage. Due to the complexity and nonlinearity of the integral terms, analytical solutions exist only for simple cases, such as constant coagulation and linear fragmentation kernels. For other cases, researchers have proposed several numerical methods, including Hounslow discretization, fixed pivot and cell average (CA) methods. The CA method offers good mass conservation but requires a large number of bins and intricate formulations to accurately capture particle redistribution. To overcome these, finite volume method (FVM) has been applied to one dimensional CPBMs, providing improvements in numerical stability and conservation. However, FVM is computationally expensive and often involves extensive parameter fitting, limiting its practicality in multi-dimensional process control. Despite their utility, these numerical approaches offer limited analytical insight into the granulation process dynamics and face scalability issues when extended to higher dimensions. To address these limitations, this work proposes the development of generalized semi-analytical methods for solving CPBMs in TSG. The central idea is to apply the Optimal Perturbation Iteration Method (OPIM) to derive accurate and efficient approximate solutions. The proposed study will construct closed-form or series-based solutions for one dimensional CPBMs using simplified kernels (e.g., sum, Kapur and power-law kernels). These results will be validated against the FVM. The framework will also incorporate various initial particle size distributions (e.g., Gamma and Gaussian) and will be extended to two and three dimensional CPBMs to capture additional granule properties such as porosity and moisture content. This research aims to bridge the gap between analytical modeling and practical granulation processes in continuous pharmaceutical manufacturing.