Analytical solutions for the modeling, optimization, and control of microwave-assisted freeze drying

Freeze drying, aka lyophilization, is a process by which a pharmaceutical product is dried via sublimation under vacuum. An alternative to the conventional process is microwave-assisted freeze drying, which relies on microwave irradiation for drying the product, offering a reduction in the drying time by 70%–80%. This article derives exact and approximate analytical solutions to a mechanistic model for conventional, microwave-assisted, and hybrid freeze drying. The exact solution serves as a reference solution for validating numerical or approximate results due to its highest accuracy up to machine precision. The approximate solution can be computed about 4-fold faster than the numerical solutions and 200-fold faster than the exact solution with the maximum error of less than 1%, which is highly computationally efficient and accurate. Applications of the analytical solutions are demonstrated in the context of parameter estimation, optimal control, and parameter space analysis.