Analytical solution of freeze-drying mathematical model based in Darcy’s law: application to an orange juice-based cake

Abstract

An analytical solution for moisture dynamic during freeze-drying based in non-ideal Darcy’s law that resolves the singularity at zero time was deducted. The non-ideal Darcy’s law is represented by a Darcy’s pseudo permeability ($${K^*}$$) and a deviation index ($$n$$). The analytical solution must be complemented with a numerical solution of Fourier’s equations for heat transfer in the two product zones. The model was fitted to experimental freeze-drying dynamics of an orange juice-based cake. The Darcy’s pseudo permeability obtained was $${K^*} = $$2.0X10−12 m2.5 with an ideal deviation index of $$n = $$0.5. The proposed equations, solved with fitted Darcy pseudo permeability and ideal deviation index, reproduced other experimental freeze-drying dynamics of the same product at different temperatures.

Keywords

• freeze drying
• mathematical model
• analytical solutions
• darcy’s law
• fourier’s law
• orange juice based cake