Mathematical Model for Simulating the Springback Effect of Gel Matrixes During Drying Processes and Its Experimental Validation

Abstract

Volume change is one a fundamental aspect in characterization of drying processes. Several attempts to simulate the volume change during drying have been reported in the open literature. However, so far no theoretical approach has been used to support these simulations, especially when it comes to dealing with the springback effect. In this contribution, a theoretical model was built to predict the volume change including the springback phenomenon. The theory behind the present model is based on three physical mechanisms, which are represented by the shrinkage, collapse, and swelling functions. The resulting set of equations was implemented and solved in MATLAB(Mathworks, Inc., Natick, MA) by formulating the model as a constrained optimization problem. Data for three gels reported by an independent group and characterized by different profiles in terms of the springback effect were used to validate the model. This validation showed excellent agreement between the predictions obtained by this model and the experimental data. The average error lies somewhere between 1.6 and 4.4% depending on the gel. The information extracted from the parameters included in this theoretical model should assist in understanding the mechanisms that occur during processes involving moisture/solvent changes. Hence, the present model can be used as a reliable tool to predict volume changes and to understand the dynamic mechanisms involved in pore formation/disappearance during drying processes.

Keywords:

• Collapse
• Drying
• Gels
• Modeling
• Shrinkage
• Simulations
• Springback
• Swelling
• Volume expansion