Influence of Bubble Growth in Non-Fickian Transfer of Mass

Dongdong Ma, Purdue University


Drying and expansion of cereals is a critical and important process in the food industry drastically impacting the quality of the final products. Quality issues include density changes, crust formation, puffing, flavor and color development. This thesis deals with numerical simulations obtained from a developed mechanistic and mathematical model that is able to predict quality changes during the processing of viscoelastic biomaterials, specifically during the drying and expansion process of cereals.^ Initially a non-Fickian model accounting for moisture diffusion during in processing of a biomaterial is proposed. The behavior of viscoelastic materials is controlled by the Deborah number that classically is defined as the ratio of a relaxation time and a experimental time. The material relaxation time provides an indication on the ability of the material to reach back its undeformed/equilibrium state after is being deformed by mechanical means in a time defined as the experimental time. Viscous or liquid behavior is observed at low Deborah numbers, i.e. when the experimental time exceeds the time necessary for the material to return to its undeformed /equilibrium. Conversely, for high Deborah numbers an elastic behavior is observed in the response of viscoelastic material to a mechanical perturbation. During processing of cereals where diffusion of water and growth of bubbles are the prevalent phenomena the Deborah number is defined considering other times, namely relevant to the de- formation of the material during the growth of bubbles and the diffusion time, which is relevant to the diffusion during the process. For the Deborah number defined for the purpose of this thesis it was observed that at low Deborah numbers, viscoelastic effects and deformation of the material can be neglected and the process can be objectively described by the Fick’s law that predicts a continuous moisture loss until the material reaches the equilibriums. Conversely, at high Deborah numbers, deformation of the material and viscoelastic effects become significant and the diffusion of water during the process is non-Fickian. During this non-Fickian diffusion regime the materials have a significant moisture loss shut-off, that can be observed by the presence of a crust in the surface of material during a drying process. This crust seals the loss of the water of the sample and generating a high pressure in the material that promote bubble growth and expansion. Thus, in addition to the diffusion of water an equation describing the growth of bubbles and expansion is incorporated to predict bubble growth equation and volume and texture changes on the sample. A new dimensionless parameter, termed the Denson number is proposed to describe the rate of bubble growth. By comparing results obtained from simulations with different Denson numbers, which imply processing at Fickain or non-Fickian conditions, the effect of bubble growth rate on diffusion based processing of viscoelastic biomaterial can be studied.^ The proposed simulation is verified by comparing results with model predictions based on typical Fickian based diffusion describing moisture transfer as well as qualitative analysis involving non-Fickian diffusive processes that explain well known phenomena such as crust formation during drying. Product characteristics including thickness, moisture profile and vapor profiles are obtained at different materials properties and conditions involving both Fickian and non-Fickian diffusive processing conditions.^




Osvaldo H. Campanella, Purdue University.

Subject Area

Food science|Agricultural engineering|Chemical engineering

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