Analytical and numerical solutions of pore formation in elastic food materials during dehydration

IF 6.2 2区 农林科学 Q1 FOOD SCIENCE & TECHNOLOGY
R.G.M. van der Sman , Michele Curatolo , Luciano Teresi
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Abstract

In this paper, we describe a model for pore formation in food materials during drying. As a proxy for fruits and vegetables, we take a spherical hydrogel, with a stiff elastic skin, and a central cavity filled with air and water vapour. The model describes moisture transport coupled to large deformation mechanics. Both stress and chemical potential are derived from a free energy functional, following the framework developed by Suo and coworkers. We have compared Finite Volume and Finite Element implementations and analytical solutions with each other, and we show that they render similar solutions. The Finite Element solver has a larger range of numerical stability than the Finite Volume solver, and the analytical solution also has a limited range of validity. Since the Finite Element solver operates using the mathematically intricate weak form, we introduce the method in a tutorial manner for food scientists.

Subsequently, we have explored the physics of the pore formation problem further with the Finite Element solver. We show that the presence of an elastic skin is a prerequisite for the growth of the central cavity. The elastic skin must have an elastic modulus of at least 10 times that of the hydrogel. An initial pore with 10% of the size of the gel can grow to 5 times its initial size. Such an increase in porosity has been reported in the literature on drying of vegetables, if a dense hard skin is formed, known as case hardening. We discuss that models as presented in this paper, where moisture transport is strongly coupled to large deformation mechanics, are required if one wants to describe pore/structure formation during drying and intensive heating (as baking and frying) of food materials from first principles.

Abstract Image

脱水过程中弹性食品材料中孔隙形成的分析和数值解决方案
本文描述了食品材料在干燥过程中形成孔隙的模型。作为水果和蔬菜的代表,我们采用了一种球形水凝胶,它有一层坚硬的弹性表皮和一个充满空气和水蒸气的中心空腔。该模型描述了与大变形力学耦合的水分传输。应力和化学势均由自由能函数导出,沿用了 Suo 及其同事开发的框架。我们比较了有限体积求解和有限元求解以及彼此的分析求解,结果表明它们的求解结果相似。与有限体积求解器相比,有限元求解器的数值稳定性范围更大,而分析解的有效范围也有限。由于有限元求解器使用的是数学上复杂的弱形式,我们以教程的方式向食品科学家介绍了该方法。随后,我们使用有限元求解器进一步探索了孔隙形成问题的物理原理。我们发现,弹性表皮的存在是中心空腔生长的先决条件。弹性表皮的弹性模量必须至少是水凝胶的 10 倍。初始孔隙大小为凝胶大小的 10%,但可以增长到初始大小的 5 倍。如果形成致密的硬表皮,即所谓的表皮硬化,这种孔隙率的增加在有关蔬菜干燥的文献中已有报道。我们认为,如果想从第一原理上描述食品材料在干燥和强化加热(如烘烤和油炸)过程中孔隙/结构的形成,就必须使用本文提出的模型,即水分传输与大变形力学的强耦合模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Current Research in Food Science
Current Research in Food Science Agricultural and Biological Sciences-Food Science
CiteScore
7.40
自引率
3.20%
发文量
232
审稿时长
84 days
期刊介绍: Current Research in Food Science is an international peer-reviewed journal dedicated to advancing the breadth of knowledge in the field of food science. It serves as a platform for publishing original research articles and short communications that encompass a wide array of topics, including food chemistry, physics, microbiology, nutrition, nutraceuticals, process and package engineering, materials science, food sustainability, and food security. By covering these diverse areas, the journal aims to provide a comprehensive source of the latest scientific findings and technological advancements that are shaping the future of the food industry. The journal's scope is designed to address the multidisciplinary nature of food science, reflecting its commitment to promoting innovation and ensuring the safety and quality of the food supply.
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