R.G.M. van der Sman , Michele Curatolo , Luciano Teresi
{"title":"Analytical and numerical solutions of pore formation in elastic food materials during dehydration","authors":"R.G.M. van der Sman , Michele Curatolo , Luciano Teresi","doi":"10.1016/j.crfs.2024.100762","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p><p>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.</p></div>","PeriodicalId":10939,"journal":{"name":"Current Research in Food Science","volume":null,"pages":null},"PeriodicalIF":6.2000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2665927124000881/pdfft?md5=86a8f4d9817a22308a1cfcd6293e4fcf&pid=1-s2.0-S2665927124000881-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Current Research in Food Science","FirstCategoryId":"97","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2665927124000881","RegionNum":2,"RegionCategory":"农林科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"FOOD SCIENCE & TECHNOLOGY","Score":null,"Total":0}
引用次数: 0
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.
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.