[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120240-en":3,"doc-seo-120240-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120240,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Capsule Rheology and Machine Learning - Doctoral Thesis","Capsules and their properties attract growing interest across science and industry, where biological systems can be modeled as liquid cores encapsulated by a skin and where capsules are engineered for functional use in medicine or food. The work derives and solves shape equations for freely pendant droplets, capsules, and time-dependent deformations including viscous dissipation, and integrates a numerical framework to fit experimental images and infer interface information, including multi-layer systems. It further studies adhesive pressurized capsule contact under external forces with a wall or another capsule and extends the theory to build elastic meta-materials. Finally, machine learning is applied to ill-conditioned inverse problems via droplet/capsule shape fitting and traction force microscopy, achieving order-of-magnitude speedups and improved stability through learned regularization.","A thesis submitted for the academic degree Doctor rerum naturalium (Dr. rer . nat.)  \nCapsule Rheology and Machine Learning  \nFelix Sebastian Kratz  \nsubmitted in July 2024  \nAG Kierfeld  \nDepartment of Physics Technische Universität Dortmund  \nii  \nAbstract  \nCapsules and their properties have provoked an increasing interest in several fields of the sciences and industry. In the sciences, several relevant biological system are modeled as a liquid core encapsulated by a skin of some sort, [e.g. red](e.g. red) blood cells. In industry, capsules are usually used the other way around – not to model nature, but rather to design for functionality, e.g. in medical application or the food industry. Given their ubiquitous application, we discuss and investigate the solution of shape equations for freely pendant droplets, capsules and derive a method to incorporate viscous dissipation for time dependent deformation sequences. These theoretical investigations are supplemented with a novel numerical framework which allows us to solve the shape equations, fit them to experimental images, and therefore infer information from experiments. We apply the theoretical and numerical insights gained during the course of this work to investigate the properties of complex interfaces, such as multi-layer systems.  \nWhile an individual capsule has interesting applications, the reality often is that a capsule can not be isolated from other capsules or some constraining boundaries. We therefore investigate – for the first time in literature – the contact problem of a pressurized, bending-stiff, adhesive, elastic capsule under an external force both with a solid wall and with another capsule of this kind. The resulting shape equations give us access to the shape-parameter diagram and allow us to understand the contact problem without performing any experiment. We rather integrate the shape equations numerically and find the solutions nature realizes, together with all relevant derived quantities, such as the contact force. Additionally, we design a meta-material (theoretically) from an elastic capsule unit-cell by extending the contact theory to a columnar structure.  \nSeveral problems encountered in physics, especially in inverse problems, can be considered illconditioned. An ill-conditioned problem reacts sensitive to perturbations of the input data and usually needs to be regularized or otherwise constrained to produce stable predictions or results. In this thesis we explore the potential of machine learning approaches for exactly this task. With liquid droplet and elastic capsule shape fitting, as well as traction force microscopy, as example problems, we convincingly show that machine learning approaches for these ill-conditioned problems are suitable and outperform conventional methods by orders of magnitude in speed, allowing for a entirely new applications.  \niv  \nContents  \nIntroduction and motivation 1  \n1 Axisymmetric interfaces attached to capillaries 3  \n1.1 Liquid interfaces ..................................... 5  \n1.2 Elastic interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9  \n1.3 Viscoelastic interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19  \n2 Numerically solving and fitting shape equations 25  \n2.1 Liquid pendant droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26  \n2.2 Elastic capsules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30  \n2.3 Viscoelastic capsules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36  \n2.4 CapSol: A highly capable capsule solver with powerful shape fitting capabilities . 38  \n3 Analysis of experimental shape sequences 40  \n3.1 Complex interfaces with liquid-solid phase transitions ................ 42  \n3.2 Multilayer elasticity and viscoelasticity ........................ 49  \n4 Contact phenomena of complex interfaces 53  \n4.1 Buckling, and why we can ignore it ..","cbCaic7AKvPINSAI","https://ap.wps.com/l/cbCaic7AKvPINSAI","pdf",18189381,1,162,"English","en",105,"# Introduction and motivation\n# Axisymmetric interfaces attached to capillaries\n## Liquid interfaces\n## Elastic interfaces\n## Viscoelastic interfaces\n# Numerically solving and fitting shape equations\n## Liquid pendant droplets\n## Elastic capsules\n## Viscoelastic capsules\n## CapSol: A highly capable capsule solver with powerful shape fitting capabilities\n# Analysis of experimental shape sequences\n## Complex interfaces with liquid-solid phase transitions\n## Multilayer elasticity and viscoelasticity\n# Contact phenomena of complex interfaces\n## Buckling, and why we can ignore it\n## Contact of a capsule with a solid wall\n## Contact shape equations for capsule-capsule contacts\n## Numerical integration of the shape equations\n## Analysis of the shape space\n## Capsule contact at constant volume\n## Elastic meta-materials and the elastic capsule unit cell\n## Discussion\n# Machine learning applications in ill-posed inverse problems\n## Liquid droplet machine learning tensiometry\n## Elastic capsule machine learning elastometry\n## Machine learning traction force microscopy\n# Discussion and outlook\n# Appendix","[{\"question\":\"What theoretical foundations does the thesis develop for capsule deformation and droplets?\",\"answer\":\"It derives solution methods for shape equations of freely pendant droplets and capsules, including viscous dissipation for time-dependent deformation sequences, and uses a numerical framework to solve and fit these equations to experimental images.\"},{\"question\":\"How is the contact problem of complex capsules addressed?\",\"answer\":\"The thesis investigates the contact of a pressurized, bending-stiff, adhesive, elastic capsule under external force with a solid wall and with another identical capsule, deriving shape equations that enable contact-force and shape-parameter analysis through numerical integration.\"},{\"question\":\"How does machine learning improve performance in ill-posed inverse problems in this work?\",\"answer\":\"By applying machine learning to liquid droplet and elastic capsule shape fitting and traction force microscopy, it demonstrates suitability for ill-conditioned tasks and reports speed improvements over conventional methods by orders of magnitude.\"}]","Capsule Rheology and Machine Learning - Doctoral Thesis | PDF",1785728939,408,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"capsule-rheology-and-machine-learning-doctoral-thesis","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/capsule-rheology-and-machine-learning-doctoral-thesis/120240/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What theoretical foundations does the thesis develop for capsule deformation and droplets?","Question",{"text":75,"@type":76},"It derives solution methods for shape equations of freely pendant droplets and capsules, including viscous dissipation for time-dependent deformation sequences, and uses a numerical framework to solve and fit these equations to experimental images.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the contact problem of complex capsules addressed?",{"text":80,"@type":76},"The thesis investigates the contact of a pressurized, bending-stiff, adhesive, elastic capsule under external force with a solid wall and with another identical capsule, deriving shape equations that enable contact-force and shape-parameter analysis through numerical integration.",{"name":82,"@type":73,"acceptedAnswer":83},"How does machine learning improve performance in ill-posed inverse problems in this work?",{"text":84,"@type":76},"By applying machine learning to liquid droplet and elastic capsule shape fitting and traction force microscopy, it demonstrates suitability for ill-conditioned tasks and reports speed improvements over conventional methods by orders of magnitude.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]