Application of Mathematical Modeling and Numerical Simulation of Blood Biomarker Transport in Paper-Based Microdevices

Carlos E. Zambra (), Diógenes Hernandez, Jorge O. Morales-Ferreiro and Diego Vasco
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Carlos E. Zambra: Department of Industrial Technologies, Faculty of Engineering, University of Talca, Curicó 3640000, Chile
Diógenes Hernandez: Department of Industrial Technologies, Faculty of Engineering, University of Talca, Curicó 3640000, Chile
Jorge O. Morales-Ferreiro: Escuela de Ingeniería, Facultad de Ciencias, Ingeniería y Tecnología, Universidad Mayor, Providencia, Santiago 7500000, Chile
Diego Vasco: Department of Mechanical Engineering, University of Santiago (USACH), Av. Bernardo O’Higgins 3363, Estación Central, Santiago 9160000, Chile

Mathematics, 2025, vol. 13, issue 12, 1-27

Abstract: This study introduces a novel mathematical model tailored to the unique fluid dynamics of paper-based microfluidic devices (PBMDs), focusing specifically on the transport behavior of human blood plasma, albumin, and heat. Unlike previous models that depend on generic commercial software, our custom-developed computational incorporates the Richards equation to extend Darcy’s law for more accurately capturing capillary-driven flow and thermal transport in porous paper substrates. The model’s predictions were validated through experimental data and demonstrated high accuracy in both two- and three-dimensional simulations. Key findings include new analytical expressions for uniform paper wetting after sudden geometric expansions and the discovery that plasma and albumin preferentially migrate along paper edges—a phenomenon driven by surface tension and capillary effects that varies with paper type. Additionally, heat transfer analysis indicates that a one-minute equilibration period is necessary for the reaction zone to reach ambient temperature, an important parameter for assay timing. These insights provide a deeper physical understanding of PBMD operation and establish a robust modeling tool that bridges experimental and computational approaches, offering a foundation for the optimized design of next-generation diagnostic devices for biomedical applications.

Keywords: heat and mass simulation; paper-based microfluidic devices; blood transport; biomarkers detections (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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