Liquid wicking behavior in paper-like materials: mathematical models and their emerging biomedical applications

Paper-like materials have found widespread applications in various fields, especially recently emerging applications in biomedicine as paper-based devices, where liquid wicking behavior plays a significant role. Although tremendous experimental evidence has indicated that fluid control is a key technology to improve the performance of these paper-based devices, the underlying mechanisms of liquid wicking behavior in paper-like materials remain unclear. Numerical and mathematical techniques provide effective strategy and great potential in understanding the liquid flowing process in the complex fibrous structure of paper-like materials. In this review, we first present the basic physical process and key factors of liquid wicking behavior in paper-like materials. Furthermore, we review various macroscopic and mesoscopic mathematical models on fluid flow in porous materials, focusing on each model's advantages and challenges, and summarize their related biomedical applications. The aims are to better understand the underlying mechanisms of liquid wicking behavior in paper-like materials through mathematical models and to provide guidance in the design and optimization of paper-based biomedical devices.