Abstract
The inverse problem of capillary filling, as defined in this work, consists in determining the capillary radius profile from experimental data of the meniscus position as a function of time . This problem is central in diverse applications, such as the characterization of nanopore arrays or the design of passive transport in microfluidics; it is mathematically ill posed and has multiple solutions; i.e., capillaries with different geometries may produce the same imbibition kinematics. Here a suitable approach is proposed to solve this problem, which is based on measuring the imbibition kinematics in both tube directions. Capillary filling experiments to validate the calculation were made in a wide range of length scales: glass capillaries with a radius of around and anodized alumina membranes with a pores radius of around were used. The proposed method was successful in identifying the radius profile in both systems. Fundamental aspects also emerge in this study, notably the fact that the kinematics (Lucas-Washburn relation) is not exclusive of uniform cross-sectional capillaries.
- Received 12 December 2013
DOI:https://doi.org/10.1103/PhysRevLett.112.134502
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