Inverse Problem of Capillary Filling

EMANUEL ELIZALDE; RAÚL URTEAGA; ROBERTO R. KOROPECKI; CLAUDIO L.A. BERLI

PHYSICAL REVIEW LETTERS

AMER PHYSICAL SOC

Lugar: New York; Año: 2014 vol. 112 p. 1345021 - 1345025

0031-9007

The inverse problem of capillary filling, as defined in this work, consists in determining the capillaryradius profile from experimental data of the meniscus position l as a function of time t. 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 150 μm and anodized alumina membranes with a pores radius of around 30 nm 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 l(t) ∝ t^0.5 kinematics (Lucas-Washburn relation) is not exclusive of uniform cross-sectional capillaries.