The inverse problem of capillary filling

EMANUEL ELIZALDE, RAUL URTEAGA, ROBERTO KOROPECKI; CLAUDIO L. A. BERLI

PHYSICAL REVIEW LETTERS

AMER PHYSICAL SOC

Lugar: New York; Año: 2014 vol. 112 p. 134502 - 134505

0031-9007

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 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 calculation were made in a wide range of length-scales: glass capillaries with radius around 150 mm and anodized alumina membranes with pores radius around 30 nm were used. The proposed method was successful to identify the radius profile in both systems. Fundamental aspects also emerge in this study, notably the fact that the x a t1/2 kinematics (Lucas-Washburn relation) is not exclusive of uniform cross-sectional capillaries