The design of paper-based assays that integrate passive pumping requires a precise programming of the fluid transport, which has to be encoded in the geometrical shape of the substrate. This requirement becomes critical in multiple-step processes, where fluid handling must be accurate and reproducible for each operation. The present work theoretically investigates the capillary imbibition in paper-like substrates to better understand fluid transport in terms of the macroscopic geometry of the flow domain. A fluid dynamic model was derived for homogeneous porous substrates with arbitrary cross-sectional shapes, which allows one to determine the cross-sectional profile required for a prescribed fluid velocity or mass transport rate. An extension of the model to slit microchannels is also demonstrated. Calculations were validated by experiments with prototypes fabricated in our lab. The proposed method constitutes a valuable tool for the rational design of paper-based assays.

An optofluidic method that accurately identifies the internal geometry of nanochannel arrays is presented. It is based on the dynamics of capillary-driven fluid imbibition, which is followed by laser interferometry. Conical nanochannel arrays in anodized alumina are investigated, which present an asymmetry of the filling times measured from different sides of the membrane. It is demonstrated by theory and experiments that the capillary filling asymmetry only depends on the ratio H of the inlet to outlet pore radii and that the ratio of filling times vary closely as H(7/3). Besides, the capillary filling of conical channels exhibits striking results in comparison to the corresponding cylindrical channels. Apart from these novel results in nanoscale fluid dynamics, the whole method discussed here serves as a characterization technique for nanoporous membranes.

An experimental study on the capillary filling of nanoporous silicon with different fluids is presented. Thin nanoporous membranes were obtained by electrochemical anodization, and the filling dynamics was measured by laser interferometry, taking advantage of the optical properties of the system, related with the small pore radius in comparison to light wavelength. This optical technique is relatively simple to implement and yields highly reproducible data. A fluid dynamic model for the filling process is also proposed including the main characteristics of the porous matrix (tortuosity, average hydraulic radius). The model was tested for different ambient pressures, porous layer morphology, and fluid properties. It was found that the model reproduces well the experimental data according to the different conditions. The predicted pore radii quantitatively agree with the image information from scanning electron microscopy. This technique can be readily used as nanofluidic sensor to determine fluid properties such as viscosity and surface tension of a small sample of liquid. Besides, the whole method can be suitable to characterize a porous matrix.

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 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)∝t1/2 kinematics (Lucas-Washburn relation) is not exclusive of uniform cross-sectional capillaries.

The transport of molecules and particles across adjacent flow streams is a key process in several operations implemented in microfluidic paper-based analytical devices (μPADs). Here, the transverse dispersion of analytes was quantitatively evaluated by theory and experiments. Different tests were carried out to independently measure the coefficients of both Brownian diffusion and mechanical dispersion under capillary-driven flow. The dispersion width was found to be independent of fluid velocity and analyte properties, and fully determined by the dispersivity coefficient, which is a characteristic of the paper microstructure. This information introduces a change of paradigm for the design of mixers, diluters, and concentration gradient generators on μPADs; therefore, efforts were made to rationalize these operations on paper. The research reveals that mixers and concentration gradient generators can be much more efficient than their counterparts made on conventional microchannels; in contrast, separators such as the H-filter need to be appropriately engineered on paper, because the working principle can be hindered by mechanical dispersion. The knowledge gained throughout this work would contribute to the design of μPADs with a new level of precision and control over the formation of localized concentration profiles.

No abstract

Your article is protected by copyright and all rights are held exclusively by Springer-Verlag Berlin Heidelberg. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

No abstract