Characterizing effects of humidity and channel size on imbibition in paper-based microfluidic channels

Paper-based microfluidic devices have gained an increasing amount of interest over the last few years. As such devices continue advancing toward more complex and sophisticated functions, obtaining accurate and consistent fluid imbibition under different conditions will become increasingly important. This study presents a series of controlled imbibition experiments investigating effects of relative humidity and channel width in paper-based microfluidic channels. The obtained imbibition data highlighted the importance in accounting for the effects of these design and environmental parameters. Additionally, fitting of the experimental data to three relevant imbibition models revealed evaporation, not water saturation, to be the main mechanism of the observed relative humidity effect. The current study has created a library of paper-specific, imbibition-related properties for commonly used filter and chromatography papers for the first time. Collectively, the presented imbibition data and the discovered relationships are expected to help researchers design more precise and reproducible paper-based microfluidic devices.     

Laminar flow in rectangular channels. Part I: Entry analysis. Part II: Numerical solution for a square channel?

Laminar incompressible flow in rectangular channels is considered. In Part I, the entry region is evaluated by a boundary layer/potential core analysis. It is shown that the three-dimensional displacement induced potential flow can be described with a pair of two-dimensional potential functions. Second-order boundary layer solutions, with and without surface mass transfer, are determined; an interesting secondary flow reversal is predicted. In Part II, numerical solutions are obtained for the viscous channel equations, which are derived from the asymptotic theory of Part I. A two stream function, velocity, vorticity system, independent of the Reynolds Number, is solved with a combined iterative ADI/point-relaxation numerical procedure. A single calculation applied for all Reynolds numbers, which appears only in the coordinate scaling. The axial flow behavior of Parts I and II are in good agreement in the asymptotic entry region where both analysis apply. Secondary flow reversal is calculated; however, the grid is too crude for quantitative comparisons. Numerical solutions are obtained until fully developed conditions are achieved. Agreement with experimental data is good.     

Data exchange and schema mappings in open and closed worlds

In the study of data exchange one usually assumes an open-world semantics, making it possible to extend instances of target schemas. An alternative closed-world semantics only moves ‘as much data as needed’ from the source to the target to satisfy constraints of a schema mapping. It avoids some of the problems exhibited by the open-world semantics, but limits the expressivity of schema mappings. Here we propose a mixed approach: one can designate different attributes of target schemas as open or closed, to combine the additional expressivity of the open-world semantics with the better behavior of query answering in closed worlds. We define such schema mappings, and show that they cover a large space of data exchange solutions with two extremes being the known open and closed-world semantics. We investigate the problems of query answering and schema mapping composition, and prove two trichotomy theorems, classifying their complexity based on the number of open attributes. We find conditions under which schema mappings compose, extending known results to a wide range of closed-world mappings. We also provide results for restricted classes of queries and mappings guaranteeing lower complexity.     

Sensitivity results in open, closed and mixed product form queueing networks

General formulas are proposed to quantify the effects of changing the model parameters in the so-called BCMP network [F. Baskett et al., J. ACM 22 (2) (April 1975) 248–260]. These formulas relate the derivative of the expectation of any function of both the state and the paramaters of the network with respect to any model parameter (i.e., arrival rate, mean service demand, service rate, visit ratio, traffic intensity) to known functions of the state variables. Applications of our results to sensitivity analysis and optimization problems are given.     

Liquid recirculation in microfluidic channels by the interplay of capillary and centrifugal forces

We demonstrate a technique to recirculate liquids in a microfluidic channel by alternating predominance of centrifugal and capillary forces to rapidly bring the entire volume of a liquid sample to within one diffusion length, δ, of the surface, even for sample volumes hundreds of times the product of δ and the geometric device area. This is accomplished by repetitive, random sampling of an on-disc sample reservoir to form a thin fluid layer of thickness δ in a microchannel, maintaining contact for the diffusion time, then rapidly exchanging the fluid layer for a fresh aliquot by disc rotation and stoppage. With this technique, liquid volumes of microlitres to millilitres can be handled in many sizes of microfluidic channels, provided the channel wall with greatest surface area is hydrophilic. We present a theoretical model describing the balance of centrifugal and capillary forces in the device and validate the model experimentally.     

Algorithms for leak detection, estimation, isolation and localization in open water channels

In this paper, a methodology for leak detection and isolation in open water channels is proposed. It consists of on-line leak detection and off-line leak isolation, estimation and localization. The on-line leak detection is carried out pool by pool using local information only, and a comparison between three leak detection methods in terms of detection performance and ease of implementation is presented. Information from neighboring pools is used to distinguish the effect of a leak from sensor faults. The proposed methods were tested on real experimental data from the Coleambally Channel no. 6 in Australia and showed good performance.     

Model reduction in model predictive control of combined water quantity and quality in open channels

Model predictive control (MPC) is an advanced real-time control technique that uses an internal model to predict the future system behavior and generates optimal control actions by solving an optimization problem. MPC has been more and more applied for controlling open water systems, especially open water channels. Most of the research however focuses on water quantity (water level) control. Since water quality management is recently attracting more attention, extending MPC on combined water quantity and quality management is a logical next step.In this paper, we study the application of complex models in MPC to control both water quantity and quality. However, because of the online optimization of MPC, the computational time becomes an issue. In order to reduce the computational time, a model reduction technique, Proper Orthogonal Decomposition (POD), is applied to reduce the model order. The method is tested on a Polder flushing case. The results show that POD can significantly reduce the model order for both water quantity and quality with high accuracy. The MPC using the reduced model performs well in controlling combined water quantity and quality in open water channels.     

Dynamics of capillary flow in an open superoleophilic microchannel and its application to sensing of oil

We report the dynamics of capillary flow of oil in an open superoleophilic channel. The superoleophilic surface is fabricated by spin coating a layer of PDMS?+?n-hexane followed by candle sooting. The occurrence of various flow regimes, including the inertial, visco-inertial, and Lucas–Washburn regimes, are studied using analytical modelling as well as experiments. In case of a superoleophilic channel, much shorter inertial regime is observed as compared to that in an oleophilic channel due to the wicking of oil into the micro-roughness grooves ahead to moving bulk liquid meniscus. The study of the effect of channel aspect ratio \(\varepsilon\) on the mobility parameter \(k~\)showed that the mobility parameter \(k\) is maximum for an aspect ratio of \(\varepsilon =1.6\), which is attributed to the balance between the capillary and viscous forces. Finally, we demonstrate the application of the superoleophilic channel integrated with electrodes for impedance-based sensing of oil from an oil–water emulsion.     

The open question of the relation between square matrix’s eigenvalues and its similarity matrix’s singular values in linear discrete system

In linear discrete system, we often need to utilize similarity transformation to extend the solution ranges of its corresponding discrete matrix equations. Consequently, how to choose the similarity transformation matrix remains an open question in recent years. In this paper, by applying the theory of matrix’s Jordan canonical form and the related properties of nonnegative matrices, we construct the similarity transformation matrix of some special similarity transformation, then present a necessary and sufficient condition and a corresponding algorithm, thus solve the open question totally.