Pore network simulation of imbibition into paper during coating: I. Model development

Recent developments in flow modeling and fluid control for paper-based microfluidic biosensors

Over the last 10 years, researchers have shown that paper is a promising substrate for affordable biosensors. The field of paper-microfluidics has evolved rapidly in that time, with simple colorimetric assays giving way to more complex electrochemical devices that can handle multiple samples at a given time. As paper devices become more complex, the ability to precisely control different fluids simultaneously becomes a challenge. Specifically, automated flow control is a necessary attribute to make paper-based devices more useable in resource-limited settings. Flow control strategies on paper are typically developed experimentally through trial-and-error, with little focus on theory. This is because flow behavior in paper is not well understood and sometimes difficult to predict precisely. Additionally, popular theoretical models are too simplistic, making them unsuitable for complex device designs and application conditions. A better understanding of flow theory would allow devices conceived straight from theoretical models. This could save time and resources by reducing experimental work. In this review, we provide an overview of different theoretical models used to characterize imbibition in paper substrates and document the latest flow control strategies that have been applied to automated fluid control on paper. Additionally, we look at current efforts to commercialize paper-based devices along with challenges facing this industry.

The Application of Polysaccharides and Their Derivatives in Pigment, Barrier, and Functional Paper Coatings

As one of the most abundant natural polymers in nature, polysaccharides have the potential to replace petroleum-based polymers that are difficult to degrade in paper coatings. Polysaccharide molecules have a large number of hydroxyl groups that can bind strongly with paper fibers through hydrogen bonds. Chemical modification can also effectively improve the mechanical, barrier, and hydrophobic properties of polysaccharide-based coating layers and thus can further improve the related properties of coated paper. Polysaccharides can also give paper additional functional properties by dispersing and adhering functional fillers, e.g., conductive particles, catalytic particles or antimicrobial chemicals, onto paper surface. Based on these, this paper reviews the application of natural polysaccharides, such as cellulose, hemicellulose, starch, chitosan, and sodium alginate, and their derivatives in paper coatings. This paper analyzes the improvements and influences of chemical structures and properties of polysaccharides on the mechanical, barrier, and hydrophobic properties of coated paper. This paper also summarizes the researches where polysaccharides are used as the adhesives to adhere inorganic or functional fillers onto paper surface to endow paper with great surface properties or special functions such as conductivity, catalytic, antibiotic, and fluorescence.

Depinning and dynamics of imbibition fronts in paper under increasing ambient humidity

We study the effects of ambient air humidity on the dynamics of imbibition in a paper. We observed that a quick increase of ambient air humidity leads to depinning and non-Washburn motion of wetting fronts. Specifically, we found that after depinning the wetting front moves with decreasing velocity v[proportionality](h(p)/h(D))(γ), where h(D) is the front elevation with respect to its pinned position at lower humidity h(p), while γ=/~1/3. The spatiotemporal maps of depinned front activity are established. The front motion is controlled by the dynamics of local avalanches directed at 30° to the balk flow direction. Although the roughness of the pinned wetting front is self-affine and the avalanche size distribution displays a power-law asymptotic, the roughness of the moving front becomes multiaffine a few minutes after depinning.

Dynamics and stability of two-potential flows in the porous media

The experimental and numerical results of the capillary-force-driven climb of wetting liquid in porous media, which is opposed by the gravity force, are analyzed with respect to the emergence of a multiphase flow front and flow stability of the climbing liquid. Two dynamic characteristics are used: (i) the multiphase flow front thickness as a function of time, and (ii) the capillary number as a function of Bond number, where both numbers are calculated from the harmonic average of pores radii. Throughout the climb, the influence of capillary, gravity, and viscous force variations on the flow behavior is investigated for different porous media. For a specific porous medium, a unique flow front power law function of time is observed for the capillary flow climbs with or without gravity force. Distinct dynamic flow front power law functions are found for different porous media. However, for capillary climb in different porous media, one is able to predict a unique behavior for the wetting height (the interface between wetted and dry regions of porous medium) using the capillary and Bond number. It is found that these two numbers correlate as a unique exponential function, even for porous media whose permeabilities vary for two orders of magnitude. For climbs without the gravity force (capillary spreads), the initial climb dynamics follows this exponential law, but for later flow times and when a significant flow front is developed, one observes a constant value of the capillary number. Using this approach to describe the capillary climb, only the capillary versus Bond number correlation is needed, which is completely measureable from the experiments.

Capillary climb dynamics in the limits of prevailing capillary and gravity force

The dynamics of capillary climb of a wetting liquid into a porous medium that is opposed by gravity force is studied numerically. We use the capillary network model, in which an actual porous medium is represented as a network of pores and throats, each following a predefined size distribution function. The liquid potential in the pores along the liquid interface within the network is calculated as a result of capillary and gravity forces. The solution is general, and accounts for changes in the climbing height and climbing velocity. The numerical results for the capillary climb reveal that there are at least two distinct flow mechanisms. Initially, the flow is characterized by high climbing velocity, in which the capillary force is higher than the gravity force, and the flow is the viscous force dominated. For this single-phase flow, the Washburn equation can be used to predict the changes of climbing height over time. Later, for longer times and larger climbing height, the capillary and gravity forces become comparable, and one observes a slower increase in the climbing height as a function of time. Due to the two forces being comparable, the gas-liquid sharp interface transforms into flow front, where the multiphase flow develops. The numerical results from this study, expressed as the climbing height as a power law function of time, indicate that the two powers, which correspond to the two distinct mechanisms, differ significantly. The comparison of the powers with experimental data indicates good agreement. Furthermore, the power value from the Washburn solution is also analyzed, where it should be equal to 1/2 for purely viscous force driven flow. This is in contrast to the power value of ∼0.43 that is found experimentally. We show from the numerical solution that this discrepancy is due to the momentum dissipation on the liquid interface.

On the influence of pore structure on the free-imbibition of sessile drops into nanoporous substrates

We report here a model experimental study on the influence of pore structure on the free-imbibition of sessile drops into nanoporous substrates. The work takes advantage of the existence of distinct pore structures on the two sides of a nanoporous alumina membrane: straight parallel channels versus a denser and tortous network. We show first that the spreading which coexists with the free-imbibition predominates in the early stage well follows on both sides the power-law scaling with time predicted by the universal Tanner's law. More interestingly, we found also that the imbibition rate scales in a similar way with the time on both sides of the membrane, showing that the pore structure does not affect qualitatively the free-imbibition kinetics. On the other hand, our results clearly show that the pore structure has a quantitative impact on the imbibition rate, which increases markedly from the A side (dense network of short and tortuous pores) to the side B (straight vertical channels). This latter result shows that, as regards the free-imbibition, the topology of the pores has a preeminent impact on their volume, which is here comparable for both sides of the membrane. More unexpectedly, this quantitative impact of the pore structure on the imbibition rate seems to display a certain sensitivity to the viscosity of the liquid.

Penetration into three-dimensional complex porous structures

The short-term uptake of a fluid by porous media is important in a number of processes, such as in coating and printing operations. We present a new model to predict short-term absorption into real pore geometries taking into account fluid properties, surface forces, and the complex pore geometry. Two assumptions are made to reduce the complexity of the situation: (1) the flow resistance between pores can be estimated from pore geometry or air permeability measurements, and (2) the volume of fluid in the constrictions between pores is small. Pores can be connected in any manner and can be in any arrangement. The absorption rates predicted by the model are compared to experimental values obtained with coating layers of plastic, kaolin, and calcium carbonate pigments. These coatings are characterized in terms of void fraction, pore size, contact angle, and permeability. The comparison is good for water and inks when the air permeability of the porous layer is used to determine the average resistance to flow in the sample. These resistance values are close to the values obtained from pore geometries estimated from particle packing simulations.