Dynamics of liquid imbibition through paper with intra-fibre pores

Abstract

We present a combined experimental and theoretical investigation of the dynamics of liquid imbibition through paper. The Washburn equation is widely used to describe the dynamics of capillary flow through paper, but this classical model has limited accuracy, which often makes it difficult to use in developing analytic systems such as paper-based microfluidic devices. We here report that the internal cavity of the cellulose fibres composing paper is significantly responsible for the limited accuracy of the Washburn equation. Our experiments demonstrated that liquid can be absorbed in the internal cavity of the cellulose fibres as well as in the inter-fibre pores formed by the fibre network. We developed a mathematical model for liquid imbibition by considering the flow through the intra-fibre pores based on experimental measurements of the intra-structure of cellulose fibres. The model markedly improves the prediction of the liquid absorption length, compared with the results of the Washburn equation, thus revealing the physics behind the limits of the Washburn equation. This study suggests that the accurate description of capillary imbibition through paper require parameters characterizing the internal pores of the cellulose fibres comprising the paper. Our results not only provide a new insight into porous media flows with different sized pores, but also provide a theoretical background for flow control in paper-based microfluidic systems.

Flow of liquids through paper

“…In order to determine the role played by the intra-fibre pores, Chang et al (2018) first used scanning electron micrographs to determine the nature and size of these void spaces, as shown in figure 1. They determined the size of the intra-fibre spaces and compared with the inter-fibre spaces.…”

“…This effect is often attributed to the slower filling of smaller inter-fibre pores as a result of the distribution of pore sizes in a complex fibre matrix like paper. But the work by Chang et al (2018) showed that the fabric made from fibres with no intra-fibre pores had a negligible amount of post-wetting flow even though the fabric would presumably have a distribution of inter-fibre pore sizes as well; therefore, the intra-fibre pores contributed to the post-wetting flow. This is an important finding because visualization of the inter-fibre pore size distribution has been used in the past to quantify post-wetting flow, but the intra-fibre pore size should also be considered and may have a dominant influence on the flow behaviour.…”

“…Their experiments showed that there was not a linear dependence between l 2 and t, as predicted by the Lucas-Washburn expression, and they attributed the slowing of liquid penetration to the slower filling of the intra-fibre pores. Chang et al (2018) modelled the influence of the intra-fibre pores by modifying the geometry of the cylindrical tube model proposed by Lucas (1918) and Washburn (1921), and included a small slit along the side of the cylinder. Their model included two new parameters, t c and ψ, which correspond to the time required to fill the intrafibre pores, and the volume ratio of intra-to inter-fibre pores, respectively, and can be attained from visualization and experiments.…”

“…There are several ways in which the intra-fibre pore dependence will impact the development of µPADs. For example, Chang et al (2018) found that paper with a large inter-fibre pore and small intra-fibre pore volume fraction had a fast flow speed. By employing papers with varying volume fractions we can predictably vary the flow speed, which is a tool that can be used in µPAD design for enhanced flow control.…”

“…Some physical mechanisms that are not included in the Lucas-Washburn relation and apply to paper involve the swelling of fibres (see Schuchardt & Berg 1991;Masoodi & Pillai 2010;Kvick 2017), inertial effects and uneven filling of smaller versus larger inter-fibre pores (see Szekely, Neumann & Chuang 1971;Sorbie, Wu & McDougall 1995;Schoelkopf et al 2002), film flow (Roberts et al 2003), evaporation (see Amaral et al 1994;Balankin et al 2013), pores that change in size (Reyssat et al 2008) and, importantly, the effect that is uncovered in the featured article by Chang et al (2018): the filling of the intra-fibre pores within the fibres. The questions answered are: (i) does the filling of the intra-fibre pores influence the flow of liquids through paper?…”