Dynamics of water imbibition through hydrogel-coated capillary tubes

Water-absorbing materials consisting of hydrogel particles are widely used for agricultural substrates, hygienic products, drug delivery systems, and microfluidic devices. Hydrogel particles absorb water with expansion, leading to dynamics involving complicated interactions of intergranular liquid flow and hydrogel deformation. It is thus difficult to predict the water absorption rate of these materials. Water flow in hydrogel-coated capillary tubes also occurs with the deformation of flow passages, so it can be analogous to capillary flow through porous structures made of hydrogels. Here we report a combined experimental and theoretical investigation of water flow through capillaries whose inner surface is covered with a hydrogel layer. We experimentally measured the flow rate of water through hydrogel-coated capillary tubes and the volume of water absorbed by the hydrogel layer. We developed a mathematical model for capillary flow including the effects of the water absorption and swelling of the hydrogel layer. Our model is in good agreement with the measurements of the water flow rate and elucidates how the absorption and swelling of hydrogel regulate capillary flow. This study provides a theoretical framework for understanding the dynamics of capillary flow through porous structures composed of hydrogels, leading to insights into the engineering applications of porous hydrogel materials.

Figure 1

(a) Schematic illustration of hydrogel-coated capillary tube production. (b) Cross-sectional images of the hydrogel-coated capillary tube before and after swelling

Figure 2

Schematic illustrations of experimental setups for (a) measuring volume of water absorbed by the hydrogel layer and (b) measuring imbibition length in hydrogel-coated capillary tubes. Sequential images of imbibing water through hydrogel-coated tubes made of hydrogels (c) I and (d) II. Arrows indicate imbibition front.

Figure 3

(a) The dependence of the water column height difference $h$ on time $t$ in experiments with cut tube pieces, illustrated in Fig. 2. Circles indicate $t_e$. (b) The dependence of the square of the imbibition length $l^2$ on time $t$ in long capillary tubes made of hydrogels I and II in experiments illustrated in Fig. 2. The experiments were repeated three times, and the error bars indicate the maxmin range.

Figure 4

Schematic illustrations of (a) a bird's eye view and (b) a cross-sectional view of the hydrogel-coated capillary tube. Dotted box indicates the control volume used for analysis.

Figure 5

(a) Prediction of dependence of ${\tilde{l}}^2$ on $\tilde{t}$ for various $\varepsilon$ values by (11). (b) Comparison between theoretical predictions and experimental measurements of imbibition length of water through the capillary tubes coated with hydrogel I or II. The measurements of $t_e$, $\lambda$, and $\varepsilon$ for each hydrogel are listed in Table 1.

Figure 6

The dependence of ${\tilde{V}}_{\mathrm{tot}}$ on $\varepsilon$ for various $a/R$.