Fig. 4: Sorptivity measurement across varied sample sizes, aspect ratios, and geometries.

a This subplot shows water absorption in pastes with aspect ratios from 1 to 2.5. Wetted area ratios remain consistent, ranging between 81.7% and 84.2% at Nick times for the tested samples. b Confirms that the Nick time is mainly determined by the square root of the prism aspect ratio (√(h/a). It also emphasizes that the primary and secondary sorptivities will stay uniform, irrespective of the aspect ratios. c Paste prisms with aspect ratios of 1.5 and 2.5 were split in half. Wetted area ratios closely matched surface measurements with USB microscope cameras, differing by only 3.2%. This supports the robustness of single-side camera measurements and suggests potential accuracy enhancement with dual-side measurements, especially for shorter samples, e.g., aspect ratio = 1.5. d Analyzing sorptivity distribution reveals dominance of initial values with wetted area ratios below 0.8. In contrast, secondary sorptivities exhibit a trend of ratios exceeding 0.8, leading to a skewed distribution towards higher values. e Our observations reveal that Nick time typically occurs between a wetted area ratio of 70–90%, averaging around 85%. This marks the intersection of the initial and secondary sorptivity fitted lines. Source data are provided as a Source Data file.