Capillary rise between cylinders

Abstract

The capillary rise of liquid in the gap between two closely spaced parallel cylinders, whose radii may be identical or different, is modelled in this paper. On the basis of the minimum free energy principle and interfacial analysis, the vertical capillary rise of liquid at equilibrium was calculated as a function of distance of separation of the two cylinders. In order to validate our theory, a piece of experimental apparatus was designed and a series of experiments was conducted on it. Compared with the experimental data, our theoretical model gave a reasonably accurate prediction within experimental error except at a small separation of cylinders. Possible experimental errors were discussed. We also showed that the wicking height at equilibrium was nonlinear to the reciprocal of the hydraulic radius.

Modelling of wicking and moisture interactions of flax and viscose fibres

“…10), along with the diameters of viscose and flax found from the ESEM results, the upper boundary for an interfibre capillary radius is 5.5 m for viscose and 2.7 m for flax. The flax lumen radii are also of a similar order and hence also in general agreement with MWE predictions (Charlet et al, 2010;Liu et al, 2007;Masoodi, 2010;Masoodi et al, 2012).…”

“…Decreases in mass subsequent to water uptakes were also observed in some cases in both phases. These rapid uptakes suggested movement of water through channels such as the lumens present in the flax fibres and in channels formed between fibres (inter-fibre) as opposed to within the fibres themselves, by absorption (Charlet et al, 2010;Liu, Choi, & Li, 2007). The occasional lack of uptake steps in a sample run that had previously exhibited rapid wicking, which occurred especially in viscose samples, was also observed.…”

“…The appearance of uptake steps in the prolonged phase did not seem to follow a pattern. These steps may have been through the formation of inter-fibre capillaries due to random fibre movements within the bundles or overcoming of blockages within the bundles (Anonymous, 1923;Gouanvé et al, 2007;Liu et al, 2007). In a small number of cases a gradual uniform increase in mass, represented as a constant positive gradient, across the time frame of the prolonged uptake phase was also observed.…”

Wicking in twisted yarns

“…(1) is composed of many parts formed between adjacent fibers in the yarn surface. In an individual curve, assuming it constitutes part of a circumference, the arc length can be obtained by the theory developed in [15,19]. When the number of the constituent fibers is large, the calculation of all the arc lengths is extremely complicated and time-consuming.…”

Equilibrium height of a liquid in a gap between corrugated walls under spontaneous capillary penetration

“…The evolution of the liquid between the plates toward its equilibrium has been recently analyzed in the case when viscous forces dominate the motion of the liquid [8]. The equilibrium height in the gaps between vertical cylindrical fibers has also been carefully analyzed under several configurations [9][10][11]. Another interesting case occurs in a capillary of square cross-section, in which the elevation of the liquid is greater near the corners than at the center of the capillary, and an approximate analytical expression for the equilibrium shape has been found [10].…”