Model of the Evaporating Meniscus in a Capillary Tube

Abstract

A mathematical model describing the evaporating meniscus in a capillary tube has been formulated incorporating the full three-dimensional Young–Laplace equation, Marangoni convection, London–van der Waals dispersion forces, and nonequilibrium interface conditions. The results showed that varying the dimensionless superheat had no apparent effect on the meniscus profile. However, varying the dispersion number produced a noticeable change in the meniscus profile, but only at the microscopic level near the tube wall. No change in the apparent contact angle was observed with changes in the dimensionless superheat or dispersion number. In all cases, the dimensionless mean curvature was asymptotic to a value equal to that for a hemispherical meniscus. The local interfacial mass flux and total mass transfer rate increased dramatically as the dispersion number was increased, suggesting that surface coatings can play an important role in improving or degrading capillary pumping. The model also predicted that the local capillary pressure remains constant and equal to 2σ/rc regardless of changes in the dimensionless superheat and dispersion number. It should be noted that the results in this study are theoretical in nature and require experimental verification.

Characteristics of an Evaporating Thin Film in a Microchannel

“…4 it is seen that P c (= σ/R) approaches a constant value in the intrinsic meniscus, indicating that the film radius approaches the value R*, which is approximately half of the channel height H when the liquid is completely wetting [6,26,27]. A larger R* corresponds to a flatter thickness profile so that the thin film region is larger, as is evident from a comparison of Fig.…”

“…In [23], the far-field condition is set by assuming that the film slope approaches a constant value (i.e., the meniscus radius R approaches infinity). For a meniscus in a channel, however, R should approach the constant radius R* in the intrinsic meniscus, which is approximately half of the channel height H when the liquid is completely wetting [26,27]. The variation of meniscus radius with respect to x is discussed 8 further in Section 3.…”

Transport from a volatile meniscus inside an open microtube

“…Therefore the influence of flow on the interface shape is negligible and the curvature is almost constant [20,21]. In the simulation, the meniscus is assumed to be part of the surface of a sphere which has an assumed contact angle with the inner wall of the tube.…”

Evaporation heat transfer of steady thin film in micro capillary tubes of micron scale

“…In this paper, the heat flux is smaller, and the reflux effect can be neglected. The qualitative analysis showed that the change of disjoining pressure would lead to a greater profile variation of the meniscus [7]. This influence is further studied.…”