Instability of Marangoni toroidal convection in a microchannel and its relevance with the flowing direction

Abstract

The instability of the Marangoni toroidal flows in microchannels is of interest in various areas such as microfluidics and heat transfer. Using pure liquid as working fluid in this study, the phenomena of Marangoni symmetry-to-asymmetry transition which does not arise from the buoyancy was observed. The experiments used a vertical cylindrical channel and the meniscus was formed at the bottom outlet to minimize the buoyant influences. Two microscopes were used to have top view and side view of the meniscus simultaneously. The Marangoni flow field on the meniscus was obtained by means of tracing particles. It was observed that the Marangoni flow on a concave meniscus was always nearly symmetrical, while that on a convex meniscus was out of symmetry with only one single vortex occupying the whole channel. The experimental results were highly consistent to the simulation results of authors' previous 3D numerical model (Pan and Wang in Microfluid Nanofluid 9:657, 2010). Theoretical analysis together with newly developed numerical models is employed to dig into the mechanisms. The inward (from the meniscus edge to the center) Marangoni flow is found not as stable as the outward one. Based on the heat transfer analysis, a concave meniscus always has a colder edge thus the flow is outward and stable; while a convex enough meniscus could have an inward flow thus not stable and tends to lose the symmetry. The amplification mechanism of the inward Marangoni flow is comprehensively explained. Two conditions are required for the inward flow to lose the symmetry, i.e., the bulk liquid must be warmer than the meniscus, and the Marangoni number must be above a certain small value.

Marangoni convection in evaporating meniscus with changing contact angle

“…They argue that the evaporation rate is higher at the meniscus wedge than at the centre; this is because the meniscus wedge is closer to the tube mouth than the centre, and therefore, the vapour transports more efficiently at the wedge. Pan et al (2011) also argue that the wedge is further away from the warmer liquid bulk than the centre for a concave meniscus.…”

“…Additionally, it was found that the Marangoni flow from the meniscus wedge to its centre is not to be found as stable as the opposite flow. Pan et al (2011) argue also that for a meniscus convex enough, the wedge should become warmer than the centre and the Marangoni convection should reverse.…”

“…Three meniscus shapes were investigated, namely concave, flat and convex. The goal of this experiment is to prove or disprove the theory postulated by Wang et al (Wang et al 2008) and Pan et al (2011) that the meniscus wedge is colder than the its centre because it is closer to the tube mouth and further away from the liquid bulk.…”

“…Surprisingly, the direction of the Marangoni rolls is always the same independently of the meniscus contact angle. According to Wang et al (2008) and Pan et al (2011), for a concave meniscus, the wedge is closer to the tube mouth and further away from the liquid bulk with respect to the meniscus centre, and therefore, the wedge is colder than the centre of the meniscus. Therefore, the Marangoni rolls spin from the centre to the wedge bringing hotter fluid to the triple line region at the meniscus wedge.…”

“…Instabilities of the toroidal Marangoni vortex have been recently reported in Pan et al (2011) for a meniscus formed inside a capillary positioned vertically with the meniscus at the bottom in order to minimize buoyancy effects. The authors showed that the Marangoni flow in a concave meniscus is always symmetrical to the tube axis, whereas that on a convex meniscus is reversed with respect to the concave meniscus, which results in an instability that is easily perturbed into a non-axisymmetric rolling motion.…”