Capillary Flow with Evaporation in Open Rectangular Microchannels

Abstract

Numerous applications rely upon capillary flow in microchannels for successful operation including lab-on-achip devices, porous media flows, and printed electronics manufacturing. Open microchannels often appear in these applications, and evaporation of the liquid can significantly affect its flow. In this work, we develop a Lucas−Washburntype one-dimensional model that incorporates the effects of concentration-dependent viscosity and uniform evaporation on capillary flow in channels of a rectangular cross section. The model yields predictions of the time evolution of the liquid front down the length of the microchannel. For the case where evaporation is absent, prior studies have demonstrated better agreement between model predictions and experimental observations in low-viscosity liquids when using a no-slip rather than a no-stress boundary condition at the upper liquid-air interface. However, flow visualization experiments conducted in this work suggest the absence of a rigidified liquid-air interface. The use of the no-stress condition results in overestimation of the time evolution of the liquid front, which appears to be due to underestimation of the viscous forces from (i) the upper and front meniscus morphology, (ii) dynamic contact angle effects, and (iii) surface roughness, none of which are accounted for in the model. When high-viscosity liquids are considered, the large bulk viscosity is found to suppress these factors, resulting in better agreement between model predictions using the no-stress condition and experiments. Model predictions are also compared to prior experiments involving poly(vinyl alcohol) in the presence of evaporation by using the evaporation rate as a fitting parameter. Scaling relationships obtained from the model for the dependence of the final liquid-front position and total flow time on the channel dimensions and rate of uniform evaporation are found to be in good agreement with experimental observations.

Capillary rise and evaporation of a liquid in a corner between a plane and a cylinder: A model of imbibition into a nanofiber mat coating

“…These points are marked in Figure 7 by diamond symbols for all λ(τ ) curves. The values λ max and τ max are depicted in Figure 8 as functions of E. It is clear that λ max ∝ E −1/2 and τ max ∝ E. The same scaling has been predicted for the capillary rise in triangular grooves in [30] and for capillary rise and evaporation in open rectangular microchannels [29].…”

“…Kolliopoulos et al [29] developed a one-dimensional model describing the imbibition and evaporation of liquids in rectangular channels. The model resulted in a scaling law for the final position of the liquid front.…”

Capillary-flow dynamics in open rectangular microchannels

“…Capillary channels were prepared by first casting a silicone stamp (Sylgard 184) over the master pattern, curing the stamp and then using the stamp to imprint UV-curable adhesive (Norland Products NOA68 or NOA73) as explained in Kolliopoulos et al. (2019). Briefly, the UV-curable adhesive was coated on glass slides and then the silicone stamp was pressed into the adhesive.…”

“…2016; Kolliopoulos et al. 2019). This is because the mechanism for capillary flow in open channels is more complex than that for closed channels.…”

“…2018; Kolliopoulos et al. 2019), trapezoidal (Chen 2014), U-shaped (Yang et al. 2011) and V-shaped (Rye, Yost & O'Toole 1998; Mann et al.…”