Evaporation rates from square capillaries limited by corner flow viscous losses

Abstract

Evaporation is an important process in water exchange between soil and atmosphere as well as applications in industry. Predictions of drying rates from porous media are very difficult due to its highly non-linear behavior with typically high and fairly constant drying rates in the beginning followed by a drop to low rates. The high drying rates at the first stage of drying are attributed to the presence of liquid patches retained in corners of the partially air filled pore space that are interconnected to form conductive pathways. Under increasingly dryer circumstances these liquid connections break leading to the diffusion dominated low drying rates of the second stage. The maximum extent of this corner flow region that determines the duration of the first stage is controlled by capillary forces opposed by gravity and viscous losses. To quantify these mechanisms, evaporation is studied from a single glass capillary with square cross section. Such geometry shows similar drying curve characteristics as macro-scale porous media with high rates as long as thick capillary sustained corner films extent between the receding meniscus and capillary surface. Increased flow resistance and gravity force as drying proceeds lead to film break-up at certain characteristic meniscus depth LC. LC was studied experimentally for drying of liquids ethanol and water from different capillary sizes under a range of evaporation rates and capillary inclination angles. This way the forces determining the extent of the corner films were changed systematically. Break-up of films as well as evolution of main meniscus depth were monitored to deduce LC and drying rates. For ethanol initial evaporation rates were in the order of 1000 mm/day and dropped abruptly when the corner films broke up. Increasing the evaporation rate led to a shortening of the films, whereas with decreasing gravity component the films became significantly longer. Maximum corner film extent for water was much shorter and mainly limited by corner geometry due to its high contact angle of 30°. Model predictions on LC based on force balance and corner flow equations gave good results that were in accordance with the experimental data. The roundedness of the capillary corners had a large influence on maximum film length by limiting the curvature of the liquid interface at the capillary surface. This roundedness represents a critical pore size in real porous media that determines the maximum extent of the corner film region.