The Effect of the Contact Angle on a Flow With Condensation and Evaporation Through a Microchannel

The flow of a fluid that is in a state of saturated vapor at the upstream side of a channel is considered. The flow is described by applying the balances of mass, momentum and energy. One-dimensional flow and heat conduction is assumed. Account is taken of the Joule-Thomson effect and, for contact angles smaller than 90°, of the capillary pressure given by the Young-Laplace equation and of the vapor pressure reduction at a curved meniscus due to Kelvin’s equation. For a diameter of the channel below a certain threshold the vapor condenses fully, liquid flows through a part of the channel, the fluid evaporates at a location within the channel and vapor flows through the remaining part of the channel. The threshold diameter below of which the fluid condenses fully is a function of the fluid properties and of the effective thermal conductivity of the fluid-filled channel. The threshold diameter lies in the range from a few tens of nanometers for bad heat conductors to a few hundreds of nanometers for very good heat conductors such as multi-walled carbon nanotubes. Solutions are given for the flow problem with a contact angle of 90° and with contact angles smaller than 90°. The mass flux is considerably larger for contact angles smaller than 90°. However, as long as the contact angle is smaller than approx. 70°, the mass flux is nearly independent of the contact angle.