Page 350 - Mechanical Engineers' Handbook (Volume 4)

3 Heat Transport Limitations 339

Table 1 Pressure Differences Across the Liquid–Vapor Curved Surfaces
Pressure Difference Across the
Names/Structures Liquid–Vapor Interface Notes
p v p l
Vapor bubble in liquid phase 1 1 2 r r 1 r 2
r 1 r 2 r
p l
r
p v

Liquid drop in vapor phase p l p v 1 2 r r 1 r 2
1
r 1 r 2 r
p v
p l
r

1
Liquid in a micro triangular groove p v p l r 2
1

p v r 1 r 2 r r constant.
r
p l
p v p l
Capillary wicking in a capillary tube 1 1 2 2 gh r r 1 r 2
σ r 1 r 2 r r b
α cos
r
p v
h
p l
2r b

according to the wicking structure, working fluid, evaporator heat flux, vapor flow channel,
and operating temperature.

Capillary Pressure
When the meniscus radius exists at a liquid–vapor interface, there is the pressure difference
across the interface, which can be determined by the Laplace-Young equation shown in Eq.
(2). During steady-state operation, it is generally defined that the maximum capillary pressure
exists when the capillary radius in the condenser approaches infinity and the capillary radius
in the evaporator reaches the smallest one. To generalize the application, the maximum
capillary pressure can be expressed as a function of only the effective capillary radius of the
evaporator wick, i.e.,

2
p c,max (4)
r c,e