Dropwise condensation occurs when a vapor condenses on a surface not wetted by the condensate. For nonmetal vapors, dropwise condensation gives much higher heat transfer coefficients than those found with film condensation. For instance, the heat transfer coefficient for dropwise condensation of steam is around 10 times that for film condensation at power station condenser pressures and more than 20 times that for film condensation at atmospheric pressure. In circumstances where the filmwise coefficient is of similar magnitude to that on the cooling side, a change of mode to dropwise condensation offers a potential improvement in overall coefficient by a factor of up to around 2.
Clean metal surfaces are wetted by nonmetallic liquids and film condensation is the mode which normally occurs in practice. Nonwetting agents, known as dropwise promoters, are needed to promote dropwise condensation. Successful industrial application of dropwise condensation has been prevented by promoter breakdown, often associated with surface oxidation. Polytetrafluorethylene (ptfe, "teflon") provides an excellent nonwetting surface, but it has not been possible to produce sufficiently thin durable surface layers. (See also Wettability.)
Various promoters have been identified and used successfully in laboratory tests, mainly with steam and also a few organic fluids having relatively high surface tension. A typical example is dioctadecyl disulphide, which has given lifetimes of hundreds or thousands of hours in laboratory investigations. Dropwise condensation of steam has been observed on chromium and gold surfaces which are very smooth, without use of a promoting agent. It seems probable, however, that nonwetting impurities were present.
The high heat transfer coefficients obtainable with dropwise condensation are very susceptible to reduction by the presence in the vapor of noncondensing gas. In the absence of significant vapor velocity, very small gas concentrations lead to appreciable lowering of the heat transfer coefficient. This was largely responsible for wide discrepancies between early published values.
During dropwise condensation, the bare surface is continually exposed to vapor by coalescences between drops and by the sweeping action of the falling drops as they are removed from the surface by gravity or vapor shear stress. "Primary" drops are formed at nucleation sites on the exposed surface (typical nucleation site densities are 107 to 108 sites/mm2). The primary drops grow by condensation until coalescences occur between neighbors. The coalesced drops continue to grow and new ones form and grow at sites exposed through coalescences. As the process continues, coalescences occur between drops of various sizes while the largest drops continue to grow until they reach their maximum size, when they are removed from the surface by gravity or vapor shear stress. The diameter ratio between the largest and smallest drops during dropwise condensation of steam is around 106.
Le Fevre and Rose (1966) have noted that three factors are involved in the mechanism of heat transfer through a single drop. These are: conduction in the liquid (important for relatively large drops), interphase matter transfer at the vapor-liquid interface (important for very small drops) and curvature of the vapor-liquid interface (important for the smallest drops).
By using an approximate expression for the distribution of drop sizes, together with their equation for the heat-transfer rate through a drop of given size, Le Fevre and Rose (1966) obtained the relation between the mean heat flux for the surface and the vapor-to-surface temperature difference. This showed, in agreement with experiment and in contrast to film condensation, that the heat transfer coefficient for dropwise condensation increases with increasing vapor-to-surface temperature difference.
Theory and experiment also indicate that the heat transfer coefficient decreases with decreasing pressure. Although in closed form and in principle applicable to any fluid, the expression giving the heat transfer coefficient is lengthy. An empirical equation in good agreement with both theory and experiment for dropwise condensation of pure, quiescent steam is:
where α is the vapor-to-surface heat-transfer coefficient, ΔT is the vapor-to-surface temperature difference and θ is the Celsius temperature of the vapor. Discussion of the theory and comparisons with experimental data are given in Rose (1988, 1994).
There is conflicting evidence for the effect of the thermal conductivity of the condenser surface material on the heat-transfer coefficient resulting from non-uniformity of the surface heat flux. The balance of evidence suggests that this is only important at very low vapor-to-surface temperature difference where the condensing side resistance would probably be negligible in practice [see Rose (1994)].
Reviews of dropwise condensation heat transfer have been made by Le Fevre and Rose (1969), Rose (1988), Tanasawa (1991), Marto (1994) and Rose (1994).
Le Fevre, E. J. and Rose, J. W. (1966) A Theory of Heat Transfer by Dropwise Condensation. Proc. Third Int. Heat Transfer Conf. 2, 362-375.
Le Fevre, E. J. and Rose, J. W. (1969) Dropwise Condensation. Proc. Symp. Bicentenary of James Watt Patent, Univ. Glasgow, 166-191.
Marto, P. J, (1994) Vapor Condenser, in McGraw Hill Year Book of Science and Technology, 428-431, McGraw Hill.
Rose, J. W. (1988) Some Aspects of Condensation Heat Transfer Theory. Int. Communications in Heat and Mass Transfer, 15, 449-473. DOI: 10.1016/0735-1933(88)90043-7
Rose, J. W. (1994) Dropwise Condensation. Heat Exchanger Design Update, 2.6.5, 1-11. Begell House.
Tanasawa, I. (1991) Advances in Condensation Heat Transfer, Advances in Heat Transfer, 21, 55-139, Academic Press.
- Le Fevre, E. J. and Rose, J. W. (1966) A Theory of Heat Transfer by Dropwise Condensation. Proc. Third Int. Heat Transfer Conf. 2, 362-375.
- Le Fevre, E. J. and Rose, J. W. (1969) Dropwise Condensation. Proc. Symp. Bicentenary of James Watt Patent, Univ. Glasgow, 166-191.
- Marto, P. J, (1994) Vapor Condenser, in McGraw Hill Year Book of Science and Technology, 428-431, McGraw Hill.
- Rose, J. W. (1988) Some Aspects of Condensation Heat Transfer Theory. Int. Communications in Heat and Mass Transfer, 15, 449-473. DOI: 10.1016/0735-1933(88)90043-7
- Rose, J. W. (1994) Dropwise Condensation. Heat Exchanger Design Update, 2.6.5, 1-11. Begell House.
- Tanasawa, I. (1991) Advances in Condensation Heat Transfer, Advances in Heat Transfer, 21, 55-139, Academic Press.
Heat & Mass Transfer, and Fluids Engineering