Smaller Water Droplets Evaporate More Gradually than Larger Ones

Although the process of evaporation has hitherto been understood completely, physicists from the Warsaw Institutes of the Polish Academy of Sciences have discovered one more element of surprise—smaller water droplets get evaporated very gradually when compared to larger ones.

Small drops of micro- and nanometer dimensions have surprised researchers: they evaporate more slowly than expected from hitherto predictions, because of the ballistic energy transfer between gas molecules and the surface of liquid. A similar mechanism drives the Newton’s cradle. CREDIT: IPC PAS, Grzegorz Krzyżewski.

Apart from water, this appears to be true for other liquids too: it has emerged that smaller droplets get evaporated more gradually than existing theories. Scientists from the Institute of Physical Chemistry of the Polish Academy of Sciences (IPC PAS) in Warsaw collaborated with the Institute of Physics of the PAS (IP PAS) and adopted theoretical analysis, computer simulations, as well as experiments to elucidate the progression of evaporation of micro- as well as nano-scale droplets. The outcomes of the study, reported in the Soft Matter journal, is an equation that precisely estimates the progression of evaporation of droplets of different fluids with varying sizes. Apart from other applications, the equation can be used to develop more correct climate models and also to create highly efficient cooling units or internal combustion engines.

At first glance, the slowdown of small droplet evaporation described by us may seem to be an effect of little significance. It must be borne in mind, however, that every drop that has ended its life due to evaporation into the environment has first had to decrease to the size of micro- and then nanometres, and thus has passed through the phase of slowed-down evaporation,” reiterated Professor Robert Holyst (IPC PAS), who stated that one such case of structures formed of more number of smaller droplets are clouds, which predominantly determine earth’s climate. “If we take into consideration that the climate is a state of a certain dynamic equilibrium in the environment that is relatively easily disturbed by even seemingly minor factors, then the slowdown of the speed of evaporation of small droplets we are examining suddenly transforms from being an issue on a laboratory scale to a global phenomenon.”

In the course of evaporation, flow of heat plays a significant part between the environment and the droplet. In prior studies, IPC PAS and IP PAS physicists demonstrated that evaporation is initiated even under local temperature differences of just ten-thousandths of Kelvins. Yet, it is not mandatory that the transfer of energy between the environment and the liquid is dependent on the occurrence of a temperature gradient every time.

When a gas molecule approaches a liquid surface at a distance of several to a dozen or so mean free paths, it virtually stops colliding with other molecules in its environment. At this point, a typical description of the phenomenon by means of thermodynamics is no longer sufficient. Near the surface of the liquid, energy transport takes place in a different manner, ballistically. The gas molecule simply takes its energy and hits the surface, sometimes several times.

Dr Marek Litniewski (IPC PAS), co-author of the study.

A molecule’s mean free path length in the air—or the length from impact with one molecule to impact with another—is nearly 70 nm. In the course of evaporation, the ballistic transport of energy already starts playing a part on behalf of gas molecules located a few micrometers away from the droplet’s surface, which, for the level of the phenomenon, must be considered to be a comparatively huge value. This paves the way for the following question: what is the amount of energy transfer in this manner and how is it transferred? Despite the fact that a single gas molecule collides with only a single liquid molecule, the liquid is more weaky or strongly linked to its farther and closer neighbors, respectively. Consequently, the collision takes place among a number of bodies and its theoretical explanation becomes very important.

If the drop is large, its surface from the point of view of the gas molecule will be practically flat. Therefore, when such a molecule bounces off the surface, it can collide with another nearby gas molecule and hit the surface again, depositing another portion of energy into it. The situation changes when the drop decreases in size and its surface becomes more and more curved. The particle then bounces off the surface generally once, after which it flies off into space. The transfer of energy to the interior of the liquid is thus less effective. As a result, the drops evaporate more slowly the smaller they are, and the process can be slowed down at least several times,” noted Professor Holyst.

Experiments performed by Dr Daniel Jakubczyk at IP PAS supported the computer analyses and simulations. Several single-drop evaporation rates were evaluated under carefully regulated conditions. The experiments were carried out for droplets of liquids as disparate as ethylene glycol and water, and of differing sizes. It emerged that the model predicted by physicists at IPC PAS in all respects precisely elucidated the phenomenon’s progression. To predict the speed at which a drop evaporates, just two parameters—enthalpy of evaporation and substance mass—were adequate.

Evaporation takes place all around us, always and everywhere. Science has been studying it more carefully for more than 120 years and so far we have all been convinced that we have a good understanding of this phenomenon. However, when we look into the details of the process of evaporation, we suddenly see how much we have missed. This teaches us humility—and encourages us to conduct further research,”

Professor Robert Holyst (IPC PAS), co-author of the paper

An OPUS grant from the Polish National Science Centre financed the study on evaporation.

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