The quantum of energy transported during evaporation: Investigation of a fundamental constant

Paper number

IAC-17,A2,4,1,x36654

Author

Dr. Aaron H. Persad, University of Toronto, Canada

Year

2017

Abstract

The Earth has the largest evaporating interface in the solar system.  Evaporation affects us personally (it cools the body perspiration), impacts everyone globally by driving the hydrological cycle and controlling Earth's  climate,  and  provides  insight  into  the  origins  of  the  universe  and  of  life  (for  instance,  drying droplets are often used create molecular self-assemblies).  Efficient management of the energy consumed during evaporation is of tremendous importance to the global multi-billion dollar energy industry, and thus to our economic welfare.  Furthermore, understanding how energy is transported to the water-vapour interface  is  critical  to  the  development  life  support  systems  for  spacesuits  and  spacecraft,  and  to  the efficient management of limited energy resources on space missions. 

It is therefore surprising that, despite its ubiquitous presence and importance, the evaporation process is still not understood.  For the past 130 years, evaporation models have used the classical kinetic theory (CKT)  approach,  which  has  neglected  important  physical  phenomena,  such  as  interfacial  temperature discontinuities, resulting in poor agreement with experiments, inconsistent predictions of liquid properties, and an incomplete picture of how the energy is transported. 

Here, the statistical rate theory (SRT) approach (based on the quantum-mechanical concept of state-transition probabilities) is used to model evaporation.  The quantum of molecular transport is generally accepted to be one molecule since no less than a single molecule can evaporate in an instant.  However, specifying the quantum of energy
transport is more difficult.  The frequencies of water O-H bonds that straddle the interface have been reported to shift with the hydrogen bonding of surface molecules with the bulk liquid phase [1].  Using SRT, an expression for the heat  flux conducted to the interface during evaporation is derived.  We examine the SRT heat  flux expression using steady evaporation experiments of water, and we show that the quantum of energy transported in an instant corresponds to the frequency shifts  of  the  water  O-H  bonds.   Our  derivation introduces  a  ratio  of  the  entropy  change  from  molecular  transport  to  that  from  energy  transport;  we   find  that  it  is  both  constant  and  independent  of  the evaporation system.  This evaporation constant leads to predictions of the heat  flux that agree with the experiments.  Thus, the SRT approach captures atomic-level details of the evaporation process and eliminates the necessity of measuring temperature gradients at the interface, thereby reducing the cost and complexity of both ground-based and space experiments.

[1] Stiopkin et al.  Nature, 2011, 474, 192-195.

Abstract document

IAC-17,A2,4,1,x36654.brief.pdf

Manuscript document

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