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Applied Thermal Engineering 62 (2014) 607e612

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Molecular dynamics simulation on rapid boiling of water on a hotcopper plate

Yijin Mao, Yuwen Zhang*

Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA

h i g h l i g h t s

� Molecular dynamics simulation is carried out to study the rapid boiling of liquid water film.� A more physically-sound thermostat is applied to control the temperature of the metal plate.� The liquid water molecules near the plate are instantly overheated and undergo a rapid boiling.� A non-vaporization molecular layer tightly attached to the surface of the plate is observed.� The piston-like motion of the bulk liquid film are computed and analyzed.

a r t i c l e i n f o

Article history:Received 12 June 2013Accepted 18 October 2013Available online 27 October 2013

Keywords:BoilingRapid phase transitionMolecular dynamics

* Corresponding author.E-mail address: zhangyu@missouri.edu (Y. Zhang)

1359-4311/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.applthermaleng.2013.10.03

a b s t r a c t

Molecular dynamics simulation is carried out to study the rapid boiling of liquid water film heated by ahot copper plate in a confined space. A more physically-sound thermostat is applied to control thetemperature of the metal plate and then to heat water molecules that are placed in the elastic wallconfined simulation domain. The results show that liquid water molecules close to the plate are instantlyoverheated and undergo a rapid phase transition. A non-vaporization molecular layer, with a constantdensity of 0.2 g/cm3, tightly attached to the surface of the plate is observed. Temperatures at threecorresponding regions, which are vapor, liquid, and vapor from the top plate surface, are also computedand analyzed along with the piston-like motion of the bulk liquid film.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In a normal boiling process, the vapor bubble is generatedheterogeneously near the heat wall. When the liquid is superheatedto a degree much higher than the normal saturation temperatureand approaching the thermodynamic critical temperature, homo-geneous vapor bubble nucleation takes place at an extremely highrate, which lead to the near-surface region of the materials beingejected rapidly [1]; this process is referred to as rapid boiling. Therapid boiling is also referred to as vapor explosion, phase flashing,thermal detonation, and rapid phase transitions. Many specialevents occur during rapid boiling, such as pressure shock wave,bubble clusters formed by tiny bubbles, and high superheat. Manyexperimental works are reported [2e5], but these experimentalworks are limited in either length or time scales. Due to the limi-tation of classical macroscopic theory, many special phenomena inphase explosion cannot be well explained.

.

All rights reserved.2

A molecular dynamics (MD) simulation, which has advantagesof describing any physical process at atomic level, is widely appliedto study micro- and nanoscale heat and mass transfer problems.Dou et al. presented a microscopic description on rapid boiling ofwater films adjacent to heated gold surface, and found that thevaporization phenomena highly depended on the initial thicknessof thewater film [6]. Gu and Urbassek performedMD simulation onrapid boiling of liquid-argon films irradiated by ultrafast laser [7].Zou et al. simulated a homogeneous nucleation of water and liquidnitrogen in the rapid boiling, and energy conversion and redistri-bution were studied [8].

Though the existing MD work have provided some molecularlevel understandings of the phase transition in the rapid boiling,few work revealed the thermal and dynamic mechanisms causedby an extremely high heat flux through metal plate, like copper.Moreover, few researchers paid attentions on the dynamic phe-nomenon associated with different phases after the rapid boiling,although mechanical factor (like thermal stress) was alwaysconsidered as an important effect determining machining perfor-mance in most applications. A study of mechanical behavior ofwater film is important from both fundamental and practical points

Nomenclature

d lattice constant, �AE Young’s modules, GPak spring constant, eV/�A2

kB Boltzmann constant, J/KkC electrostatic constant, �A$kcal/molm molar mass, g/molN number of atomsq electron charge, erij distance between two atoms i and j, �AT temperature, KUab potential function, JV volume, �A3

vs speed of sound, m/s

Greek symbolsDt time step, ps3 depth of potential well, kcal/molq angle, �

s minimal distance between atoms when potentialenergy equal to zero, �A

uD Debye frequency, s�1

Y. Mao, Y. Zhang / Applied Thermal Engineering 62 (2014) 607e612608

of view, due to the trends of miniaturization of devices (e.g.: MEMSand NEMS) and a demand by the development in many othertechnologies like water photo-electrolysis [9] and boundary lubri-cation [10].

In this paper, both thermal and dynamic phenomena of an ul-trathin water film will be investigated during and after rapidboiling.

Fig. 1. Structures of the copper plate, artificial harmonic bond are created by con-necting neighbor atom within a distance of 2.56 �A.

2. Physical models and methods

The computational domain is divided into three regions, namelyvapor, liquid and solid region. Both vapor and liquid regions arefilled with water molecules, and the solid is a copper plate. Inconsideration of accuracy in description of water’s dynamic andthermal properties, a four-site water model (TIP4P) [11] is adaptedto model vapor and liquid water. The well-accepted water molec-ular potential function, which consists of the contributions fromelectrostatic, dispersion and repulsive forces, is used to describeintermolecular interaction of water molecules:

Uab ¼Xai

Xbj

kCqaiqbj

raibjþXai

Xbj

4 3aibj

" saibjraibj

!12

� saibj

raibj

!6#

(1)

where, a and b denote two different molecules, subscript i and jrepresent atoms of hydrogen or oxygen in one individual TIP4Pmolecule, and kC is the electrostatic constant. The long-rangecolumbic contribution to the entire system is computed by PPPM(particleeparticle particleemesh) approach [12] with an accuracyof 1.0 � 10�6. It should be pointed out that the pair potential onlycounts the interaction between oxygen atoms within the cutoffdistance of 12 �A; both bond and angle interactions within a singlewater molecule are considered as rigid, thus SHAKE [13] algorithmis applied to each water molecule to hold its geometry shape suchthat a longer time step of 1 fs can be utilized. The water region isbuilt with face-center cubic unit (FCC) with lattice constant of37.0�A and 3.103�A, respectively, subjected to the densities of vapor

and liquid at 1 atm [14]. For the copper plate, it is alsomodeledwithface-centered cubic unit (FCC) with the lattice constant of 3.615 �A,which is consistent with the density of 8.9� 103 kg/m3. It should bementioned that the interaction between copper atoms is notconsidered, instead, many artificial CueCu harmonic bonds arecreated for the plate to introduce CueCu spring-like interaction,which will be discussed later. The interaction between copper andoxygen or hydrogen atoms is considered using the Lenard Jonespotential.

In order to introduce a more physically-sound thermostat tocreate heat flux through copper plate rather than artificiallyrescaling velocity of atoms, the copper plate is modeled using theapproach described in Ref. [15]. As shown in Fig. 1, five layers ofatoms are created in FCC configuration. The top three layers (white)are “real” copper atoms. The fourth layer (blue in web version) isconsidered to be phantom atoms exerted with a force combinedwith a damping force and random force that subject to Gaussiandistribution. The fifth layer is fixed in order to prevent atoms frompenetration. The standard deviation of the random force is,

sF ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi2akBTDt

r(2)

where a is dependent on desired temperature and integration timelength,

a ¼ muDp6

(3)

where Debye frequency uD can be estimated by,

uD ¼�

34p

NV

�13

vs (4)

where vs is the speed of sound in the solid. Thus, the energy flux tothe simulation system can be accurately calculated by integratingthe exciting force and the damping force applied to those phantomatoms. It can also be seen from Fig. 1 that an artificial harmonicbond is created by connecting neighbor copper atoms that arewithin its shortest distance of 2.56�A. Since the interaction betweenatoms within the second layer of phantom atom is modeled withartificial harmonic bond, it is important to use a reasonable springconstant to obtain an accurate thermostat. The interatomic springconstant k is tightly related to Young’s Modules thus it could beestimated with formula below,

k ¼ Ed (5)

Table 1Water potential parameters.

Parameters Values Units

3OO 0.006998 eVsOO 3.16438 �AqH 0.52 eqO �1.04 e3CuO 0.06387 eVsCuO 2.7172 �A3CuH 0.03396 eVsCuH 1.335 �AE 274e306 GPad 3.615 �Avs 3901 m/s

Y. Mao, Y. Zhang / Applied Thermal Engineering 62 (2014) 607e612 609

where E is Young’s Modules of solid copper, and d is correspondinglattice constant of solid metal. Table 1 gives all the parametersrequired in this simulation.

The simulation is carried out within the framework of the openSource MD code LAMMPS [16]. The entire simulation box has bothlength and width of 82.89 �A, and a height of 240 �A. Periodicboundary conditions are applied to all directions parallel to thesurface of the plate, while a reflecting wall, which will bound themolecules back when they collide to the wall, is placed at the top toseal the simulation box. No energy transfer will occur through theinteraction between molecules and this wall. By creating this wall,the water film can be successfully confined in the simulation boxand form a stable floating film during the later stage of rapidboiling. At the same time, an empty space is included in the z-di-rection to remove dipole interactions between the slab and itsimages by extending the volume by two times. The water regionsare filled with 12,504 molecules (w6.2 nm in thickness) and thereare 5290 copper atoms in the hot plate. It is worth to mention thatthe size of simulation box and number of watermolecules is chosenbased on the water density at 298 K and 1 atm pressure. Before theliquid water is heated by the hot plate, the system must be equil-ibrated in the following two steps: (1) the entire water zones arefirst equilibrated with certain thermostat (Berendsen thermostat)[17] until the temperature of water system was equilibrated to astable value of 298 K, and (2) the copper plate is then heated to1000 K with “phantom atom” thermostat as stated above while thewater molecules are isolated from the integration. After thosepreparations steps are done, the liquid water at 298 K is suddenlyplaced on the hot plate. The entire system is still integrated withNVE ensemble during the simulation and copper plate is stillcontrolled to desired temperature of 1000 K with “phantom atom”

Fig. 2. Temperature variation of water and hot copper plate.

thermostat. The value of 1000 K is chosen to guarantee that thetemperature above the threshold as above in bubble formation [18]while it is still below the melting point of copper.

3. Results and discussions

The monitored temperatures of the copper plate and entirewater region are recorded and shown in Fig. 2. It can be seen thatthere is an obvious temperature drop from 1000 K to a minimumvalue of 800 Kwhen the “cold”water film touches the hot plate dueto heat conduction mechanism of solid copper. It takes around50 ps before the temperature of the hot copper turning back to1000 K the continuingly added heat flux. The temperature of waterregion keeps increasing from 298 K to 400 K during the initial 80 ps.Fig. 3 gives several snapshots of molecules spatial distribution atrepresentative times (the arrow in the parenthesis denotes the

Fig. 3. Snapshots of water molecule distribution through time 10 pse400 ps.

Fig. 4. z-Component of COM associated to water molecules within the simulation box.

Y. Mao, Y. Zhang / Applied Thermal Engineering 62 (2014) 607e612610

moving direction of the bulk fluid). An obvious volume expansionof liquid water can be observed during the period from 10 to 20 psby measuring the height of the liquid film. A low density vaporregion appears at time of 30 ps, and the entire water domain can beclearly divided into three regions: top vapor region, liquid regionand the lower vapor region near the hot plate. Due to continuousheat flux absorbed by water molecules, the lower vapor regionkeeps expanding up to 80 ps when the water film collide with thetop wall. During this period, the entire wall surface is covered byvapor and the water film floats on the top of the vaporized watermolecules layer in a manner reminiscent of the Leidenfrost phe-nomenon [19]. After the elastic collision with the wall, the film isforced to move backward, as shown in Fig. 3(f). At approximately200 ps, water film starts moving upward again due to larger

Fig. 5. One-dimensional spatial dens

pressure in the lower vapor region. The film hits against the topwall and rebound at 300 ps and suspended at 400 ps again. Incorresponding to piston-like motion of liquid film, the COM’s tra-jectory (z-component) of water region is recorded and shown inFig. 4. The period from 0 to 80 ps is rapid boiling transition, and therest is the bulk liquid’s piston-like motion moment. It can be seenthat the stationary point is flatter and higher, which means that thebulk liquid water will be stationary and eventually suspendedsomewhere adjacent to the wall due to the fact that the systemkeeps receiving the constant flux through copper plate.

In order to have a closer look at the density variation, the spatialdensity profile is computed by averaging density in 63 bins whichare built by uniformly chopping the simulation box in the verticaldirection; the final profile of density are shown in Fig. 5 and thebulk liquid water moving directions are denoted by the arrow. Itcan be seen that themaximum bulk liquid density keeps decreasingduring the moving process until it impact with the wall (seeFig. 5(a)) due to rapid boiling. The increase in themaximum densityat 80 ps comes from the water molecules’ compression due to theirinertia when they hit against the wall. In Fig. 5(b), the maximumdensity also decreases when the bulk liquid moving backwardmainly due to liquid expansion. Comparison between Fig. 5(c) and(d) indicates that the maximum density does not change anymoreand the height of the bulk liquidwater keeps almost a constant; thisindicates that phase change at the liquidevapor interface isbalanced during this period. Interestingly, a non-vaporized watermolecule layer always exists at the interface between solid copperand lower vapor region no matter how long the heating processinglasts. This special zone, which is denoted as “hot gas-like zone”, isalso observed during evaporation process [20]. The density of thiszone decreases during the period of rapid boiling and graduallystabilized at 0.2 g/cm3. Fig. 6 shows the variation of the “hot gas-

ity distribution at various times.

Fig. 6. Top views of water molecules distribution on the surface of the copper plate.

Y. Mao, Y. Zhang / Applied Thermal Engineering 62 (2014) 607e612 611

like”water molecule distribution on the surface of the copper plate.From0 to 60 ps, it can be seenmore andmore localized “dry” regionappears on the wall surface. However, during the later period, afixed number of hot gas-like water molecules attached on thecopper plate even continuous heat flux flows through the plate towater regions. This phenomenon is attributed to disjoining pres-sure that arise from Van der Waals attractive interaction betweentwo parallel layers [21], here, by lower surface of water vapor andtop surface of the copper plate.

The temporal density profile is also computed and rendered intoa 2-D plot in Fig. 7 where the vertical axis is the distance measuredfrom the surface of the copper plate and the horizontal axis is thesimulation time. The band that represents the bulk water film be-comes narrower and narrower during the period of rapid boiling(0e80 ps). It expands a little back to original thickness and keepsconstant due to phase transition balance at the interface, which isconsistent with the results in Fig. 5.

Fig. 8 shows the temperature variation in each region bydynamically detecting the liquidevapor interfaces. During theperiod of rapid boiling, temperature in the lower vapor region ismuch higher than middle liquid film and top vapor regions. Themaximum temperature of lower vapor region is 780 Kwhich is only220 K below the initial temperature of the plate (1000 K). Inconsideration of the temperature drop of the plate, the temperaturedifference between bottom vapor and copper plate is even smaller.

Fig. 7. Variation of one dimensional spatial density distribution with time.

For the lower vapor region, it can be seen that temperature sud-denly fell at around 45 ps when the vapor regions is fully expandedsuch that the amount of kinetic energy of molecules are convertedto potential energy. A similar drop also appear in middle bulk waterfilm due to energy conversion to potential energy during mass fluxflow to the lower vapor region. For the newly created vapor region,an increase at time 70 ps is caused by absorbing the heat fluxcontinuously entering the vapor region. Because the compressionprocess where the kinetic energy is converted to be potential en-ergy again when bulk liquid hit against the wall, a temperaturedrop occurs again. Since all the three regions are compressed at thistime, so all of them have drops at 80 ps. Similarly, at 300 ps, anobvious temperature drop appeared in middle bulk liquid and topvapor again due to compression. The temperature in the lowervapor region does not fall because the volume of this region islarger enough to overcome the kinetic energy loss due tocompression. In addition, continuously entering heat flux providesenough energy to fill the small amount of the lost energy.

4. Conclusions

Molecular dynamics simulation is carried out to study the rapidboiling of liquid water film on a hot copper plate. It was found thatthe bulk liquid water moves like a pistonwith two vapor regions atbottom and top after phase explosion. The trajectory variation of

Fig. 8. Temperature variation in three regions.

Y. Mao, Y. Zhang / Applied Thermal Engineering 62 (2014) 607e612612

water molecule’s COM value (z-component) indicates that thepiston-like motion of the liquid filmwill finally stop and suspendedsomewhere close to the top wall. A group of non-vaporizationmolecular, which has a constant density of 0.2 g/cm3 and tightlyattached to the localized “dry” surface of the plate, is observed nomatter how long the heat process lasts. It is also found that tem-perature at each region decreases during the compression processwhere kinetic energy of molecules is converted to potential energywhen water film hits the fixed top wall. Obviously the moleculardynamics simulation is highly dependent on the accuracy of po-tential functions that are employed; thus different results may beobtained based on different choices of potential functions for watermodels, copper plate, and interaction between them. In otherwords, uncertainties of the potential functions may attribute touncertainty of the final results. It will be worthwhile to study rapidboiling of water using different water models.

Acknowledgements

Support for this work by the U.S. National Science Foundationunder grant number CBET-1066917 is gratefully acknowledged.

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