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Compu a ional cha ac e iza ion
o he beha io o a sali a d ople
in a social en i onmen
Aina a Uga e‑Ane o1, Unai Fe nandez‑Gamiz1*, Koldo Po al‑Po as1, Ekai z Zulue a2 &
Oska U bina‑Ga cia1
The conduc o espi a o y d ople s is he basis o he s udy o educe he sp ead o a i us in socie y.
The pandemic su e ed in ea ly 2020 due o COVID‑19 shows he lack o esea ch on he e apo a ion
and a e o d ople s exhaled in he en i onmen . The cu en s udy, a emp s o p o ide solu ion
h ough compu a ional luid dynamics echniques based on a mul iphase s a e wi h he help o
Eule ian–Lag angian echniques o he ac i i y o espi a o y d ople s. A nume ical s udy has shown
how he beha io o d ople s o pu e wa e exhaled in he en i onmen a e a sneeze o cough ha e
a dynamic equal o he expe imen al cu e o Wells. The d ople s o sali a ha e been in oduced as a
saline solu ion. Conside ing he mass ans e ed and he u bulence c ea ed, he esul s has showed
ha he ambien empe a u e and ela i e humidi y a e pa ame e s ha signi ican ly a ec he
e apo a ion p ocess, and he e o e o he a e. E apo a ion ime ends o be o a highe alue when
he empe a u e a ec ing he en i onmen is lowe . Wi h cons an pa ame e s o pa icle diame e
and ambien empe a u e, an inc ease in ela i e humidi y inc eases he e apo a ion ime. A la ge
pa icle diame e is consequen ly anspo ed a a g ea e dis ance, since he opposi e o ce i a ec s
is he weigh . Finally, a neu al ne wo k‑based model is p esen ed o p edic pa icle e apo a ion ime.
A e expe iencing he bigges pandemic in he wo ld, so a , o he wen y- i s cen u y, expe s ha e ocused on
he in es iga ion o he consequences o li ing his si ua ion, bo h, economically and sani a ily. The s a e li ed
du ing hese wo yea s ago, has le a socie y e y di e en om he one known be o e his phenomenon. Two
yea s o unce ain y ha e de eloped se e al measu es o comba his i us. The i s measu e was qua an ine
o app oxima ely wo mon hs. Once on he s ee , he use o masks was o ced. Di e en ypes o masks we e
designed. No ably, ma hema ical s udies such as Uga e-Ane o e al.1 demons a e h ough a Compu a ional Fluid
Dynamics (CFD) esea ch ha he ace-shields, which co e he en i e su ace o he ace, do no ully p o ec a
pe son om sneezing. La e , and cu en ly is de eloping, he in en ion o di e en accines. Al hough di e en
accines designed by la ge pha maceu ical companies a e known, he Wo ld Heal h O ganiza ion (WHO) di -
e en ia es be ween 3 ypes; hose ha use a i us o a whole bac e ium, hose ha use agmen s ha in oduce
an immune sys em esponse and hose ha use only gene ic ma e ial. Bu he si ua ion go wo se. As expec ed,
he i us mu a ed, c ea ing new a ian s. Va ian B.1.617.2 (del a) iden i ied in India and a ian B.1.1.7 (Alpha)
iden i ied in England, show di e en beha io o accine e icacy, acco ding o Be nal e al.2. Al hough, a e
se e al es s, be ween hese wo ypes o a ian s, a sligh di e ence in e ec i eness is obse ed when he wo
doses a e gi en, on he o he hand, he e is a g ea e di e ence when only one dose has been applied. The s udy
by Su e al.3 epo s ha p o ein S is he bes an igen ha should be included in accines agains COVID-19 o
achie e an e ec i e and sa e.
This disease has gi en a boos o he ield o esea ch ha d i es ae osol s udies. I has been esea ched wi h
he aim o p o iding a solu ion o he amous SARS-CoV-2, bu all hese s udies a e based on explaining he
unc ioning o he exhaled ai o he en i onmen , which is he ou e o con agion o all diseases, ei he by majo
d ople s o by ae osols, acco ding o Leung e al.4. The human body exhales pa icles be ween 10µm and 100µm
o diame e in a sneeze, acco ding o he nume ical s udy o Chillón e al.4, bu i is no conside ed ae osol un il
he pa icle eaches 5µm o diame e , Cha e jee e al.5. When a pe son coughs, speaks, o sneezes, exhales o
he en i onmen pa icles wi h g ea con agion powe . These pa icles a e o med o sali a and epi helial lining
luid (ELF), Pöhlke 6. Sali a can a y i s composi ion depending on he pe son, acco ding o Almeida PDV e al.7.
OPEN
1Nuclea Enginee ing and Fluid Mechanics Depa men , Uni e si y o he Basque Coun y, UPV/EHU, Nie es Cano
12, 01006 Vi o ia-Gas eiz, A aba, Spain. 2Sys em Enginee ing and Au oma ion Con ol Depa men , Uni e si y o
he Basque Coun y, UPV/EHU, Nie es Cano 12, 01006 Vi o ia-Gas eiz, A aba, Spain. *email: unai. e nandez@
ehu.eus
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E en i you ocus on he same pe son, depending on wha you ea du ing ha day, i can a y he composi ion
o sali a. Composed o 99% o wa e and 1% composed o o he elemen s, no ably sodium and chlo ine o
being mo e abundan , Almeida PDV e al.7, CFD s udies make an app oxima ion o sali a as a saline solu ion
o 0.9 w/ , Xie e al.8, being he mos accu a e app oxima ion o e apo a ion ime o he ae osol, Uga e-Ane o
e al.1. E en so, d ople s o sali a ha e he same me hod o e apo a ion as a d ople o pu e wa e . Acco ding o
Bozic e al.9 , he d ople g adually e apo a es o e ime, educing i s size. In his i s s age i ge s id o wa e
(H2O) molecules. Once ha H2O has e apo a ed, he esul is wha is called d ople esidue, which depends on
non-wa e solu es inside he d ople . Liebe e al.10 indica es ha he so-called d ople esidue will emain in he
en i onmen o hou s and will ha e a size ha is 20% o he ini ial size o he pa icle s udied. The la e esul is
wha di e en ia es i om he e apo a ion mechanism o a d ople o pu e wa e , becoming ae osol. The e apo a-
ion a e o pu e wa e is highe han he e apo a ion a e o a d op o saline solu ion by he high solubili y ha
NaCl has, a ec ing he apo p essu e o sa u a ed wa e , Shahidzadeh e al.11. This phenomenon is ma ked by
a ious cha ac e is ics ha occu in he en i onmen , such as, o example, ela i e humidi y (RH) and ambien
empe a u e among o he s, Uga e-Ane o e al.1, Wang e al.12 and Sen e al.13. G egson e al.14 indica es wo
impo an ac o s in he e apo a ion a e o an aqueous sodium d ople , he empe a u e o he gaseous phase
and he solu e concen a ion in he s a ing d ople , de i ing ha a highe concen a ion o solu e indica es a
longe e apo a ion a e ime. S i i e al.15 shows ha a d ople o an ini ial diame e o 21µm in 2s could become
an ae osol when a empe a u e abo e 20°C and an RH below 80% occu s. S udies such as Xie e al.8 , Liu e al.16
and Uga e-Ane o e al.1 s a e ha a highe ela i e humidi y he e apo a ion ime o hese is longe . These same
s udies, obse e ha he la ge diame e o size he e apo a ion ime is g ea e . The s udy o Xie e al.8 shows us
ha a pa icle o pu e wa e a 33°C in a space a a empe a u e o 18°C and a 0% RH e apo a es in 2s when
he ini ial diame e is 50µm, ins ead, wi h a diame e o 100µm he ime amoun s o 7.2s. As he size inc eases
he e apo a ion ime inc eases. Acco ding wi h he s udy o Shahidzadeh e al.11 he e apo a ion a e inc eases
linea ly wi h he diame e o he ini ial d ople . I he ocus is shi ed o in es iga e he eac ion o hese d ople s
o ambien empe a u e, he in es iga ion o Wang e al.12 shows ha he li e ime o a d ople in we spaces is less
when he empe a u e dec eases. In d y en i onmen s, on he o he hand, he shel li e o he d ople is longe
when he empe a u e dec eases. He also poin s ou ha a e age pa icles a e e y sensi i e o ela i e humidi y,
and i migh be di e en o s udy hei p ecise beha io .
E apo a ion is impo an o s udy how long i akes o become ae osol and achie es a s ong con agion
capaci y. Al hough, once you ha e ha pa icle less han 5µm in diame e , you need o know whe e i ’s going.
This phenomenon depends on many ac o s; he speed a which i is gene a ed, whe he we a e in a closed o
open place, anyhow he e is a high-speed wind o a so b eeze, ega dless he e is en ila ion, e c. In ac , he
s udy by C a e o e al.17, indica es ha wi h adequa e en ila ion in an indoo en i onmen comple ely changes
he di ec ion o exhaled low. S i i15 has ound ha a pa icula 80µm becomes solid was e be o e eaching he
g ound when he pe son exhaling i has a heigh o 1.6m om he mou h o he g ound. CFD s udies such as
Dbouk e al.18 and Li e al.19 wa n ha wi h an ex e nal wind g ea e han 1.1m/s can each up o 6m away. This
cu en , i i is descending, can emo e he in ec ed d ople s in jus 10s, on he con a y, an ascending cu en
helps o ha e a i al load o 50% a ound he heigh o people, acco ding o de Oli ei a20. Consequen ly, in a
closed space, such as he s udy by Chillon e al.4 he pa icles do no exceed one and a hal me e s o dis ance. The
s udy by Zhao e al.21 combines a e wi h RH and ambien empe a u e and ensu es ha in humid en i onmen s
and low empe a u e d ople s a el a g ea e space. In d y en i onmen s and high empe a u e, he numbe o
ae osols is highe , unde line wha p e iously ci ed by he s udies o Xie e al.8 and Wang e al.12 ha in d y space
he e apo a ion is slowe .
The aim o his wo k is o s udy h ough compu a ional simula ions he beha io o a single sali a pa icle
exposed o di e en en i onmen al cha ac e is ics in a social en i onmen . Launch he pa icle, wi hou eloci y,
om a heigh o 1.6m and s udy in a i s case i s e apo a ion ime a 0°C, 14°C and 35°C in a ela i e humidi y
ange o 0% o 80%. The diame e o he pa icle a e 25µm, 50µm, 75µm and 100µm. Finally, he a e o d ople s
sali a (10–90µm) is s udied a a empe a u e o 14°C and 35°C and ela i e humidi y o 0%, 20%, 40%, 60% and
80%, wi h a eloci y o 0m/s, a ec ing only he g a i y and weigh o he d ople o sali a.
Ma e ials and me hods
Compu a ional domain and ini ial condi ions. In o de o analyze h ough CFD echniques he mos
ema kable p ope ies o a d ople o sali a, he domain used has been a box o 2m X 2m X 1.6m (X, Y, Z). The
gene a ed compu a ional domain, he cube, composed o a single bounda y, aken as a wall. The six walls ac
as a ba ie o s op he pa icle ge ing injec ed he e. Enclosed space, s udy based on an indoo en i onmen ,
wi hou ai o ex e nal wind a ec ing he pa icle. I should be no ed ha he alue o Z is equal o 1.6m o he
a e age heigh ha can ake he mou h o a human. Figu e1 shows he bucke wi h he cone injec o , placed in
he cen al pa o he uppe ace, speci ically [1, 1, 1.6]. This injec o launches a pa icle in o ou e space simula -
ing a human cough. Ins ead o gene a ing a pa icle size dis ibu ion, a pa icula pa icle will be s udied, wi h a
speci ic diame e he impo ance i has when exhaled. The injec o will make as i i we e a human mou h when
gene a ing a sneeze.
Fi s , aking as a e e ence he empe a u es eached by Eu opean coun ies, he pu e wa e pa icle has been
subjec ed o 3 di e en empe a u es: 0°C, 14°C and 35°C. In con as , ela i e humidi y a ies om 0 o 80%.
The diame e o he pa icle akes alues o 25µm, 50µm 75µm and 100µm a 36°C. Acco ding o he s udy o
Almeida PDV e al.7, sali a is composed o 99% wa e and he es is o med by p o eins, enzymes and elec oly es,
among o he s. Also, he elec oly es, sodium and chlo ide s and ou . Resea ch by Xie e al.8 models sali a as a
saline solu ion wi h a concen a ion o 150mM o ions and ca ions, a ec ing only sa u a ion p essu e. In Fig.2,
you can see he p ocess o e apo a ion o an exhaled d ople in o he human en i onmen . The cu en wo k
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has he limi a ion o no being able o s udy ae osol beha io . The p ocess o comple e e apo a ion o a d ople
o sali a has been gi en as a d ople o pu e wa e , wi hou eaching he esidue o he d ople .
In he o he hand, he beha io o he sali a pa icle in ela ion o he dis ance a elled has been s udied.
Fo his case, he empe a u es a e 14°C and 35°C and ela i e humidi y o 0%, 20%, 40%, 60% and 80%, wi h
a s a ing speed o 0m/s, so i has only a ec ed he o ces o g a i y, he weigh o he d op, acco ding o Bozic9.
Acco ding o he CFD model o Penda e al.22, app oxima ely he expe imen al a e age speed ha can ca ch a
sneeze is 20m/s, bu when i is emi ed o he en i onmen in jus a ew seconds loses he speed adap ing o ha
o he en i onmen , Uga e-Ane o e al.1. Figu e3 shows a ske ch o he o ces o which a pa icle is subjec ed.
A gene alized Richa dson ex apola ion me hod23,24 was pe o med o achie e he mesh independency s udy.
This me hod consis s o es ima ing he alue o he analyzed pa ame e when he cell quan i y ends o in ini e
om a minimum o h ee meshes. In he cu en s udy, a coa se mesh (1176 cells), a medium mesh (2528 cells),
and a ine mesh (4360 cells) we e conside ed. Figu e4a shows he meshed domain and Fig.4b illus a es he plane
h ough which he pa icle alls down. Appendix A shows a comple e desc ip ion o he mesh dependency s udy
ca ied in he p esen wo k. The es ima ed alues (RE) o he e alua ed pa ame e s a e close o he ones ob ained
wi h he ine mesh o all cases. No e ha a mono onic con e gence is achie ed since R alues a e posi i e and
less han one. A mesh e inemen a io o app oxima ely = 2 has been chosen and p is he o de -o -accu acy, see
S e n e al.25. TablesA1 and A2 show he esul s o he Richa dson Ex apola ion based me hod.
Nume ical se up
The s udy is sol ed as a wo-phase low si ua ion, in oducing he wo-way coupling module. The d ople o pu e
wa e has o m he Lag angian phase. The pa icle, in ques ion, has an ini ial empe a u e o 36°C bu hen will
go down, aking he empe a u e o he ex e nal en i onmen , acco ding o he s a emen o e ed by Redow26.
Sa u a ion p essu e ollows An oine equa ion, when he pa icle is pu e wa e . The la e cha ac e is ic a ies
Figu e1. Geome y o he domain. I consis s o a box wi h measu es o 2m × 2m × 1.6m (X, Y, Z). A a
heigh o 1m × 1m × 1.6m a cone injec o is collapsing simula ing he pa icle.
Figu e2. E apo a ion p ocess o a d ople o sali a. Once he pa icle is exhaled in o he en i onmen , he
e apo a ion p ocess begins by e apo a ing sali a wa e . When i eaches 5µm o diame e i becomes ae osol,
becoming d ople esidue.
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when i comes o simula ing sali a. A saline solu ion o 0.9% w/ , ha e a sa u a ion p essu e in acco dance wi h
Raoul ’s Law, as indica ed by Xie8.
whe e
P a,s
is he sa u a ion p essu e o he d ople in he saline mix u e,
P a
is he sa u a ion p essu e indica ed
by he An oine equa ion a an indica ed empe a u e (in his case a 36°C)
(Tw)
and
Xd
is he mole ac ion o
he d ople , ha is calcula ed as shown in Eq.(2).
whe e ms he mass o solu e in he d ople ;
dp
is he diame e o he d ople s udied; Mw is he molecula weigh
o wa e and Ms is he molecula weigh o solu e, he ion ac o “i” is equal o 2.
The Reynolds-a e aged Na ie –S okes (RANS) equa ions wi h k-ω Shea S ess T anspo (SST) u bulence
model, de eloped by Men e e al.27 ha e been in oduced in his wo k. The UpWind algo i hm was employed
o he p essu e– eloci y coupling and a linea upwind second o de scheme was used o disc e ize he mesh.
Figu e3 shows he o ces o which he d ople is subjec ed, which is ini ially assumed o be sphe ical. The in lu-
ence o he g a i y o ce was aken in o accoun . The Taylo analogy b eakup (TAB) model was implemen ed o
p o ide a solu ion o pa icle dis o ion and b eak up. Also, he u bulen pa icle dispe sion wi h he exac eddy
in e ac ion ime is aken in o accoun . The d ag o ce akes he alue acco ding o Schille -Naumann ma hema -
ics model. Model used in he nume ical s udy o Wang e al.12 and in he in es iga ion o de Oli ei a e al.20. The
model simula ed he d ag be ween he wo cu en phases. Equa ion3 shows he exp ession o calcula e he
d ag coe icien Cd.
(1)
P a,s =XdP a(Tw)
(2)
Xd=
1+6imsMw
πρ
LMs
(
dp
)3
−1
Figu e3. Fo ces ha a ec a d ople o sali a. D ople alling eely a ec ed by g a i y, whe he weigh , and
d ag o ce.
Figu e4. Mesh dis ibu ion. (a) Geome y o he mesh cube; (b) plane h ough which he pa icle passes.
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whe e Re is he Reynolds numbe .
Once he espi a o y d ople s a e exhaled in o he social en i onmen whe e humans a e ound, he p ocess
o e apo a ion begins. Fo his, Busco e al.28 in oduces he quasi-s eady e apo a ion model, inco po a ed in
his p ojec . Fo mula 4 shows he equa ion in which he model is go e ned, subjec o mass loss.
whe e
g∗
is he mass ans e conduc ance and
As
is he d ople su ace a ea. B is he Spalding ans e numbe .
g∗
and B a e de ined as:
In he Eqs.(5 and 6),
ρp
is he densi y o he pa icle liquid phase,
D
and
Dp
a e he molecula di usi i y o
he apo phase and o he liquid phase, espec i ely. Sh is he co ela ion o de She wood numbe .
Yi,s
is he
apo mass ac ion a he su ace and
Yi,∞
is he apo mass ac ion inside he luid phase.
The second impo an pa o his esea ch is he simula ion o he a mosphe e. The cube has simula ed his
and ha e been sol ed by equa ions o he con inuous phase exp essed in Eule ian o m. Non- eac i e species ha
a e de e mining hei p ope ies, he o al binding p ope y is calcula ed as a mass unc ion o he componen s
o he mix u e. Busco e al.28 inco po a es Eq.(7), based on he mass-weigh ed mix u e me hod.
whe e Yi is he mass ac ion o ai and wa e apo and фi is he p ope y alues o mix u e componen . N is
he o al numbe o componen s in he mix u e.
Composed o d y ai and wa e apo , a ying hei mass composi ion gi es ise o ela i e humidi y. By
obse ing he Kukkonen e al.29 appendix he densi y and iscosi y o he wa e apo ai and liquid wa e ha e
been aken as he alue ma ked by he equa ions o ha epo when changing empe a u e. In he cu en
wo k, he comme cial CFD code STAR-CCM + .14.02 (Siemens, London, UK) was used o de ine and sol e he
nume ical model o ae osols. A pe sonal se e -clus e ed pa allel compu e wi h In el Xeon © E5-2609 2 CPU
@ 2.5GHz (16 co es) and 45GB RAM we e used o un all he simula ions.
Valida ion. In he case o compu a ional simula ions, alida ion wi h expe imen al esul s is equi ed. The
cu en wo k epo s on he e apo a ion o pu e wa e d ople s and on he a e o sali a d ople s, he e o e, has
alida ed bo h, e apo a ion and dis ance.
The same me hod used by Redow26, Mow aska30, Li19 and Uga e-Ane o1 was used o he alida ion o
e apo a ion. A s udy in which di e en diame e s o d ople s o pu e wa e (1µm 10µm and 100µm) wi h a
empe a u e o 310.15K a e subjec ed o an en i onmen o 293.15K and RH a ies o see he e apo a ion ime.
The esul s ob ained a e simila o hose shown by he a o emen ioned wo ks, shown in Fig.5.
Following he same philosophy, a pu e wa e d ople and a sali a d ople only ha e di e ence in he apo
p essu e in his s udy, he e o e, a ec he same o ces and we can go ahead wi h s udies like Hamey e al.31 and
Spillman e al.32 ha show he pa h o a d ople o pu e wa e . Hamey s udy consis s o wo d ople s o wa e , one
o 110µm and ano he o 115µm o diame e , a a empe a u e o 289K in an en i onmen a 293K and ela i e
humidi y o 70% and obse e i s pa h ha ing le he d ople all eely. Wi h he same objec i e, he Spillman
s udio launches a 170µm o diame e pa icle a 25°C in a 31°C en i onmen wi h a ela i e humidi y o 68%.
Figu es5 and 6 show he esul s ob ained by compa ing ou CFD da a wi h he expe imen al s udies. Ins ead,
Table1 shows he e o as a pe cen age be ween he expe imen al da a o he Hamey and Spillman and he esul s
ob ained wi h CFD echniques.
Resul s
In a sneeze, a pa icle dis ibu ion o 10–100µm diame e is gene a ed. The a e age diame e s selec ed o s udy
he case a e: 25µm, 50µm, 75µm and 100µm. The human body is a a empe a u e o app oxima ely 36°C, so
he exhaled pa icles ha e an ini ial empe a u e o 36°C. Wi h a minimum empe a u e o 0°C, a pa icle o
100µm o diame e , in an en i onmen wi h ela i e humidi y o 80%, eaches an e apo a ion ime o 61.2s. In
con as , wi h a empe a u e o 14°C and cons an RH he e apo a ion ime is equal o 54.4s. And, wi h 35°C,
and he same cha ac e is ics, 30.3s is he ime i akes o ha pa icle o e apo a e.
When i is a 50µm pa icle wi h a empe a u e o 14°C, in an en i onmen wi h a ela i e humidi y o 50%
he e apo a ion ime is 5,2s and RH 80% he e apo a ion ime is equal o 13.7s. The dis ibu ion o e apo a ion
o he es d ople s is analyzed in Figs.7, 8 and 9.
(3)
C
d
24
Re ,Re ≤1
24
Re
�
1+0.15Re0.687
�
,
0.44, Re >1000
1<Re ≤
1000
(4)
˙mp=g∗×Asln(1+B)
(5)
g
∗=−
ρ
p
D
Sh
D
p
(6)
B
=
Y
i,s
−Y
i,∞
1
−
Yi,s
(7)
φ
mix =
N=2
i=1
φiY
i
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By con e ing sali a in o a saline solu ion, he e apo a ion ime o saline solu ion d ople is 17s app oxima ely
mo e in compa ison wi h pu e wa e d ople . Bo h cases we e pe o med unde he condi ions o a RH = 50%
and an en i onmen empe a u e o 14°C, and he diame e s o he d ople was 50µm. Ins ead, as he diame e
o he saline pa icle inc eases his di e ence is mo e no a y. A pa icle o pu e wa e wi h 100µm o diame e
e apo a es 50s be o e one o saline solu ion d ople . Figu e10 shows he di e ence in he e apo a ion p ocess
be ween a d ople o pu e wa e and a d ople o saline solu ion o a 50µm and 100µm d ople .
In he case o s udying he dis ance ha he d ople s gene a ed in a sneeze o cough can a el, he law o
g a i y is kep , he mo e diame e he mo e weigh , he longe dis ance a eled. An a e age pa icle o 50µm, a
a ela i e humidi y o 60% a els 0.24m, be o e e apo a ing. Ra he , a a humidi y o 20% he pa icle s ays a a
dis ance o 1.5m om he g ound, all in an en i onmen wi h a empe a u e o 14°C. Wi h he same peculia i ies,
0.1
1
10
100
D ople diame e (µm)
Time (s)
Wa e pu e d ople s e apo aon
RH 0% RH 20% RH 60% RH 80%
Figu e5. Wa e pu e d ople s e apo a ion. Pa icle diame e o 1µm, 10µm and 100µm a a empe a u e o
310.15K. Simula ed in an en i onmen wi h a iable ela i e humidi y o 0%, 20%, 60% and 80% a a cons an
empe a u e o 293.15K.
0
0.8
1.6
90 100 110 120 130140 150160 17
0
Dis ance (m)
D ople diame e (µm)
CFD (Hamey 1982 (115 µm))
CFD (Hamey 1982 (110 µm))
Hamey 1982 exp. (115 µm)
Hamey 1982 exp. (110 µm)
Spillman exp.
CFD (Spillman)
Figu e6. Wa e pu e d ople s a e. D ople s o 110µm and 115µm all eely a an ini ial empe a u e o 289K
in an en i onmen o 293K o an RH o 70%, called as Hamey s udy. Spillman s udy wi h he same pu pose as
he abo e, o a pa icle o 170µm o diame e a a empe a u e o 25°C in an en i onmen o 31°C empe a u e
and HR o 68%.
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when RH = 60%, a pa icle o 90µm has a elled he 1.6m be o e e apo a ing and when he RH = 20% he
dis ance a eled has been 0.95m.
Conside ing Figs.7, 8 and 9, he e ec o he e apo a ion p ocess, a 50µm o diame e pa icle a ambien
empe a u e o 35°C and a ela i e humidi y o 60% passes h ough a dis ance o 0.13m be o e e apo a ing,
om a heigh o 1.6m. Figu es11 and 12 show he a e o he pa icles eleased om a heigh o 1.6m om he
g ound, co esponding o he a e age heigh o he mou h o an adul pe son. The hea ie d ople s manage o
each he soil ins ead, he smalle d ople s e apo a e in o he ai lea ing he d ople esidue in he en i onmen .
The d ople esidue gene a ed by he la ge d ople s would se le on he su ace.
Then, acco ding wi h he esul s ob ained by s udying he pa icle dynamics, he esul s o he ime o hi s
de e mined by empi ical o mulas is s udied. Equa ion8, p o ided by he s udy o Bozic e al.9 ,indica es he
pa ame e s ha in luence he sedimen a ion ime. Table2 shows he esul s ob ained om ou examples a a
ela i e humidi y o 50%. I should be no ed ha a pa icle wi h a diame e o 80µm in an en i onmen wi h a
empe a u e o 35°C and RH = 80%, can be anspo ed om a heigh o 1.6m, be o e e apo a ion, a a dis ance
o 0.015m om he g ound o e a ime o 7.9s. Wi h he empi ical o mula we ob ain ha he sedimen a ion
ime o ha d ople is 0.2s mo e han he e apo a ion ime, ime ha would elapse o a el he dis ance o
0.015m p e iously men ioned. Only he 100μm pa icle has been e apo a e a e deposi ion in he soil, he
o he s ha e e apo a ed in he ai be o e eaching he ma ked dis ance.
(8)
sedimen a ion
=h÷(ξ ×
R
d ople
)
2
Table 1. Calcula ed e o be ween he esul s ob ained by CFDs and he expe imen al da a o he Hamey and
Spillman s udies.
Hamey 1982 110µm Hamey 1982 115µm Spillman
0.000301% 0.034% 0.161%
1.160% 0.019% 0.287%
0.393% 0.554% 0.852%
3.615% 0.597% 1.348%
2.693% 1.645% 2.201%
2.955% 0.932% 3.114%
6.379% 4.083% 3.801%
3.532% 4.995%
0.1
1
10
100
01020304050607
080
Time (s)
RH (%)
Wa e pu e d ople e apo aon a T=0ºC
100
75
50
25
Figu e7. Wa e pu e d ople s e apo a ion. Time elapsed in he e apo a ion p ocess o a d ople o pu e wa e
a an ambien empe a u e o 0°C, wi h a iable ela i e humidi y and pa icle diame e o 25µm, 50µm, 75µm
and 100µm.
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whe e h = 1.6m, in his case since i is he a e age heigh o he human mou h, Rd ople is he adius o he pa icle
and he le e ξ equals o he numbe
1.2 ×108
m−1 s−1.
ANN‑based e apo a ion ime p edic ion model
Aiming o ob ain he e apo a ion ime o he pa icles, an A i icial Neu al Ne wo k (ANN) is de eloped. Deep
Lea ning echniques, which include neu al ne wo ks, a e excep ional ools o modelling a wide a ie y o sys-
ems due o hei p ope ies and ad an ages in compa ison wi h o he adi ional echniques, see Lopez-Guede
0.1
1
10
100
01020304050607
080
Time (s)
RH (%)
Wa e pu e d ople e apo aon a T=14ºC
100
75
50
25
Figu e8. Wa e pu e d ople s e apo a ion. Time elapsed in he e apo a ion p ocess o a d ople o pu e wa e
a an ambien empe a u e o 14°C, wi h a iable ela i e humidi y and pa icle diame e o 25µm, 50µm,
75µm and 100µm.
0.1
1
10
100
01020304050607
080
Time (s)
RH (%)
Wa e pu e d ople e apo aon a T=35ºC
100
75
50
25
Figu e9. Wa e pu e d ople s e apo a ion. Time elapsed in he e apo a ion p ocess o a d ople o pu e wa e
a an ambien empe a u e o 35°C, wi h a iable ela i e humidi y and pa icle diame e o 25µm, 50µm,
75µm and 100µm.
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e al.33,34. Among hese ad an ages and p ope ies, he mos ema kable ones a e hei abili y o lea n and hei
as compu a ional speed.
In he p esen pape a mul i-laye model wi h wo hidden laye s is used. The e apo a ion ime o he pa -
icle is calcula ed by Eq.(9), and he ou pu s o each neu on o he hidden laye s ollow a sigmoid unc ion,
which is de ined in Eq.(10). The ANN wi h hese pa ame e s ep esen s a ypical Mul ilaye Pe cep on wi h
0
20
40
60
80
100
120
01020304050607
080
D ople diame e (μm)
Time (s)
E apo aon p ocess
Wa e pu e d ople Saline soluon d ople
Figu e10. Di e ence o e apo a ion p ocess. Unde condi ions o ela i e humidi y o 50% and ambien
empe a u e o 14°C. A pa icle o pu e wa e wi h 50µm o diame e e apo a es 17s be o e one o saline
solu ion d ople . Howe e , a pa icle o pu e wa e wi h 100µm o diame e e apo a es 50s be o e one o saline
solu ion d ople .
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
10 20 30 40 50 60 70 80
90
Dis ance (m)
D ople diame e (µm)
TT==1144ººCC
RH 0% RH 20% RH 40% RH 60% RH 80%
Figu e11. Dis ance co e ed by d ople s o sali a (10µm, 20µm, 30µm, 40µm, 50µm, 60µm, 70µm, 80µm
and 90µm) om a heigh o 1.6m a a empe a u e o 14°C and wi h a a iable ela i e humidi y.
