Evaporation kinetics of a polydisperse ensemble of drops

A mathematical model of the evaporation of a polydisperse ensemble of drops, with allowance for a nonlinear ‘diffusion’ term in the kinetic equation for the population density distribution function, is developed. The model describes the interaction of a gas phase with vaporizing drops: it has great...

Full description

Saved in:
Bibliographic Details
Published inPhilosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 379; no. 2205; p. 20200309
Main Authors Ivanov, Alexander A., Alexandrova, Irina V., Alexandrov, Dmitri V.
Format Journal Article
LanguageEnglish
Published 06.09.2021
Online AccessGet full text

Cover

Abstract A mathematical model of the evaporation of a polydisperse ensemble of drops, with allowance for a nonlinear ‘diffusion’ term in the kinetic equation for the population density distribution function, is developed. The model describes the interaction of a gas phase with vaporizing drops: it has great potential for application in condensed matter physics, thermophysics and engineering devices (e.g. spray drying, cooling, power engineering). The kinetics of heat transfer between phases is theoretically studied. An analytical solution to the integro-differential equations of the process of droplet evaporation is found in a parametric form. Analytical solutions in the presence and absence of the ‘diffusion’ term are compared. It is shown that the fluctuations in particle evaporation rates (‘diffusion’ term in the Fokker–Planck equation) play a decisive role in the evolutionary behaviour of a polydisperse ensemble of vaporizing liquid drops. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.
AbstractList A mathematical model of the evaporation of a polydisperse ensemble of drops, with allowance for a nonlinear ‘diffusion’ term in the kinetic equation for the population density distribution function, is developed. The model describes the interaction of a gas phase with vaporizing drops: it has great potential for application in condensed matter physics, thermophysics and engineering devices (e.g. spray drying, cooling, power engineering). The kinetics of heat transfer between phases is theoretically studied. An analytical solution to the integro-differential equations of the process of droplet evaporation is found in a parametric form. Analytical solutions in the presence and absence of the ‘diffusion’ term are compared. It is shown that the fluctuations in particle evaporation rates (‘diffusion’ term in the Fokker–Planck equation) play a decisive role in the evolutionary behaviour of a polydisperse ensemble of vaporizing liquid drops. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.
Author Ivanov, Alexander A.
Alexandrov, Dmitri V.
Alexandrova, Irina V.
Author_xml – sequence: 1
  givenname: Alexander A.
  orcidid: 0000-0002-2490-160X
  surname: Ivanov
  fullname: Ivanov, Alexander A.
  organization: Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federation
– sequence: 2
  givenname: Irina V.
  orcidid: 0000-0002-9606-4759
  surname: Alexandrova
  fullname: Alexandrova, Irina V.
  organization: Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federation
– sequence: 3
  givenname: Dmitri V.
  orcidid: 0000-0002-6628-745X
  surname: Alexandrov
  fullname: Alexandrov, Dmitri V.
  organization: Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federation
BookMark eNotkM1Lw0AUxBepYFu9es7RS-LbzyRHKdUKBS8K3pbd5C1E02zclwr9722opxmYYQZ-K7YY4oCM3XMoONTVY6LJFQIEFCChvmJLrkqei9qIxdlLo3IN8vOGrYi-ADg3WixZtf11Y0xu6uKQfXcDTl1DWQyZy8bYn9qORkyEGQ6EB9_jHLUpjnTLroPrCe_-dc0-nrfvm12-f3t53Tzt80ZqM-VN8K2sTBnU-c7XxpdaSRAcMAQfeBmMdugFYmVk2fDWOM_b1hsNlVYca7lmD5fdMcWfI9JkDx012PduwHgkK7SWQqmyFudqcak2KRIlDHZM3cGlk-VgZ0R2RmRnRHZGJP8AiGZcOw
CitedBy_id crossref_primary_10_1098_rsta_2020_0301
crossref_primary_10_1098_rsta_2020_0306
crossref_primary_10_1098_rsta_2020_0308
crossref_primary_10_1098_rsta_2020_0307
crossref_primary_10_1140_epjs_s11734_023_00824_6
crossref_primary_10_3390_cryst12070949
Cites_doi 10.1098/rsta.2019.0247
10.1088/1757-899X/192/1/012001
10.1140/epjst/e2020-000037-9
10.1088/1751-8121/aaa5b7
10.1016/j.physleta.2014.03.051
10.1098/rsta.2020.0307
10.1098/rsta.2020.0325
10.1098/rsta.2019.0245
10.1002/mma.3553
10.1002/9783527627769
10.1007/BF00827264
10.1002/mma.6749
10.1098/rsta.2017.0327
10.1007/978-3-642-39660-1
10.1016/0017-9310(94)90354-9
10.1016/j.jcrysgro.2009.02.035
10.1016/j.ces.2014.06.012
10.1016/j.ijheatmasstransfer.2006.05.046
10.1098/rsta.2019.0243
10.1615/978-1-56700-213-3.0
10.1080/09500839.2014.977975
10.1098/rsta.2017.0217
10.1098/rsta.2020.0306
10.1002/mma.6987
10.1080/09500839.2018.1522459
10.1098/rsta.2018.0210
10.1016/j.physleta.2020.126259
10.1134/S0036029519080020
10.1140/epjst/e2020-000113-3
10.1134/S1028335806060024
10.1016/0009-2509(94)E0052-R
10.1140/epjst/e2019-900049-4
10.1098/rsta.2018.0215
10.1098/rsta.2018.0209
10.1007/978-3-662-02377-8
10.1016/j.ijheatmasstransfer.2018.08.119
10.1098/rsta.2018.0214
10.1016/0022-0248(90)90112-X
10.1080/09500839.2016.1177222
10.1002/9781118863985
10.1016/j.jcrysgro.2017.03.053
10.1016/S0967-0661(01)00048-X
10.1098/rsta.2020.0308
ContentType Journal Article
DBID AAYXX
CITATION
7X8
DOI 10.1098/rsta.2020.0309
DatabaseName CrossRef
MEDLINE - Academic
DatabaseTitle CrossRef
MEDLINE - Academic
DatabaseTitleList CrossRef
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Mathematics
Sciences (General)
Physics
EISSN 1471-2962
EndPage 20200309
ExternalDocumentID 10_1098_rsta_2020_0309
GroupedDBID ---
-~X
0R~
18M
2WC
4.4
5VS
AACGO
AANCE
AAYXX
ABFAN
ABPLY
ABTLG
ABYWD
ACGFO
ACIWK
ACMTB
ACNCT
ACQIA
ACTMH
ADBBV
AEUPB
AFVYC
ALMA_UNASSIGNED_HOLDINGS
ALMYZ
BTFSW
CITATION
DIK
EBS
F5P
H13
HH5
HZ~
JLS
JSG
JST
KQ8
MRS
MV1
NSAHA
O9-
OK1
OP1
P2P
RHF
RRY
TN5
TR2
V1E
W8F
XSW
YNT
~02
7X8
ID FETCH-LOGICAL-c356t-cfbd3867f4652b96b75430210effbf17f65aeb2ee8637c1d6ab1ddb6508541e93
ISSN 1364-503X
IngestDate Fri Aug 16 22:57:52 EDT 2024
Thu Sep 26 19:33:17 EDT 2024
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2205
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c356t-cfbd3867f4652b96b75430210effbf17f65aeb2ee8637c1d6ab1ddb6508541e93
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ORCID 0000-0002-2490-160X
0000-0002-9606-4759
0000-0002-6628-745X
OpenAccessLink https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2020.0309
PQID 2553244792
PQPubID 23479
PageCount 1
ParticipantIDs proquest_miscellaneous_2553244792
crossref_primary_10_1098_rsta_2020_0309
PublicationCentury 2000
PublicationDate 2021-09-06
PublicationDateYYYYMMDD 2021-09-06
PublicationDate_xml – month: 09
  year: 2021
  text: 2021-09-06
  day: 06
PublicationDecade 2020
PublicationTitle Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences
PublicationYear 2021
References e_1_3_5_28_2
e_1_3_5_27_2
e_1_3_5_26_2
Alexandrova IV (e_1_3_5_34_2) 2021; 379
e_1_3_5_25_2
Randolph A (e_1_3_5_3_2) 1988
e_1_3_5_23_2
e_1_3_5_22_2
e_1_3_5_21_2
e_1_3_5_44_2
e_1_3_5_45_2
e_1_3_5_46_2
e_1_3_5_48_2
e_1_3_5_49_2
e_1_3_5_29_2
e_1_3_5_40_2
e_1_3_5_42_2
e_1_3_5_8_2
e_1_3_5_20_2
Makoveeva EV (e_1_3_5_41_2) 2021; 379
e_1_3_5_7_2
e_1_3_5_9_2
e_1_3_5_6_2
e_1_3_5_5_2
Nikishina MA (e_1_3_5_43_2) 2021; 379
e_1_3_5_17_2
Fedoruk MV (e_1_3_5_38_2) 1977
e_1_3_5_39_2
e_1_3_5_16_2
Alexandrov DV (e_1_3_5_47_2) 2021; 379
e_1_3_5_15_2
e_1_3_5_14_2
e_1_3_5_36_2
e_1_3_5_12_2
e_1_3_5_35_2
e_1_3_5_13_2
e_1_3_5_10_2
e_1_3_5_33_2
e_1_3_5_11_2
e_1_3_5_32_2
Ditkin VA (e_1_3_5_37_2) 1965
Buyevich YuA (e_1_3_5_4_2) 2005
Lifshitz EM (e_1_3_5_2_2) 1981
Masters K (e_1_3_5_24_2) 2002
e_1_3_5_19_2
e_1_3_5_18_2
e_1_3_5_31_2
e_1_3_5_30_2
References_xml – volume-title: Physical kinetics
  year: 1981
  ident: e_1_3_5_2_2
  contributor:
    fullname: Lifshitz EM
– ident: e_1_3_5_15_2
  doi: 10.1098/rsta.2019.0247
– ident: e_1_3_5_21_2
  doi: 10.1088/1757-899X/192/1/012001
– volume-title: Saddle-point method
  year: 1977
  ident: e_1_3_5_38_2
  contributor:
    fullname: Fedoruk MV
– ident: e_1_3_5_44_2
  doi: 10.1140/epjst/e2020-000037-9
– ident: e_1_3_5_26_2
  doi: 10.1088/1751-8121/aaa5b7
– ident: e_1_3_5_35_2
  doi: 10.1016/j.physleta.2014.03.051
– volume: 379
  start-page: 20200307
  year: 2021
  ident: e_1_3_5_41_2
  article-title: The influence of non-stationarity and interphase curvature on the growth dynamics of spherical crystals in a metastable liquid
  publication-title: Phil. Trans. R. Soc. A
  doi: 10.1098/rsta.2020.0307
  contributor:
    fullname: Makoveeva EV
– volume: 379
  start-page: 20200325
  year: 2021
  ident: e_1_3_5_47_2
  article-title: A review on the theory of stable dendritic growth
  publication-title: Phil. Trans. R. Soc. A
  doi: 10.1098/rsta.2020.0325
  contributor:
    fullname: Alexandrov DV
– ident: e_1_3_5_13_2
  doi: 10.1098/rsta.2019.0245
– ident: e_1_3_5_49_2
  doi: 10.1002/mma.3553
– ident: e_1_3_5_5_2
  doi: 10.1002/9783527627769
– ident: e_1_3_5_16_2
  doi: 10.1007/BF00827264
– ident: e_1_3_5_39_2
  doi: 10.1002/mma.6749
– ident: e_1_3_5_11_2
  doi: 10.1098/rsta.2017.0327
– ident: e_1_3_5_6_2
  doi: 10.1007/978-3-642-39660-1
– ident: e_1_3_5_18_2
  doi: 10.1016/0017-9310(94)90354-9
– ident: e_1_3_5_29_2
  doi: 10.1016/j.jcrysgro.2009.02.035
– ident: e_1_3_5_9_2
  doi: 10.1016/j.ces.2014.06.012
– ident: e_1_3_5_19_2
  doi: 10.1016/j.ijheatmasstransfer.2006.05.046
– ident: e_1_3_5_46_2
  doi: 10.1098/rsta.2019.0243
– volume-title: Heat transfer in dispersions
  year: 2005
  ident: e_1_3_5_4_2
  doi: 10.1615/978-1-56700-213-3.0
  contributor:
    fullname: Buyevich YuA
– ident: e_1_3_5_31_2
  doi: 10.1080/09500839.2014.977975
– ident: e_1_3_5_32_2
  doi: 10.1098/rsta.2017.0217
– volume: 379
  start-page: 20200306
  year: 2021
  ident: e_1_3_5_43_2
  article-title: Nucleation and growth dynamics of ellipsoidal crystals in metastable liquids
  publication-title: Phil. Trans. R. Soc. A
  doi: 10.1098/rsta.2020.0306
  contributor:
    fullname: Nikishina MA
– ident: e_1_3_5_45_2
  doi: 10.1002/mma.6987
– ident: e_1_3_5_22_2
  doi: 10.1080/09500839.2018.1522459
– ident: e_1_3_5_12_2
  doi: 10.1098/rsta.2018.0210
– ident: e_1_3_5_36_2
  doi: 10.1016/j.physleta.2020.126259
– volume-title: Integral transforms and operational calculus
  year: 1965
  ident: e_1_3_5_37_2
  contributor:
    fullname: Ditkin VA
– ident: e_1_3_5_40_2
  doi: 10.1134/S0036029519080020
– ident: e_1_3_5_42_2
  doi: 10.1140/epjst/e2020-000113-3
– ident: e_1_3_5_20_2
  doi: 10.1134/S1028335806060024
– ident: e_1_3_5_8_2
  doi: 10.1016/0009-2509(94)E0052-R
– ident: e_1_3_5_23_2
  doi: 10.1140/epjst/e2019-900049-4
– ident: e_1_3_5_10_2
  doi: 10.1098/rsta.2018.0215
– ident: e_1_3_5_28_2
  doi: 10.1098/rsta.2018.0209
– volume-title: Theory of particulate processes
  year: 1988
  ident: e_1_3_5_3_2
  contributor:
    fullname: Randolph A
– ident: e_1_3_5_7_2
  doi: 10.1007/978-3-662-02377-8
– ident: e_1_3_5_27_2
  doi: 10.1016/j.ijheatmasstransfer.2018.08.119
– ident: e_1_3_5_14_2
  doi: 10.1098/rsta.2018.0214
– ident: e_1_3_5_17_2
  doi: 10.1016/0022-0248(90)90112-X
– ident: e_1_3_5_33_2
  doi: 10.1080/09500839.2016.1177222
– volume-title: Spray drying in practice
  year: 2002
  ident: e_1_3_5_24_2
  contributor:
    fullname: Masters K
– ident: e_1_3_5_25_2
  doi: 10.1002/9781118863985
– ident: e_1_3_5_30_2
  doi: 10.1016/j.jcrysgro.2017.03.053
– ident: e_1_3_5_48_2
  doi: 10.1016/S0967-0661(01)00048-X
– volume: 379
  start-page: 20200308
  year: 2021
  ident: e_1_3_5_34_2
  article-title: Ostwald ripening in the presence of simultaneous occurrence of various mass transfer mechanisms: an extension of the Lifshitz–Slyozov theory
  publication-title: Phil. Trans. R. Soc. A
  doi: 10.1098/rsta.2020.0308
  contributor:
    fullname: Alexandrova IV
SSID ssj0011652
Score 2.430549
Snippet A mathematical model of the evaporation of a polydisperse ensemble of drops, with allowance for a nonlinear ‘diffusion’ term in the kinetic equation for the...
SourceID proquest
crossref
SourceType Aggregation Database
StartPage 20200309
Title Evaporation kinetics of a polydisperse ensemble of drops
URI https://search.proquest.com/docview/2553244792
Volume 379
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bi9QwFA7jiqAP4q6K640Kgkrp2Gsuj4sou8qKwq7sW0kmCQy602HaWdA_51_znLTpReZh9aVk0iZDew7nlnO-Q8jLQifcmsRGhksegX3LI5lYzHVNdWwEU9zBMZx-psfn-ceL4mI2-z3KWto2ar74tbOu5H-oCnNAV6yS_QfK9pvCBIyBvnAFCsP1WjQGM3jtSfgdzEUHuewKHtfVj596iSjgtQnBUzWXqs0i1JtqXY8t0i--l4GjVjO0D699-kAbYfDpnXim4FqAzFHOgJ8duhD9aQ__6joIdBGTdoyxeTPgHoad1u2t-ROw5qurSblNeDTvWbGd21RXzs49gS1k-G3HbSc-L5fNZulvd9GMNHHpWnQkgDOaR0XsegSDfmrnQIFGqZhK7aztQdOxJ5YLj8VwnLoz3p06IhZY94B1Q3N8bu4fnIJx_6Uk-9TF9tCel7i-xPUlrr9BbqZMFJhT-unrcIyVUNfyqX-pHjWUv53-_9QqmhoFztI5u0fudi5KcNTy2z6ZmdUBuTMCroRfA7nrA3LLpRHjaL9TFXXwusMzf3Of8BGbBp5Ng8oGMhizaeDZFG85Nn1Azj-8P3t3HHUNO6JFVtAmWlilM06ZzeG9laCKFXmGQQVjrbIJs7SQRqXGcJqxRaKpVInWCp2EIk-MyB6SvVW1Mo9IgF0VhNSxFUwixJ9imaQpLLGMCaGLQ_LKf7By3eKylLtJc0he-O9ZgujE8zC5MtW2LsGbBnciZyJ9fO3dnpDbA9s-JXvNZmuegVnaqOeO9H8A_AGOog
link.rule.ids 315,786,790,27955,27956
linkProvider Colorado Alliance of Research Libraries
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Evaporation+kinetics+of+a+polydisperse+ensemble+of+drops&rft.jtitle=Philosophical+transactions+of+the+Royal+Society+of+London.+Series+A%3A+Mathematical%2C+physical%2C+and+engineering+sciences&rft.au=Ivanov%2C+Alexander+A.&rft.au=Alexandrova%2C+Irina+V.&rft.au=Alexandrov%2C+Dmitri+V.&rft.date=2021-09-06&rft.issn=1364-503X&rft.eissn=1471-2962&rft.volume=379&rft.issue=2205&rft.spage=20200309&rft_id=info:doi/10.1098%2Frsta.2020.0309&rft.externalDBID=n%2Fa&rft.externalDocID=10_1098_rsta_2020_0309
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1364-503X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1364-503X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1364-503X&client=summon