Analysis of laminar-to-turbulent transition for isothermal gas flows in microchannels View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2009-08

AUTHORS

Gian Luca Morini, Marco Lorenzini, Sandro Salvigni, Marco Spiga

ABSTRACT

In this work the laminar-to-turbulent transition in microchannels of circular cross-section is studied experimentally. In order to single out the effects of relative roughness, compressibility and channel length-to-diameter ratio on the Reynolds number at which transition occurs, experimental runs have been carried out on circular microchannels in fused silica—smooth for all purposes—and in stainless steel (which possess a high surface roughness), with a diameter between 125 and 180 μm and a length of 5–50 cm through which nitrogen flows. For each tube the friction factor has been computed. The values of the critical Reynolds number have been determined plotting the Poiseuille number (i.e., the product of the friction factor, f, times the Reynols number, Re) as a function of the average Mach number between inlet and outlet. The transitional regime was found to start no earlier than at values of the Reynolds number around 1,800–2,000. It has been observed that surface roughness has no effect on the hydraulic resistance in the laminar region for a relative roughness lower than 4.4%, and that friction factor obeys the Poiseuille law, if it is correctly computed taking compressibility into account. It is found that recent correlations for the prediction of the critical Reynolds number in microchannels that link the relative roughness of the microtubes to the critical Reynolds number do not agree with the present results. More... »

PAGES

181-190

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10404-008-0369-2

DOI

http://dx.doi.org/10.1007/s10404-008-0369-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1018589679


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0915", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Interdisciplinary Engineering", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/09", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Engineering", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Bologna", 
          "id": "https://www.grid.ac/institutes/grid.6292.f", 
          "name": [
            "DIENCA, Universit\u00e0 degli Studi di Bologna, Viale Risorgimento 2, 40136, Bologna, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Morini", 
        "givenName": "Gian Luca", 
        "id": "sg:person.016136725555.26", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016136725555.26"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Bologna", 
          "id": "https://www.grid.ac/institutes/grid.6292.f", 
          "name": [
            "DIENCA, Universit\u00e0 degli Studi di Bologna, Viale Risorgimento 2, 40136, Bologna, Italy", 
            "DIENCA, Universit\u00e0 degli Studi di Bologna, Via Terracini 34, 40131, Bologna, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Lorenzini", 
        "givenName": "Marco", 
        "id": "sg:person.013742476454.22", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013742476454.22"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Bologna", 
          "id": "https://www.grid.ac/institutes/grid.6292.f", 
          "name": [
            "DIENCA, Universit\u00e0 degli Studi di Bologna, Viale Risorgimento 2, 40136, Bologna, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Salvigni", 
        "givenName": "Sandro", 
        "id": "sg:person.016345307602.92", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016345307602.92"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Parma", 
          "id": "https://www.grid.ac/institutes/grid.10383.39", 
          "name": [
            "Dipartimento di Ingegneria Industriale, Universit\u00e0 di Parma, Via G.P. Usberti 181A, 43100, Parma, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Spiga", 
        "givenName": "Marco", 
        "id": "sg:person.016126176256.80", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016126176256.80"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/j.ijheatmasstransfer.2004.10.030", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017707432"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/01457630701326308", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020806715"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.ijheatfluidflow.2006.05.005", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024322307"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.ijheatmasstransfer.2006.10.034", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024406847"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1098/rstl.1883.0029", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026624834"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/aic.690310315", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027404533"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/10893950390219083", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029815441"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.ijthermalsci.2006.01.004", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030957993"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0011-2275(83)90150-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032850263"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0011-2275(83)90150-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032850263"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.expthermflusci.2006.03.003", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045997930"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/b978-008044527-4/50005-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052016335"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0022112007009111", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053957819"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0022112007009111", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053957819"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.1896985", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057831032"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.1896985", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057831032"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1115/1.1797036", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062074744"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1115/1.3243574", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062111061"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1115/1.3448250", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062126583"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1115/icmm2004-2356", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1092776014"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2009-08", 
    "datePublishedReg": "2009-08-01", 
    "description": "In this work the laminar-to-turbulent transition in microchannels of circular cross-section is studied experimentally. In order to single out the effects of relative roughness, compressibility and channel length-to-diameter ratio on the Reynolds number at which transition occurs, experimental runs have been carried out on circular microchannels in fused silica\u2014smooth for all purposes\u2014and in stainless steel (which possess a high surface roughness), with a diameter between 125 and 180 \u03bcm and a length of 5\u201350 cm through which nitrogen flows. For each tube the friction factor has been computed. The values of the critical Reynolds number have been determined plotting the Poiseuille number (i.e., the product of the friction factor, f, times the Reynols number, Re) as a function of the average Mach number between inlet and outlet. The transitional regime was found to start no earlier than at values of the Reynolds number around 1,800\u20132,000. It has been observed that surface roughness has no effect on the hydraulic resistance in the laminar region for a relative roughness lower than 4.4%, and that friction factor obeys the Poiseuille law, if it is correctly computed taking compressibility into account. It is found that recent correlations for the prediction of the critical Reynolds number in microchannels that link the relative roughness of the microtubes to the critical Reynolds number do not agree with the present results.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s10404-008-0369-2", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1040365", 
        "issn": [
          "1613-4982", 
          "1613-4990"
        ], 
        "name": "Microfluidics and Nanofluidics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "7"
      }
    ], 
    "name": "Analysis of laminar-to-turbulent transition for isothermal gas flows in microchannels", 
    "pagination": "181-190", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "5892332bbb1ad9047193ed56097e9b1235814e2df452cb1e262a9fbffc66eb35"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10404-008-0369-2"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1018589679"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10404-008-0369-2", 
      "https://app.dimensions.ai/details/publication/pub.1018589679"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T14:33", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000373_0000000373/records_13106_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs10404-008-0369-2"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10404-008-0369-2'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10404-008-0369-2'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10404-008-0369-2'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10404-008-0369-2'


 

This table displays all metadata directly associated to this object as RDF triples.

137 TRIPLES      21 PREDICATES      44 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10404-008-0369-2 schema:about anzsrc-for:09
2 anzsrc-for:0915
3 schema:author Nc4e0b4ce5f6a4fab9ba860194c1e9e38
4 schema:citation https://doi.org/10.1002/aic.690310315
5 https://doi.org/10.1016/0011-2275(83)90150-9
6 https://doi.org/10.1016/b978-008044527-4/50005-0
7 https://doi.org/10.1016/j.expthermflusci.2006.03.003
8 https://doi.org/10.1016/j.ijheatfluidflow.2006.05.005
9 https://doi.org/10.1016/j.ijheatmasstransfer.2004.10.030
10 https://doi.org/10.1016/j.ijheatmasstransfer.2006.10.034
11 https://doi.org/10.1016/j.ijthermalsci.2006.01.004
12 https://doi.org/10.1017/s0022112007009111
13 https://doi.org/10.1063/1.1896985
14 https://doi.org/10.1080/01457630701326308
15 https://doi.org/10.1080/10893950390219083
16 https://doi.org/10.1098/rstl.1883.0029
17 https://doi.org/10.1115/1.1797036
18 https://doi.org/10.1115/1.3243574
19 https://doi.org/10.1115/1.3448250
20 https://doi.org/10.1115/icmm2004-2356
21 schema:datePublished 2009-08
22 schema:datePublishedReg 2009-08-01
23 schema:description In this work the laminar-to-turbulent transition in microchannels of circular cross-section is studied experimentally. In order to single out the effects of relative roughness, compressibility and channel length-to-diameter ratio on the Reynolds number at which transition occurs, experimental runs have been carried out on circular microchannels in fused silica—smooth for all purposes—and in stainless steel (which possess a high surface roughness), with a diameter between 125 and 180 μm and a length of 5–50 cm through which nitrogen flows. For each tube the friction factor has been computed. The values of the critical Reynolds number have been determined plotting the Poiseuille number (i.e., the product of the friction factor, f, times the Reynols number, Re) as a function of the average Mach number between inlet and outlet. The transitional regime was found to start no earlier than at values of the Reynolds number around 1,800–2,000. It has been observed that surface roughness has no effect on the hydraulic resistance in the laminar region for a relative roughness lower than 4.4%, and that friction factor obeys the Poiseuille law, if it is correctly computed taking compressibility into account. It is found that recent correlations for the prediction of the critical Reynolds number in microchannels that link the relative roughness of the microtubes to the critical Reynolds number do not agree with the present results.
24 schema:genre research_article
25 schema:inLanguage en
26 schema:isAccessibleForFree false
27 schema:isPartOf Ndf634af725af494f840994d82cc6a008
28 Ne2bd81e09ffd48dea9d042a446b862af
29 sg:journal.1040365
30 schema:name Analysis of laminar-to-turbulent transition for isothermal gas flows in microchannels
31 schema:pagination 181-190
32 schema:productId N0ffacba304db4de2a79b55bf66412895
33 N3140da91781347a596ce36fda46b9525
34 N6f7497e14614494187c0d19ad14e971d
35 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018589679
36 https://doi.org/10.1007/s10404-008-0369-2
37 schema:sdDatePublished 2019-04-11T14:33
38 schema:sdLicense https://scigraph.springernature.com/explorer/license/
39 schema:sdPublisher N5a2df3feb96f4956aeed6d1ee70c892c
40 schema:url http://link.springer.com/10.1007%2Fs10404-008-0369-2
41 sgo:license sg:explorer/license/
42 sgo:sdDataset articles
43 rdf:type schema:ScholarlyArticle
44 N0ffacba304db4de2a79b55bf66412895 schema:name readcube_id
45 schema:value 5892332bbb1ad9047193ed56097e9b1235814e2df452cb1e262a9fbffc66eb35
46 rdf:type schema:PropertyValue
47 N3140da91781347a596ce36fda46b9525 schema:name dimensions_id
48 schema:value pub.1018589679
49 rdf:type schema:PropertyValue
50 N362f9d6180404bc392a301870158e84d rdf:first sg:person.016126176256.80
51 rdf:rest rdf:nil
52 N5a2df3feb96f4956aeed6d1ee70c892c schema:name Springer Nature - SN SciGraph project
53 rdf:type schema:Organization
54 N614ee6a148754df89c324dae0383d957 rdf:first sg:person.016345307602.92
55 rdf:rest N362f9d6180404bc392a301870158e84d
56 N6f7497e14614494187c0d19ad14e971d schema:name doi
57 schema:value 10.1007/s10404-008-0369-2
58 rdf:type schema:PropertyValue
59 Nc4e0b4ce5f6a4fab9ba860194c1e9e38 rdf:first sg:person.016136725555.26
60 rdf:rest Nc8582a81550a4829a718556a564c849e
61 Nc8582a81550a4829a718556a564c849e rdf:first sg:person.013742476454.22
62 rdf:rest N614ee6a148754df89c324dae0383d957
63 Ndf634af725af494f840994d82cc6a008 schema:issueNumber 2
64 rdf:type schema:PublicationIssue
65 Ne2bd81e09ffd48dea9d042a446b862af schema:volumeNumber 7
66 rdf:type schema:PublicationVolume
67 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
68 schema:name Engineering
69 rdf:type schema:DefinedTerm
70 anzsrc-for:0915 schema:inDefinedTermSet anzsrc-for:
71 schema:name Interdisciplinary Engineering
72 rdf:type schema:DefinedTerm
73 sg:journal.1040365 schema:issn 1613-4982
74 1613-4990
75 schema:name Microfluidics and Nanofluidics
76 rdf:type schema:Periodical
77 sg:person.013742476454.22 schema:affiliation https://www.grid.ac/institutes/grid.6292.f
78 schema:familyName Lorenzini
79 schema:givenName Marco
80 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013742476454.22
81 rdf:type schema:Person
82 sg:person.016126176256.80 schema:affiliation https://www.grid.ac/institutes/grid.10383.39
83 schema:familyName Spiga
84 schema:givenName Marco
85 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016126176256.80
86 rdf:type schema:Person
87 sg:person.016136725555.26 schema:affiliation https://www.grid.ac/institutes/grid.6292.f
88 schema:familyName Morini
89 schema:givenName Gian Luca
90 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016136725555.26
91 rdf:type schema:Person
92 sg:person.016345307602.92 schema:affiliation https://www.grid.ac/institutes/grid.6292.f
93 schema:familyName Salvigni
94 schema:givenName Sandro
95 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016345307602.92
96 rdf:type schema:Person
97 https://doi.org/10.1002/aic.690310315 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027404533
98 rdf:type schema:CreativeWork
99 https://doi.org/10.1016/0011-2275(83)90150-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032850263
100 rdf:type schema:CreativeWork
101 https://doi.org/10.1016/b978-008044527-4/50005-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052016335
102 rdf:type schema:CreativeWork
103 https://doi.org/10.1016/j.expthermflusci.2006.03.003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045997930
104 rdf:type schema:CreativeWork
105 https://doi.org/10.1016/j.ijheatfluidflow.2006.05.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024322307
106 rdf:type schema:CreativeWork
107 https://doi.org/10.1016/j.ijheatmasstransfer.2004.10.030 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017707432
108 rdf:type schema:CreativeWork
109 https://doi.org/10.1016/j.ijheatmasstransfer.2006.10.034 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024406847
110 rdf:type schema:CreativeWork
111 https://doi.org/10.1016/j.ijthermalsci.2006.01.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030957993
112 rdf:type schema:CreativeWork
113 https://doi.org/10.1017/s0022112007009111 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053957819
114 rdf:type schema:CreativeWork
115 https://doi.org/10.1063/1.1896985 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057831032
116 rdf:type schema:CreativeWork
117 https://doi.org/10.1080/01457630701326308 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020806715
118 rdf:type schema:CreativeWork
119 https://doi.org/10.1080/10893950390219083 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029815441
120 rdf:type schema:CreativeWork
121 https://doi.org/10.1098/rstl.1883.0029 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026624834
122 rdf:type schema:CreativeWork
123 https://doi.org/10.1115/1.1797036 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062074744
124 rdf:type schema:CreativeWork
125 https://doi.org/10.1115/1.3243574 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062111061
126 rdf:type schema:CreativeWork
127 https://doi.org/10.1115/1.3448250 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062126583
128 rdf:type schema:CreativeWork
129 https://doi.org/10.1115/icmm2004-2356 schema:sameAs https://app.dimensions.ai/details/publication/pub.1092776014
130 rdf:type schema:CreativeWork
131 https://www.grid.ac/institutes/grid.10383.39 schema:alternateName University of Parma
132 schema:name Dipartimento di Ingegneria Industriale, Università di Parma, Via G.P. Usberti 181A, 43100, Parma, Italy
133 rdf:type schema:Organization
134 https://www.grid.ac/institutes/grid.6292.f schema:alternateName University of Bologna
135 schema:name DIENCA, Università degli Studi di Bologna, Via Terracini 34, 40131, Bologna, Italy
136 DIENCA, Università degli Studi di Bologna, Viale Risorgimento 2, 40136, Bologna, Italy
137 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...