Rigorous theory for transient capillary imbibition in channels of arbitrary cross section
Abstract This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inhere...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Bhattacharya, S. [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2016 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2016 |
|---|
| Übergeordnetes Werk: |
Enthalten in: Theoretical and computational fluid dynamics - Springer Berlin Heidelberg, 1989, 31(2016), 2 vom: 31. Okt., Seite 137-157 |
|---|---|
| Übergeordnetes Werk: |
volume:31 ; year:2016 ; number:2 ; day:31 ; month:10 ; pages:137-157 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00162-016-0409-6 |
|---|
| Katalog-ID: |
OLC2071166337 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | OLC2071166337 | ||
| 003 | DE-627 | ||
| 005 | 20230401070851.0 | ||
| 007 | tu | ||
| 008 | 200820s2016 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s00162-016-0409-6 |2 doi | |
| 035 | |a (DE-627)OLC2071166337 | ||
| 035 | |a (DE-He213)s00162-016-0409-6-p | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 530 |a 620 |q VZ |
| 082 | 0 | 4 | |a 510 |a 530 |q VZ |
| 100 | 1 | |a Bhattacharya, S. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Rigorous theory for transient capillary imbibition in channels of arbitrary cross section |
| 264 | 1 | |c 2016 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 500 | |a © Springer-Verlag Berlin Heidelberg 2016 | ||
| 520 | |a Abstract This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon. | ||
| 650 | 4 | |a Time-dependent fluid penetration | |
| 650 | 4 | |a Capillary action | |
| 650 | 4 | |a Unsteady channel flow | |
| 650 | 4 | |a Transient velocity profile | |
| 650 | 4 | |a Eigenfunction expansion | |
| 700 | 1 | |a Azese, M. N. |4 aut | |
| 700 | 1 | |a Singha, S. |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Theoretical and computational fluid dynamics |d Springer Berlin Heidelberg, 1989 |g 31(2016), 2 vom: 31. Okt., Seite 137-157 |w (DE-627)130799521 |w (DE-600)1007949-X |w (DE-576)023042370 |x 0935-4964 |7 nnns |
| 773 | 1 | 8 | |g volume:31 |g year:2016 |g number:2 |g day:31 |g month:10 |g pages:137-157 |
| 856 | 4 | 1 | |u https://doi.org/10.1007/s00162-016-0409-6 |z lizenzpflichtig |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a SSG-OLC-TEC | ||
| 912 | |a SSG-OLC-PHY | ||
| 912 | |a SSG-OLC-MAT | ||
| 912 | |a SSG-OPC-MAT | ||
| 912 | |a GBV_ILN_20 | ||
| 912 | |a GBV_ILN_70 | ||
| 912 | |a GBV_ILN_267 | ||
| 912 | |a GBV_ILN_2018 | ||
| 912 | |a GBV_ILN_2088 | ||
| 912 | |a GBV_ILN_4277 | ||
| 951 | |a AR | ||
| 952 | |d 31 |j 2016 |e 2 |b 31 |c 10 |h 137-157 | ||
| author_variant |
s b sb m n a mn mna s s ss |
|---|---|
| matchkey_str |
article:09354964:2016----::iooshoyotasetailribbtoicanlo |
| hierarchy_sort_str |
2016 |
| publishDate |
2016 |
| allfields |
10.1007/s00162-016-0409-6 doi (DE-627)OLC2071166337 (DE-He213)s00162-016-0409-6-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Bhattacharya, S. verfasserin aut Rigorous theory for transient capillary imbibition in channels of arbitrary cross section 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2016 Abstract This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon. Time-dependent fluid penetration Capillary action Unsteady channel flow Transient velocity profile Eigenfunction expansion Azese, M. N. aut Singha, S. aut Enthalten in Theoretical and computational fluid dynamics Springer Berlin Heidelberg, 1989 31(2016), 2 vom: 31. Okt., Seite 137-157 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:31 year:2016 number:2 day:31 month:10 pages:137-157 https://doi.org/10.1007/s00162-016-0409-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4277 AR 31 2016 2 31 10 137-157 |
| spelling |
10.1007/s00162-016-0409-6 doi (DE-627)OLC2071166337 (DE-He213)s00162-016-0409-6-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Bhattacharya, S. verfasserin aut Rigorous theory for transient capillary imbibition in channels of arbitrary cross section 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2016 Abstract This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon. Time-dependent fluid penetration Capillary action Unsteady channel flow Transient velocity profile Eigenfunction expansion Azese, M. N. aut Singha, S. aut Enthalten in Theoretical and computational fluid dynamics Springer Berlin Heidelberg, 1989 31(2016), 2 vom: 31. Okt., Seite 137-157 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:31 year:2016 number:2 day:31 month:10 pages:137-157 https://doi.org/10.1007/s00162-016-0409-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4277 AR 31 2016 2 31 10 137-157 |
| allfields_unstemmed |
10.1007/s00162-016-0409-6 doi (DE-627)OLC2071166337 (DE-He213)s00162-016-0409-6-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Bhattacharya, S. verfasserin aut Rigorous theory for transient capillary imbibition in channels of arbitrary cross section 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2016 Abstract This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon. Time-dependent fluid penetration Capillary action Unsteady channel flow Transient velocity profile Eigenfunction expansion Azese, M. N. aut Singha, S. aut Enthalten in Theoretical and computational fluid dynamics Springer Berlin Heidelberg, 1989 31(2016), 2 vom: 31. Okt., Seite 137-157 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:31 year:2016 number:2 day:31 month:10 pages:137-157 https://doi.org/10.1007/s00162-016-0409-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4277 AR 31 2016 2 31 10 137-157 |
| allfieldsGer |
10.1007/s00162-016-0409-6 doi (DE-627)OLC2071166337 (DE-He213)s00162-016-0409-6-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Bhattacharya, S. verfasserin aut Rigorous theory for transient capillary imbibition in channels of arbitrary cross section 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2016 Abstract This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon. Time-dependent fluid penetration Capillary action Unsteady channel flow Transient velocity profile Eigenfunction expansion Azese, M. N. aut Singha, S. aut Enthalten in Theoretical and computational fluid dynamics Springer Berlin Heidelberg, 1989 31(2016), 2 vom: 31. Okt., Seite 137-157 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:31 year:2016 number:2 day:31 month:10 pages:137-157 https://doi.org/10.1007/s00162-016-0409-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4277 AR 31 2016 2 31 10 137-157 |
| allfieldsSound |
10.1007/s00162-016-0409-6 doi (DE-627)OLC2071166337 (DE-He213)s00162-016-0409-6-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Bhattacharya, S. verfasserin aut Rigorous theory for transient capillary imbibition in channels of arbitrary cross section 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2016 Abstract This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon. Time-dependent fluid penetration Capillary action Unsteady channel flow Transient velocity profile Eigenfunction expansion Azese, M. N. aut Singha, S. aut Enthalten in Theoretical and computational fluid dynamics Springer Berlin Heidelberg, 1989 31(2016), 2 vom: 31. Okt., Seite 137-157 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:31 year:2016 number:2 day:31 month:10 pages:137-157 https://doi.org/10.1007/s00162-016-0409-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4277 AR 31 2016 2 31 10 137-157 |
| language |
English |
| source |
Enthalten in Theoretical and computational fluid dynamics 31(2016), 2 vom: 31. Okt., Seite 137-157 volume:31 year:2016 number:2 day:31 month:10 pages:137-157 |
| sourceStr |
Enthalten in Theoretical and computational fluid dynamics 31(2016), 2 vom: 31. Okt., Seite 137-157 volume:31 year:2016 number:2 day:31 month:10 pages:137-157 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Time-dependent fluid penetration Capillary action Unsteady channel flow Transient velocity profile Eigenfunction expansion |
| dewey-raw |
530 |
| isfreeaccess_bool |
false |
| container_title |
Theoretical and computational fluid dynamics |
| authorswithroles_txt_mv |
Bhattacharya, S. @@aut@@ Azese, M. N. @@aut@@ Singha, S. @@aut@@ |
| publishDateDaySort_date |
2016-10-31T00:00:00Z |
| hierarchy_top_id |
130799521 |
| dewey-sort |
3530 |
| id |
OLC2071166337 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2071166337</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230401070851.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2016 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00162-016-0409-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2071166337</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00162-016-0409-6-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="a">620</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bhattacharya, S.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Rigorous theory for transient capillary imbibition in channels of arbitrary cross section</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag Berlin Heidelberg 2016</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Time-dependent fluid penetration</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Capillary action</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Unsteady channel flow</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Transient velocity profile</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Eigenfunction expansion</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Azese, M. N.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Singha, S.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Theoretical and computational fluid dynamics</subfield><subfield code="d">Springer Berlin Heidelberg, 1989</subfield><subfield code="g">31(2016), 2 vom: 31. Okt., Seite 137-157</subfield><subfield code="w">(DE-627)130799521</subfield><subfield code="w">(DE-600)1007949-X</subfield><subfield code="w">(DE-576)023042370</subfield><subfield code="x">0935-4964</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:31</subfield><subfield code="g">year:2016</subfield><subfield code="g">number:2</subfield><subfield code="g">day:31</subfield><subfield code="g">month:10</subfield><subfield code="g">pages:137-157</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s00162-016-0409-6</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_267</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2018</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4277</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">31</subfield><subfield code="j">2016</subfield><subfield code="e">2</subfield><subfield code="b">31</subfield><subfield code="c">10</subfield><subfield code="h">137-157</subfield></datafield></record></collection>
|
| author |
Bhattacharya, S. |
| spellingShingle |
Bhattacharya, S. ddc 530 ddc 510 misc Time-dependent fluid penetration misc Capillary action misc Unsteady channel flow misc Transient velocity profile misc Eigenfunction expansion Rigorous theory for transient capillary imbibition in channels of arbitrary cross section |
| authorStr |
Bhattacharya, S. |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)130799521 |
| format |
Article |
| dewey-ones |
530 - Physics 620 - Engineering & allied operations 510 - Mathematics |
| delete_txt_mv |
keep |
| author_role |
aut aut aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
0935-4964 |
| topic_title |
530 620 VZ 510 530 VZ Rigorous theory for transient capillary imbibition in channels of arbitrary cross section Time-dependent fluid penetration Capillary action Unsteady channel flow Transient velocity profile Eigenfunction expansion |
| topic |
ddc 530 ddc 510 misc Time-dependent fluid penetration misc Capillary action misc Unsteady channel flow misc Transient velocity profile misc Eigenfunction expansion |
| topic_unstemmed |
ddc 530 ddc 510 misc Time-dependent fluid penetration misc Capillary action misc Unsteady channel flow misc Transient velocity profile misc Eigenfunction expansion |
| topic_browse |
ddc 530 ddc 510 misc Time-dependent fluid penetration misc Capillary action misc Unsteady channel flow misc Transient velocity profile misc Eigenfunction expansion |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| hierarchy_parent_title |
Theoretical and computational fluid dynamics |
| hierarchy_parent_id |
130799521 |
| dewey-tens |
530 - Physics 620 - Engineering 510 - Mathematics |
| hierarchy_top_title |
Theoretical and computational fluid dynamics |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 |
| title |
Rigorous theory for transient capillary imbibition in channels of arbitrary cross section |
| ctrlnum |
(DE-627)OLC2071166337 (DE-He213)s00162-016-0409-6-p |
| title_full |
Rigorous theory for transient capillary imbibition in channels of arbitrary cross section |
| author_sort |
Bhattacharya, S. |
| journal |
Theoretical and computational fluid dynamics |
| journalStr |
Theoretical and computational fluid dynamics |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science 600 - Technology |
| recordtype |
marc |
| publishDateSort |
2016 |
| contenttype_str_mv |
txt |
| container_start_page |
137 |
| author_browse |
Bhattacharya, S. Azese, M. N. Singha, S. |
| container_volume |
31 |
| class |
530 620 VZ 510 530 VZ |
| format_se |
Aufsätze |
| author-letter |
Bhattacharya, S. |
| doi_str_mv |
10.1007/s00162-016-0409-6 |
| dewey-full |
530 620 510 |
| title_sort |
rigorous theory for transient capillary imbibition in channels of arbitrary cross section |
| title_auth |
Rigorous theory for transient capillary imbibition in channels of arbitrary cross section |
| abstract |
Abstract This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon. © Springer-Verlag Berlin Heidelberg 2016 |
| abstractGer |
Abstract This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon. © Springer-Verlag Berlin Heidelberg 2016 |
| abstract_unstemmed |
Abstract This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon. © Springer-Verlag Berlin Heidelberg 2016 |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4277 |
| container_issue |
2 |
| title_short |
Rigorous theory for transient capillary imbibition in channels of arbitrary cross section |
| url |
https://doi.org/10.1007/s00162-016-0409-6 |
| remote_bool |
false |
| author2 |
Azese, M. N. Singha, S. |
| author2Str |
Azese, M. N. Singha, S. |
| ppnlink |
130799521 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s00162-016-0409-6 |
| up_date |
2024-07-04T03:06:25.958Z |
| _version_ |
1803616136432975872 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2071166337</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230401070851.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2016 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00162-016-0409-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2071166337</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00162-016-0409-6-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="a">620</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bhattacharya, S.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Rigorous theory for transient capillary imbibition in channels of arbitrary cross section</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag Berlin Heidelberg 2016</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Time-dependent fluid penetration</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Capillary action</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Unsteady channel flow</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Transient velocity profile</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Eigenfunction expansion</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Azese, M. N.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Singha, S.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Theoretical and computational fluid dynamics</subfield><subfield code="d">Springer Berlin Heidelberg, 1989</subfield><subfield code="g">31(2016), 2 vom: 31. Okt., Seite 137-157</subfield><subfield code="w">(DE-627)130799521</subfield><subfield code="w">(DE-600)1007949-X</subfield><subfield code="w">(DE-576)023042370</subfield><subfield code="x">0935-4964</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:31</subfield><subfield code="g">year:2016</subfield><subfield code="g">number:2</subfield><subfield code="g">day:31</subfield><subfield code="g">month:10</subfield><subfield code="g">pages:137-157</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s00162-016-0409-6</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_267</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2018</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4277</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">31</subfield><subfield code="j">2016</subfield><subfield code="e">2</subfield><subfield code="b">31</subfield><subfield code="c">10</subfield><subfield code="h">137-157</subfield></datafield></record></collection>
|
| score |
7.3979874 |