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Relevant bibliographies by topics / Homfly

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Academic literature on the topic 'Homfly'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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Journal articles on the topic "Homfly"

1

Zhu, Shengmao. "A simple proof of the strong integrality for full colored HOMFLYPT invariants." Journal of Knot Theory and Its Ramifications 28, no. 07 (June 2019): 1950046. http://dx.doi.org/10.1142/s0218216519500469.

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MORTON, H. R. "Mutant knots with symmetry." Mathematical Proceedings of the Cambridge Philosophical Society 146, no. 1 (January 2009): 95–107. http://dx.doi.org/10.1017/s0305004108001862.

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AbstractMutant knots, in the sense of Conway, are known to share the same Homfly polynomial. Their 2-string satellites also share the same Homfly polynomial, but in general theirm-string satellites can have different Homfly polynomials form> 2. We show that, under conditions of extra symmetry on the constituent 2-tangles, the directedm-string satellites of mutants share the same Homfly polynomial form< 6 in general, and for all choices ofmwhen the satellite is based on a cable knot pattern.We give examples of mutants with extra symmetry whose Homfly polynomials of some 6-string satellites are different, by comparing their quantumsl(3) invariants.

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LAVROV, MIKHAIL, and DAN RUTHERFORD. "ON THE S1 × S2 HOMFLY-PT INVARIANT AND LEGENDRIAN LINKS." Journal of Knot Theory and Its Ramifications 22, no. 08 (July 2013): 1350040. http://dx.doi.org/10.1142/s0218216513500405.

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In [On the HOMFLY-PT skein module of S1 × S2, Math. Z. 237(4) (2001) 769–814], Gilmer and Zhong established the existence of an invariant for links in S1 × S2 which is a rational function in variables a and s and satisfies the HOMFLY-PT skein relations. We give formulas for evaluating this invariant in terms of a standard, geometrically simple basis for the HOMFLY-PT skein module of the solid torus. This allows computation of the invariant for arbitrary links in S1 × S2 and shows that the invariant is in fact a Laurent polynomial in a and z = s – s-1. Our proof uses connections between HOMFLY-PT skein modules and invariants of Legendrian links. As a corollary, we extend HOMFLY-PT polynomial estimates for the Thurston–Bennequin number to Legendrian links in S1 × S2 with its tight contact structure.

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MORTON, H. R., and N. D. A. RYDER. "Relations between Kauffman and Homfly satellite invariants." Mathematical Proceedings of the Cambridge Philosophical Society 149, no. 1 (March 16, 2010): 105–14. http://dx.doi.org/10.1017/s0305004110000058.

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Kawagoe, Kenichi. "On the skeins in the annulus and applications to invariants of 3-manifolds." Journal of Knot Theory and Its Ramifications 07, no. 02 (March 1998): 187–203. http://dx.doi.org/10.1142/s0218216598000127.

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In this paper, we relate Schur functions and a linear skein of annulus derived from the Homfly polynomail. Using this relations, we define topological invariants of 3-manifolds from the Homfly polynomial.

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Dowlin, Nathan. "The knot Floer cube of resolutions and the composition product." Journal of Knot Theory and Its Ramifications 29, no. 03 (March 2020): 2050006. http://dx.doi.org/10.1142/s0218216520500066.

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We examine the relationship between the oriented cube of resolutions for knot Floer homology and HOMFLY-PT homology. By using a filtration induced by additional basepoints on the Heegaard diagram for a knot [Formula: see text], we see that the filtered complex decomposes as a direct sum of HOMFLY-PT complexes of various subdiagrams. Applying Jaeger’s composition product formula for knot polynomials, we deduce that the graded Euler characteristic of this direct sum is the HOMFLY-PT polynomial of [Formula: see text].

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Altun, Y. "On the Homfly polynomial." International Mathematical Forum 2 (2007): 2753–57. http://dx.doi.org/10.12988/imf.2007.07247.

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CHAN, TAT-HUNG. "POLYNOMIALS FOR A FAMILY OF BRUNNIAN LINKS." Journal of Knot Theory and Its Ramifications 09, no. 05 (August 2000): 587–609. http://dx.doi.org/10.1142/s0218216500000335.

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We apply skein relations to derive recurrence relations for the HOMFLY polynomials of a family of Brunnian links. Solution of the recurrence relations yields closed-form formulas for the HOMFLY and hence the Jones polynomials.

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KAUFFMAN, LOUIS H., and PIERRE VOGEL. "LINK POLYNOMIALS AND A GRAPHICAL CALCULUS." Journal of Knot Theory and Its Ramifications 01, no. 01 (March 1992): 59–104. http://dx.doi.org/10.1142/s0218216592000069.

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This paper constructs invariants of rigid vertex isotopy for graphs embedded in three dimensional space. For the Homfly and Dubrovnik polynomials, the skein formalism for these invariants is as shown below. Homfly. [Formula: see text] Dubrovnik. [Formula: see text]

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KIM, JAEHOO PARK. "A HOMFLY-PT POLYNOMIAL OF LINKS IN A SOLID TORUS." Journal of Knot Theory and Its Ramifications 08, no. 06 (September 1999): 709–20. http://dx.doi.org/10.1142/s0218216599000456.

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In this paper a Homfly-pt type Laurant polynomial1 for links in S1 × D2 is defined. This invariant is defined by giving an algebra and a trace, analogous to the Hecke algebra construction of the Homfly-pt polynomial for links in S3.

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Dissertations / Theses on the topic "Homfly"

1

Lukac, Sascha Georg. "Homfly skeins and the Hopf link." Thesis, University of Liverpool, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343969.

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Hadji, Richard John. "Homfly skein theory of reversed string satellites." Thesis, University of Liverpool, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.408554.

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Castellini, Roberto. "A homological definition of the HOMFLY polynomial." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amslaurea.unibo.it/2511/.

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Vertigan, Dirk Llewellyn. "On the computational complexity of Tutte, Jones, Homfly and Kauffman invariants." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.291600.

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Roberts, Sharleen Adrienne. "Knots Not for Naught." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1446.pdf.

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Wagner, Emmanuel. "Sur l'homologie de Khovanov-Rozansky des graphes et des entrelacs." Phd thesis, Université Louis Pasteur - Strasbourg I, 2007. http://tel.archives-ouvertes.fr/tel-00192447.

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Cette thèse est consacrée à la catégorification d'invariants polynomiaux d'entrelacs et de graphes. Pour tout entier strictement positif n, Khovanov et Rozansky ont introduit en 2004 une homologie bigraduée d'entrelacs, ainsi qu'une homologie de graphes planaires. Etant donné n, leur homologie d'entrelacs catégorifie la n-ième spécialisation du polynôme d'entrelacs HOMFLYPT et leur homologie de graphes planaires catégorifie un polynôme de graphes associé.

Dans cette thèse, on étudie ces homologies et on généralise leur construction en introduisant une graduation supplémentaire. Tout d'abord, on généralise une formule de Jaeger pour les polynômes d'entrelacs aux polynômes de graphes planaires, ainsi qu'à l'homologie de graphes planaires; on étend ensuite l'homologie d'entrelacs de Khovanov-Rozansky aux graphes plongés. Puis on construit une homologie trigraduée d'entrelacs. Cette homologie recouvre l'homologie bigraduée d'entrelacs de Khovanov et Rozansky. Enfin, on donne des exemples, des applications et des généralisations de l'homologie trigraduée d'entrelacs. On développe des outils d'algèbre homologique qui permettent de calculer explicitement l'homologie trigraduée d'entrelacs pour des exemples et on considère des déformations de l'homologie trigraduée d'entrelacs.

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Wagner, Emmanuel. "On Khovanov-Rozansky homology of graphs and links." Université Louis Pasteur (Strasbourg) (1971-2008), 2007. https://publication-theses.unistra.fr/restreint/theses_doctorat/2007/WAGNER_Emmanuel_2007.pdf.

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Cette thèse est consacrée à la catégorification d'invariants polynomiaux d'entrelacs et de graphes. Pour tout entier strictement positif n, Khovanov et Rozansky ont introduit en 2004 une homologie bigraduée d'entrelacs, ainsi qu'une homologie de graphes planaires. Etant donné n, leur homologie d'entrelacs catégorifie la n-ième spécialisation du polynôme d'entrelacs HOMFLYPT et leur homologie de graphes planaires catégorifie un polynôme de graphes associé. Dans cette thèse, on étudie ces homologies et on généralise leur construction en introduisant une graduation supplémentaire. Tout d'abord, on généralise une formule de Jaeger pour les polynômes d'entrelacs aux polynômes de graphes planaires, ainsi qu'à l'homologie de graphes planaires; on étend ensuite l'homologie d'entrelacs de Khovanov-Rozansky aux graphes plongés. Puis on construit une homologie trigraduée d'entrelacs. Cette homologie recouvre l'homologie bigraduée d'entrelacs de Khovanov et Rozansky. Enfin, on donne des exemples, des applications et des généralisations de l'homologie trigraduée d'entrelacs. On développe des outils d'algèbre homologique qui permettent de calculer explicitement l'homologie trigraduée d'entrelacs pour des exemples et on considère des déformations de l'homologie trigraduée d'entrelacs
This thesis is devoted to the categorification of polynomial invariants of graphs and links. For any positive integer n, Khovanov and Rozansky introduced in 2004 a bigraded link homology, and an homology of planar graphs. Given n, their link homology categorifies the n-th specialization of the HOMFLY-PT polynomial and their homology of planar graphs categorifies an associated graph polynomial. In this thesis, we study these homology and generalize their constructions by introducing an additional grading. First, we generalize a formula of Jaeger for link polynomials to polynomials of planar graphs and associated homology of planar graphs; we extend also the link homology of Khovanov and Rozansky to embedded graphs. Then we construct a triply graded link homology. This homology recovers the bigraded link homology of Khovanov and Rozansky. Finally, we give examples, applications and generalizations of the triply graded link homology. We develop homological tools that permit to compute explicitly the triply graded link homology for some knots and we consider deformations of the triply graded link homology

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Avery, Dwayne. "(Un)homely cinema." Thesis, McGill University, 2011. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103637.

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This dissertation offers an analysis of the cinematic (un)homely. Loosely based on Freud's concept of the uncanny – that frightful and inexplicable experience of the home as a foreign and strange space – the (un)homely is a poignant sign of the times, a contemporary trope of the various kinds of spatial dislocation, transience, homelessness and disempowerment symptomatic of contemporary global societies. In short the (un)homely conjures up the decline of family, its faltering role as the moral center of the world and all the unpleasant ramifications that come from the destabilization of the home. The (un)homely speaks to the breakdown of what is deemed proper – the distinction between public and private space, the unraveling of gender norms, the troubling de-localization of mobile technologies. While the uncanny nature of the home is a mainstay in many science fiction and horror films, my analysis uses the concept of the (un)homely to explore a wide range of contemporary films that explore every day domestic environments and the way the home is the site for a wide range of devastating intrusions – from the precarious nature of the nation in an age of globalization to the way mobile work seeps into the protective spaces of the home. These intrusions I contend provide themes and images related to the ways in which contemporary social relations, work and new technologies prevent characters from ever finding their way home. However, while an encounter with the (un)homely represents a painful experience with the loss of home, the (un)homely can offer an ethics of dwelling, as the impossibility of narrative closure or the shift in power relations offer new and more hopeful ways of dwelling in the world.
Cette thèse présente une analyse du « (un)homely » filmique. Vaguement basée sur le concept de Freud sur l'étrange – cette expérience inexplicable et effroyable du foyer familial vu en tant qu'espace étranger et bizarre – le « (un)homely » est un signe poignant des temps, un trope contemporain des divers types de dislocations spatiales, de déplacements, d'itinérance et de la privation de pouvoir, symptomatiques des sociétés globales contemporaines. En bref, « (un)homely » évoque le déclin de la famille, son rôle incertain en tant que centre moral du monde, ainsi que toutes les ramifications désagréables qui découlent de la déstabilisation du foyer familial. « (un)homely » fait référence à la dégradation de ce qui est jugé convenable – la distinction entre l'espace public et privé, le démantèlement des normes du genre, la délocalisation inquiétante des technologies mobiles. Bien que l'étrange nature du foyer familial soit représentée comme un des piliers de base dans un grand nombre de films de science-fiction et d'horreur, mon analyse utilise le concept de « (un)homely » pour examiner un vaste ensemble de films contemporains qui explorent les environnements quotidiens et la façon dont le foyer est le lieu d'un ensemble étendu d'intrusions dévastatrices – allant de la nature précaire de la nation dans un âge de globalisation, jusqu'à la façon dont le travail mobile s'insère dans les espaces protégés du foyer. J'avance que ces intrusions procurent des thèmes et des images liés aux façons dont les relations sociales contemporaines, le travail et les nouvelles technologies empêchent les personnages de trouver à jamais leur chemin vers leur foyer. Néanmoins, bien qu'une rencontre avec le « (un)homely » constitue l'expérience douloureuse de la perte de son foyer, « (un)homely » peut offrir une éthique du logement, étant donné que l'impossibilité de conclusion narrative ou le changement dans les relations de pouvoir offrent des façons nouvelles et plus optimistes d'établir une résidence dans le monde.

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Bidgood, Lee. "Towards an Appalachian Liturgy Homily." Digital Commons @ East Tennessee State University, 2015. https://dc.etsu.edu/etsu-works/1092.

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Moore, Scott Ronald. "Affinities of the Epistle of James with synagogue homily and midrash." Theological Research Exchange Network (TREN), 2007. http://www.tren.com/search.cfm?p090-0348.

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Books on the topic "Homfly"

1

Li, Su Yi. Distinguishing homely dishes. Hong Kong: Food Paradise, 1993.

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Peter, Doig. Peter Doig: Homely. Bremen: Gesellschaft für aktuelle Kunst, 1996.

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(Firm), CREACES, ed. The homely knight. London: Popular UK, 2006.

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Li, Su Yi. Distinguishing homely dishes. [S.l.]: Guangxijiaoyu, 1999.

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Law, Bernard F. Mission Sunday homily. Boston, Mass: Daughters of St. Paul, 1985.

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Kleist, Aaron J., ed. The Old English Homily. Turnhout: Brepols Publishers, 2007. http://dx.doi.org/10.1484/m.sem-eb.6.09070802050003050107090206.

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Arthur, Miller. Homely girl: A life. New York: Peter Blum Edition, 1992.

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Cun, Zhen Mei Ye. Ours! Homely English flavor house. Taiwan: Zong Wen, 2004.

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An introduction to the homily. Collegeville, Minn: Liturgical Press, 1998.

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Christopher, Webber. The art of the homily. Harrisburg, PA: Morehouse Pub., 1992.

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Book chapters on the topic "Homfly"

1

Lickorish, W. B. Raymond. "Exploring the HOMFLY and Kauffman Polynomials." In An Introduction to Knot Theory, 179–92. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-0691-0_16.

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Queffelec, Hoel, and Antonio Sartori. "A Note on $$\mathfrak {gl}_{m|n}$$ Link Invariants and the HOMFLY–PT Polynomial." In Knots, Low-Dimensional Topology and Applications, 277–86. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16031-9_13.

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Penner, Barbara. "Homely Affinities." In Forty Ways To Think About Architecture, 48–53. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2015. http://dx.doi.org/10.1002/9781118822531.ch4.

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Mironov, Andrei, Alexei Morozov, and Andrey Morozov. "Character expansion for HOMFLY polynomials I: Integrability and difference equations." In Strings, Gauge Fields, and the Geometry Behind, 101–18. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814412551_0003.

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Forness, Philip Michael. "Homilies and Reading Communities." In Preaching Christology in the Roman Near East, 134–56. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198826453.003.0005.

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This chapter addresses the most controversial homily in Jacob of Serugh’s corpus, the Homily on the Council of Chalcedon. Recently discovered manuscripts provide a solid basis for viewing this homily as an integral part of his corpus, despite the long debate over its authenticity. The close correspondence of his Christological thought here with that examined in his letters provides an even firmer basis for asserting its authenticity. Although the physical context in which Jacob delivered this homily remains elusive, this chapter demonstrates how scholars can productively interpret it as a text that circulated among reading communities in late antiquity. Two periods of Jacob’s life, known from his letters, would have made ideal contexts in which he circulated this homily as part of a dossier of texts for elite reading communities.

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Dusenbury, David Lloyd. "“You Acted in Ignorance”." In The Innocence of Pontius Pilate, 133–40. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780197602799.003.0013.

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This chapter offers a close reading of certain texts of Paul and Luke-Acts which have been misread in Christian tradition. It is suggested, here, that the first Christian homily (meaning the first homily in Acts) sharply distinguishes between the killing of Jesus and the killing of the Christ. This distinction structures Peter’s homily in Acts 2, which begins with what his hearers know (that a man named Jesus had been crucified by Pilate on the insistence of Caiaphas), and it ends with what they do not know (that Jesus had been legitimated by his resurrection as the Christ). The logic of Peter’s homily is precisely that Jesus’ killers had killed the Christ; but it is no less precisely that Jesus’ killers had unknowingly killed the Christ. A crucial idea in the first Christian homily, then, is that there are no ‘Christ-killers’ (a venomous term of later centuries). Christian anti-Semitism not only reveals a deep vein of malice and bitterness, but a failure to comprehend the Christians’ canonical texts.

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"HOMILY I." In Gregory of Nyssa: Homilies on the Beatitudes, 21–90. BRILL, 2000. http://dx.doi.org/10.1163/9789004313187_003.

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"Homily 10." In The Syriac Pseudo-Clementines, 251–66. Turnhout: Brepols Publishers, 2014. http://dx.doi.org/10.1484/m.apocr-eb.4.00018.

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"Homily 11." In The Syriac Pseudo-Clementines, 267–89. Turnhout: Brepols Publishers, 2014. http://dx.doi.org/10.1484/m.apocr-eb.4.00019.

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"Homily 12." In The Syriac Pseudo-Clementines, 291–311. Turnhout: Brepols Publishers, 2014. http://dx.doi.org/10.1484/m.apocr-eb.4.00020.

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Conference papers on the topic "Homfly"

1

Morton, Hugh R. "Power sums and Homfly skein theory." In Invariants of Knots and 3--manifolds. Mathematical Sciences Publishers, 2002. http://dx.doi.org/10.2140/gtm.2002.4.235.

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KAWAGOE, Kenichi. "LIMITS OF THE HOMFLY POLYNOMIALS OF THE FIGURE-EIGHT KNOT." In Intelligence of Low Dimensional Topology 2006 - The International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770967_0018.

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KANENOBU, TAIZO. "AN EVALUATION OF THE COEFFICIENT POLYNOMIALS OF THE HOMFLY POLYNOMIAL OF A LINK." In Proceedings of the International Conference on Knot Theory and Its Ramifications. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792679_0010.

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Takayama, Leila, Caroline Pantofaru, David Robson, Bianca Soto, and Michael Barry. "Making technology homey." In the 2012 ACM Conference. New York, New York, USA: ACM Press, 2012. http://dx.doi.org/10.1145/2370216.2370292.

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Marlow, D. W. "Investigating technical trouble tickets: an analysis of a homely CMC genre." In 37th Annual Hawaii International Conference on System Sciences, 2004. Proceedings of the. IEEE, 2004. http://dx.doi.org/10.1109/hicss.2004.1265272.

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Vilciu, Marian. "PRINCIPLES CONCERNING THE EDUCATION OF THE YOUNG REFLECTED IN SAINT BASIL OF CAESAREAS HOMILY TO THE YOUNG." In SGEM 2014 Scientific SubConference on PSYCHOLOGY AND PSYCHIATRY, SOCIOLOGY AND HEALTHCARE, EDUCATION. Stef92 Technology, 2014. http://dx.doi.org/10.5593/sgemsocial2014/b13/s3.088.

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Nascimento, Luis Henrique da Hora, and Jorge Alberto Prado de Campos. "HOML: LINGUAGEM HIERÁRQUICA PARA MAPEAMENTO DE OBJETOS." In 12th CONTECSI International Conference on Information Systems and Technology Management. TECSI, 2015. http://dx.doi.org/10.5748/9788599693117-12contecsi/rf-2581.

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Lopez Mata, J. L., S. Perez, H. H. Vizcarra, Alex Ngan, E. A. Garcia Gil, and J. Basto Liewald. "Redefining Technical Limit – Managed Pressure Directional Drilling Solution in Mexico Homol Field." In International Petroleum Technology Conference. IPTC, 2021. http://dx.doi.org/10.2523/iptc-21398-ms.

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Abstract This paper will discuss the Managed Pressure Directional Drilling fit-for-purpose solution deployed to meet drilling challenges in Mexico's offshore Homol field. This innovative solution integrates a new state-of-the-art Rotary Steerable System (RSS) with Managed Pressure Drilling (MPD) technology. Drilling hazards such as the ballooning effect due to drilling plastic formations, losses, wellbore instability, and stuck pipe were effectively mitigated, and improved drilling performance with reduced NPT was delivered compared to other directional drilling systems. The solution requires the integration of two highly technical disciplines, MPD and Directional Drilling. Hence, a Joint Operating & Reporting Procedure (JORP) and a defined communication protocol proved crucial for effective execution. The solution is based on a rigorous Drilling Engineering process, including detailed offset well analysis to deliver a comprehensive risk assessment and mitigation plan jointly with the Operator to tackle drilling hazards such as ballooning without compromising the directional drilling requirements. In addition, flow processes and procedures were developed for contingency events, including but not limited to losses, stuck pipe, wellbore instability, and well control. After successfully deploying the new RSS tool in Mexico offshore, the Operator came across a challenging directional well with a history of ballooning effect, losses, stuck pipe, and wellbore instability. Combining the RSS tool with MPD Constant Bottom Hole Pressure (CBHP) technique to mitigating the ballooning effect while maintaining constant surface back pressure (SBP), the well was drilled while minimizing the downhole pressure fluctuation to mitigate against wellbore instability until reaching the lower paleocene formation, taking care to maintain an equivalent circulating density (ECD) of 2.04g/cc while drilling, and 1.99g/cc during connections, in order to reduce the ballooning effect observed in offset wells. As a result of careful planning, the RSS and downhole-surface communication continued to work well, while the MPD CBHP variant successfully mitigated against ballooning and well control hazards. The paper will also discuss the effective communication protocol between directional drilling, MPD services, and rig contractors to ensure safe operational alignment. Rotary steerable systems (RSS) for directional drilling must drill in increasingly hostile environments and with different challenges inherent to formations; examples of this are formations with plastic behavior that cause ballooning effect. This phenomenon can confuse drilling crew cause its behavior is very similar to kicks from wells. Homol is an oilfield with marked ballooning characteristics, causing significant Non-Productive Time (NPT). Drilling challenges in the Homol field require the utilization of both Directional Drilling technology and MPD techniques to improve drilling performance and reduce NPT at the same time. However, the technologies need to be optimized for one another. Also, directional services had to ensure reliability and accurately position wells, while the MPD technology to discern ballooning from actual influx and managing wellbore stability. This article describes the teamwork carried out by the directional team and MPD to avoid/minimize the ballooning effect while drilling directional jobs, improving operational time. The paper also includes a planning and operational blueprint to reduce NPT related to, while increasing drilling performance in terms of rate of penetration (ROP) and wellbore quality to allow the liner to be run to section TD in the Lower Paleocene formation.

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Ozbakan, Ahmet Tolga. "An Agent-based Model for Exploring Formation of Housing Prices: Housing Market Laboratory (HoML)." In Construction Research Congress 2014. Reston, VA: American Society of Civil Engineers, 2014. http://dx.doi.org/10.1061/9780784413517.012.

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Gursel, Gokalp, Ufuk Olgac, and Metin Muradoglu. "Effects of Surfactant on the Motion of a Large Bubble in a Capillary Tube." In ASME 2011 9th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2011. http://dx.doi.org/10.1115/icnmm2011-58067.

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Abstract:

The finite-difference/front-tracking method is used to study the motion and deformation of a large bubble moving through a capillary tube in the presence of both insoluble and soluble surfactants. Emphasis is placed on the effects of surfactant on the liquid film thickness between the bubble and the tube wall. The numerical method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier-Stokes equations. A non-linear equation of state is used to relate interfacial surface tension to surfactant concentration at the interface. The film thickness is first computed for the clean bubble case and the results are compared with the lubrication theory in the limit of small capillary numbers, i.e., Ca ≪ 1, and found to be in good agreement with the predictions of Bretherton [1]. Thereafter, the method is used to investigate the effects of insoluble and soluble surfactants on the film thickness for a wide range of governing non-dimensional numbers. It is found that both the insoluble and soluble surfactants have a thickening effect on the liquid film, which compares well with both the experimental results of Krechetnikov and Homsy [2] and analytical predictions of Daripa and Pasa [3].

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