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dc.creatorVlachomitrou M., Lytra A., Pelekasis N.en
dc.date.accessioned2023-01-31T11:36:53Z
dc.date.available2023-01-31T11:36:53Z
dc.date.issued2021
dc.identifier10.1007/s10665-021-10144-0
dc.identifier.issn00220833
dc.identifier.urihttp://hdl.handle.net/11615/80634
dc.description.abstractThe dynamic translation of a micron-sized encapsulated bubble is investigated numerically inside a horizontal tube where liquid flows under constant pressure drop, when the effect of gravity is neglected. The coating of the bubble is treated as an infinitesimally thin viscoelastic shell with bending resistance. The Galerkin Finite Element Methodology is employed to solve the axisymmetric flow configuration combined with the spine or elliptic mesh generation techniques for updating the mesh. The microbubble is initially elongated and the Reynolds number of the flow is relatively small, i.e. Re < 5. Benchmark simulations for long free bubbles robustly recover the scaling of the film thickness with the 2/3 power of the capillary number based on surface tension. In the case of encapsulated bubbles, for a sufficiently small capillary number and after a short transient period, the bubble acquires a Bretherton type shape that slowly expands in order to accommodate changes in the liquid pressure. The speed of translation is nearly constant, close to the mean velocity of the flow, and does not depend on surface tension, shell elasticity or bending resistance. Fluid motion in the thin film “contact” region that forms in the gap between the tube and the shell is seen to be a stable flow arrangement that entails a mixture of pressure driven and shear driven flow, with the latter greatly affected by the area dilatation modulus via the tangential stress balance. By introducing a modified capillary number based on the area dilatational modulus, rather than surface tension, it is seen that the dimensionless film thickness that occupies the region between the bubble and the tube wall increases with the 1/3 power of the modified capillary number with increasing area dilatation. Simulations when surface tension is absent indicate that tangential shear generated due to variation of the membrane stress in the transition region that joins the bulk of the flow configuration with the contact region, leads to film thinning via the 5/7 power of the modified capillary number. Variations in the transverse shear of the viscoelastic shell generate large lubrication overpressures in the thin film region between the tube and the shell that are exerted radially on the shell and are conjectured to be responsible for the onset of 3d buckled shapes. The latter are often observed experimentally in similar flow configurations of capsules and are characterized by wrinkles that develop in the azimuthal direction around the shell equator. © 2021, The Author(s), under exclusive licence to Springer Nature B.V.en
dc.language.isoenen
dc.sourceJournal of Engineering Mathematicsen
dc.source.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85109079726&doi=10.1007%2fs10665-021-10144-0&partnerID=40&md5=a0b115578b54cf024d5d2cd7abc338c1
dc.subjectBubbles (in fluids)en
dc.subjectCapillarityen
dc.subjectFilm thicknessen
dc.subjectMesh generationen
dc.subjectMicrofluidicsen
dc.subjectReynolds numberen
dc.subjectShells (structures)en
dc.subjectSurface tensionen
dc.subjectThin filmsen
dc.subjectTubes (components)en
dc.subjectViscoelasticityen
dc.subjectAzimuthal directionen
dc.subjectBending resistanceen
dc.subjectConstant pressure dropsen
dc.subjectDilatational modulusen
dc.subjectDynamic translationen
dc.subjectFlow configurationsen
dc.subjectGalerkin finite elementsen
dc.subjectGeneration techniquesen
dc.subjectShear flowen
dc.subjectSpringer Science and Business Media B.V.en
dc.titleDynamic simulations of an encapsulated microbubble translating in a tube at low capillary and Reynolds numbersen
dc.typejournalArticleen


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