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Constitutive equations for dilute bubble suspensions and rheological behavior in simple shear and uniaxial elongational flow fields

Constitutive equations for dilute bubble suspensions and rheological behavior in simple shear and... A theoretical model is proposed in order to investigate rheological behavior of bubble suspension with large deformation. Theoretical constitutive equations for dilute bubble suspensions are derived by applying a deformation theory of ellipsoidal droplet [1] to a phenomenological suspension theory [2]. The rate of deformation tensor within the bubble and the time evolution of interface tensor are predicted by applying the proposed constitutive equations, which have two free fitting parameters. The transient and steady rheological properties of dilute bubble suspensions are studied for several capillary numbers (Ca) under simple shear flow and uniaxial elongational flow fields. The retraction force of the bubble caused by the interfacial tension increases as bubbles undergo deformation. The transient and steady relative viscosity decreases asCa increases. The normal stress difference (NSD) under the simple shear has the largest value whenCa is around 1 and the ratio of the first NSD to the second NSD has the value of 3/4 for largeCa but 2 for smallCa. In the uniaxial elongational flow, the elongational viscosity is three times as large as the shear viscosity like the Newtonian fluid. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Fibers and Polymers Springer Journals

Constitutive equations for dilute bubble suspensions and rheological behavior in simple shear and uniaxial elongational flow fields

Seo, Dongjin; Youn, Jae Ryoun
Fibers and Polymers , Volume 6 (2): 8 – Jun 1, 2005
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References (32)

Publisher
Springer Journals
Copyright
Copyright © The Korean Fiber Society 2005
ISSN
1229-9197
eISSN
1875-0052
DOI
10.1007/bf02875604
Publisher site
See Article on Publisher Site

Abstract

A theoretical model is proposed in order to investigate rheological behavior of bubble suspension with large deformation. Theoretical constitutive equations for dilute bubble suspensions are derived by applying a deformation theory of ellipsoidal droplet [1] to a phenomenological suspension theory [2]. The rate of deformation tensor within the bubble and the time evolution of interface tensor are predicted by applying the proposed constitutive equations, which have two free fitting parameters. The transient and steady rheological properties of dilute bubble suspensions are studied for several capillary numbers (Ca) under simple shear flow and uniaxial elongational flow fields. The retraction force of the bubble caused by the interfacial tension increases as bubbles undergo deformation. The transient and steady relative viscosity decreases asCa increases. The normal stress difference (NSD) under the simple shear has the largest value whenCa is around 1 and the ratio of the first NSD to the second NSD has the value of 3/4 for largeCa but 2 for smallCa. In the uniaxial elongational flow, the elongational viscosity is three times as large as the shear viscosity like the Newtonian fluid.

Journal

Fibers and Polymers – Springer Journals

Published: Jun 1, 2005

Keywords: Dilute bubble suspension; Bubble deformation; Interface tensor; Capillary number

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