Area tensors for modeling microstructure during laminar liquid-liquid mixing

Fluid-fluid mixtures often possess a fine structure, or morphology, whose length scale is much smaller than the length scale over which the flow field and morphology vary. We define a microstructural variable called the area tensor, which describes the local morphology of such mixtures through volum...

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Bibliographic Details
Published in:International journal of multiphase flow 1999-02, Vol.25 (1), p.35-61
Main Authors: Wetzel, E.D., Tucker, C.L.
Format: Article
Language:English
Subjects:
Approximation theory
area tensor
closure approximation
Cross-disciplinary physics: materials science
rheology
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Heterogeneous liquids: suspensions, dispersions, emulsions, pastes, slurries, foams, block copolymers, etc
Hydrodynamic stability
interface tensor
Material form
Microstructure
microstructured fluids
Mixing
Morphological instability
phase changes
Morphology
Physics
polymer blend
Polymer blends
Rheology
Surface tension
Viscosity of liquids
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Summary:Fluid-fluid mixtures often possess a fine structure, or morphology, whose length scale is much smaller than the length scale over which the flow field and morphology vary. We define a microstructural variable called the area tensor, which describes the local morphology of such mixtures through volume-averaged size, shape, and orientation characteristics. The area tensor is equivalent to the interface tensor of the rheological model, and is closely related to the general microstructural tensors. The evolution equation for the area tensor during laminar mixing is derived for the case of equal component viscosities and negligible surface tension. Solution of this evolution equation requires a closure approximation for estimating higher-order microstructural statistics. A closure approximation is generated based on exact area tensor relations for ellipsoidal shapes, and is shown to provide highly accurate evolutions of the area tensor. Area tensor histories are calculated in homogeneous elongational and shearing flows, as well as in temporally and spatially varying flows. The results are shown to be consistent with well-known mixing principles.
ISSN:0301-9322
1879-3533
DOI:10.1016/S0301-9322(98)00013-5