ISSN:
1089-7666
Quelle:
AIP Digital Archive
Thema:
Physik
Notizen:
Shaqfeh and Koch have shown that the flow through a dilute disordered fixed bed of fibers produces large polymer conformation change beyond a certain critical flow rate [J. Fluid Mech. 244, 17 (1992)]. We now examine the effect of this flow on the shape and breakup of viscous drops. Because the flow through a dilute fixed bed is equivalent to a certain anisotropic Gaussian flow field, we follow our previous paper and reproduce a model of the flow through a spectral expansion where the wave number vectors are chosen from statistical distributions which ensure that the desired velocity field will be realized [Phys. Fluids 9, 1222 (1997)]. We examine the dynamics of model drop shapes, averaged over the Gaussian statistics of the flow field, by synthesizing a large number of flow realizations. The drop surface is modeled using the first, second, and third order small deformation theories which can accurately predict critical conditions in classical strong flows. While the first order model yields a bounded average drop shape for all flow conditions, the second and third order models demonstrate that the flow through fixed beds is indeed "strong" since beyond a certain value of the pore-size capillary number, Ca∼0.15, large average drop deformation occurs and the average drop shape becomes unbounded ("drop breakup"). This critical condition is determined for various viscosity ratios and fixed bed particle volume fractions. Similar to a simple shear flow, we find that there is a critical viscosity ratio, χ∼2.5, beyond which breakup is not observed in the fixed bed for any Ca. In addition, the critical condition is shown to depend heavily on the transient nature of the flow in the bed since approximately half of the flow fields in which drop breakup occurs would not break an initially spherical drop at any Ca if they were steady. For supercritical capillary numbers, we define conditions under which the unbounded drop shapes fragment into smaller droplets and we examine the drop breakup rates as a percentage of the drop population. © 1997 American Institute of Physics.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1063/1.869437
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