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  • 1
    Electronic Resource
    Electronic Resource
    The conformation change of model polymers in stochastic flow fields: Flow through fixed beds (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 1222-1234 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Simulations of the conformation change of model polymers in various steady, anisotropic Gaussian random flow fields are presented. These flow fields have been chosen because they are models for the flow through porous media and have been predicted to be "stochastic strong flows" according to the criteria developed by Shaqfeh and Koch [J. Fluid Mech. 244, 17 (1992)]. To be specific, beyond a certain Deborah number (based on the sampling time of a velocity fluctuation), large average conformation change in the polymer is predicted. In our simulations, the polymers are modeled as dumbbells, but beyond this restriction, the assumptions of the theory by Shaqfeh and Koch are removed. Many realizations of the Gaussian fields are synthesized spectrally following a modified version of the method developed by Kraichnan [Phys. Fluids 13, 22 (1970)]. Moreover, the ratio of the mean "plug" flow to the amplitude of the fluctuations is varied from mean-dominant to fluctuation-dominant flows. The simulated conformation change shows that, in fact, these flows are "strong" in the sense that the average second moment of the end-to-end distance becomes large (relative to equilibrium) beyond a critical value of the fluctuation Deborah number. Although qualitatively capturing these trends, the theory by Shaqfeh and Koch underestimates the strength of the flows and thus overestimates the critical Deborah number. We present a new theory which includes spring relaxation and Brownian motion in the sampling of a velocity fluctuation (two factors which were neglected in the existing theory), thereby breaking the fore–aft symmetry of the sampling, thus increasing the average polymer stretch. The new theory quantitatively predicts the simulation results. To the authors knowledge, this is the first evidence via direct simulation that these random flows can produce large conformation change in model polymer molecules, even when the mean flow would produce no such change. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869262
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  • 2
    Electronic Resource
    Electronic Resource
    Drop breakup in the flow through fixed beds via stochastic simulation in model Gaussian fields (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 3209-3226 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869437
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    Paper (German National Licenses)
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