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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    The journal of membrane biology 54 (1980), S. 89-102 
    ISSN: 1432-1424
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Summary The standard one-dimensional model of the unstirred layer is applied in a re-examination of the experimental results of Wright, Smulders and Tormey (Wright, E.M., Smulders, A.P., Tormey, J. McD., 1972,J. Membrane Biol. 7:198) who reported large transients in the osmotic flux of water from the serosal to the mucosal side of rabbit gallbladder epithelium. They initiated osmosis by the addition of sucrose to the mucosal bathing solution (initially, approximately 300mOsm NaCl) and observed that the initial flux was more than ten times its eventual steady-state value; they interpreted this as a consequence of the piling-up of NaCl in the unstirred tissue layer on the serosal side of the epithelium. The present analysis (both steady-state and unsteady) shows that if measured values of layer thickness δ are used, together with reasonable values of the reduced diffusivity of NaCl in the tissue and of the fraction of tissue available for water flow, then one would predict a discrepancy of only about 10%, not tenfold, between the initial and final values of the flux. Thus the standard model is inconsistent with the observations. Furthermore, Wright et al's results cannot be used to infer that the osmotic permeability of epithelial cell membranes is much larger than steadystate measurements on whole epithelia would indicate. Mucosal-to-serosal flow is also analyzed, and in this case a considerably greater osmotic permeability is predicted; this result is consistent with the observed changes in structure of the lateral intercellular spaces when the direction of flow is reversed.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Fluid Mechanics 24 (1992), S. 313-358 
    ISSN: 0066-4189
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Fluid Mechanics 9 (1977), S. 229-274 
    ISSN: 0066-4189
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 199-208 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: It is known that a propagating wave train can be generated in unsteady flow in a nonuniform channel. A small amplitude inviscid theory is derived in which the forced displacement of the streamlines is governed by a linearized Korteweg–de Vries equation with time-dependent coefficients. Solutions of this equation for a channel with an asymmetric expansion show a standing wave with a propagating wave front, the amplitude of which is modified by a forced oscillation and by wave packets which travel downstream at a velocity greater than the group velocity for the main wave. An analytical model, based on the assumption of a standing wave, successfully predicts the wavelength of the main wave, the magnitude of the forced oscillation, and the velocity of the wave packets. Predictions from the theory are also compared with numerical solutions of the full Navier–Stokes equations for flow in nonuniform channels; there is agreement on some but not all properties of the wave.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 404 (1983), S. 0 
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 57 (1995), S. 299-344 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract When a suspension of bacterial cells of the speciesBacillus subtilis is placed in a chamber with its upper surface open to the atmosphere complex bioconvection patterns are observed. These arise because the cells: (1) are denser than water; and (2) usually swim upwards, so that the density of an initially uniform suspension becomes greater at the top than the bottom. When the vertical density gradient becomes large enough, an overturning instability occurs which ultimately evolves into the observed patterns. The reason that the cells swim upwards is that they are aerotactic, i.e. they swim up gradients of oxygen, and they consume oxygen. These properties are incorporated in conservation equations for the cell (N) and oxygen (C) concentrations, and these are solved in the pre-instability phase of development whenN andC depend only on the vertical coordinate and time. Numerical results are obtained for both shallow- and deep-layer chambers, which are intrinsically different and require different mathematical and numerical treatments. It is found that, for both shallow and deep chambers, a thin boundary layer, densely packed with cells, forms near the surface. Beneath this layer the suspension becomes severely depleted of cells. Furthermore, in the deep chamber cases, a discontinuity in the cell concentration arises between this cell-depleted region and a cell-rich region further below, where no significant oxygen concentration gradients develop before the oxygen is fully consumed. The results obtained from the model are in good qualitative agreement with the experimental observations.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 305 (1983), S. 692-695 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] The lOx 10 mm channel was adapted from one used in an earlier study on impulsively-started flow past a fixed constriction3. In the present study the constriction is a thick rubber membrane which is pushed from behind by a sinusoidally oscillating 100 x 100 mm piston; the retracted position of the ...
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 36 (1998), S. 269-298 
    ISSN: 1432-1416
    Keywords: Key words: Suspensions ; Fokker-Planck Equation ; Dipolar particles ; Orientation distributions ; Bioconvection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  Analytic approximations are obtained to solutions of the steady Fokker-Planck equation describing the probability density functions for the orientation of dipolar particles in a steady, low-Reynolds-number shear flow and a uniform external field. Exact computer algebra is used to solve the equation in terms of a truncated spherical harmonic expansion. It is demonstrated that very low orders of approximation are required for spheres but that spheroids introduce resolution problems in certain flow regimes. Moments of the orientation probability density function are derived and applications to swimming cells in bioconvection are discussed. A separate asymptotic expansion is performed for the case in which spherical particles are in a flow with high vorticity, and the results are compared with the truncated spherical harmonic expansion. Agreement between the two methods is excellent.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 62 (2000), S. 775-791 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The biased random walk undergone by chemotactic bacteria such as Escherichia coli will be influenced at the microscopic level by flow in the ambient medium. In this paper, we model swimming bacteria being advected and rotated by a simple shear flow. Under certain scaling assumptions, we obtain an advection—diffusion equation for cell density, when the chemotactic response is small, which shows a coupling between the rotation and chemotaxis. We also present an alternative method for calculating the chemotactic flux in an unbounded region which is valid for more general chemotactic responses.
    Type of Medium: Electronic Resource
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  • 10
    Publication Date: 2008-02-27
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
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