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L. Mitnik, C. Heller, J. Prost, and J-L. Viovy, Science 267, 219 (1995).SCIEAS
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Mitnik, L.1
Heller, C.2
Prost, J.3
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85037209890
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thèse de l’Université de Paris 6 (1995)
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L. Mitnik, thèse de l’Université de Paris 6 (1995).
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Mitnik, L.1
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H. Isambert, A. Ajdari, J-L. Viovy, and J. Prost, Phys. Rev. Lett. 78, 971 (1997).PRLTAO
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Isambert, H.1
Ajdari, A.2
Prost, J.3
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Y. Hu, J. L. Glass, A. E. Griffith, and S. Fraden, J. Chem. Phys. 100, 4674 (1994).JCPSA6
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Hu, Y.1
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85037213965
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82, 1424 (1978).
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85037229836
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See, e.g., R. J. Hunter, Foundations of Colloid Science, Vol. 2 (Clarendon Press, Oxford, 1989); or W. B. Russel, D. A. Saville, and W. R. Schowalter, Colloidal Dispersions (Cambridge University Press, Cambridge, 1989)
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See, e.g., R. J. Hunter, Foundations of Colloid Science, Vol. 2 (Clarendon Press, Oxford, 1989);or W. B. Russel, D. A. Saville, and W. R. Schowalter, Colloidal Dispersions (Cambridge University Press, Cambridge, 1989).
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13
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85037232818
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Although the present work merely applies for colloidal dispersions of high ionic strength, i.e., (Formula presented) the electrohydrodynamic effects we predict become enhanced at lower ionic strength, that is as (Formula presented) Furthermore this suggests that the usual assumption of small perturbations beyond the Debye layers might well be jeopardized in many practical situations as, e.g., for the dielectric constant measurements of colloidal dispersions
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Although the present work merely applies for colloidal dispersions of high ionic strength, i.e., (Formula presented) the electrohydrodynamic effects we predict become enhanced at lower ionic strength, that is as (Formula presented) Furthermore this suggests that the usual assumption of small perturbations beyond the Debye layers might well be jeopardized in many practical situations as, e.g., for the dielectric constant measurements of colloidal dispersions.
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14
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85037221146
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fact different diffusion constants of the coions and counterions (i.e., (Formula presented)) do not change the main conclusions of our paper as one can show that the leading part of the out-of-equilibrium charge density in the solution surrounding the macroions, (Formula presented) does not depend upon these diffusion constants. Namely, (Formula presented) under the strong electric field condition, (Formula presented)
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In fact different diffusion constants of the coions and counterions (i.e., (Formula presented)) do not change the main conclusions of our paper as one can show that the leading part of the out-of-equilibrium charge density in the solution surrounding the macroions, (Formula presented) does not depend upon these diffusion constants. Namely, (Formula presented) under the strong electric field condition, (Formula presented)
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85037180193
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is related to the a priori assumption of stationarity, which eliminates the transient regimes and therefore prevents detection of the dynamical instabilities of the ionic distributions under the application of any finite electric field
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is related to the a priori assumption of stationarity, which eliminates the transient regimes and therefore prevents detection of the dynamical instabilities of the ionic distributions under the application of any finite electric field.
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85037194452
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This can be shown, e.g., using the same formalism developed in Sec. II to describe the salt profile in the frame of reference moving at the velocity (Formula presented) With the hydrodynamic flow described in this “transported” frame of reference—i.e., (Formula presented)—the linearized Navier-Stokes equation becomes (see Appendix A for justification of the term (Formula presented)) (Formula presented) which simplifies at low frequency, (Formula presented) to the usual Stokes equation if the vorticity diffuses faster than the electrophoretic motion over the typical width, (Formula presented) of the macroion aggregates, i.e., (Formula presented)
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This can be shown, e.g., using the same formalism developed in Sec. II to describe the salt profile in the frame of reference moving at the velocity (Formula presented) With the hydrodynamic flow described in this “transported” frame of reference—i.e., (Formula presented)—the linearized Navier-Stokes equation becomes (see Appendix A for justification of the term (Formula presented)) (Formula presented) which simplifies at low frequency, (Formula presented) to the usual Stokes equation if the vorticity diffuses faster than the electrophoretic motion over the typical width, (Formula presented) of the macroion aggregates, i.e., (Formula presented)
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85037214168
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This result implies in fact that the double inequality (Formula presented) holds so that the nonlinear corrections of order (Formula presented) are indeed negligible in Eqs. (2.15), (3.10), and (3.11) as compared to those of order (Formula presented) in Eqs. (3.9), (3.10), and (3.11)
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This result implies in fact that the double inequality (Formula presented) holds so that the nonlinear corrections of order (Formula presented) are indeed negligible in Eqs. (2.15), (3.10), and (3.11) as compared to those of order (Formula presented) in Eqs. (3.9), (3.10), and (3.11).
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85037225782
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M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett.
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Isambert, H.1
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85037193729
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Scale Invariance, Interfaces, and Non-Equilibrium Dynamics, edited by A. McKane, M. Droz, J. Vannimenus, and D. Wolf (Plenum Press, New York, 1995); and A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995)
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Scale Invariance, Interfaces, and Non-Equilibrium Dynamics, edited by A. McKane, M. Droz, J. Vannimenus, and D. Wolf (Plenum Press, New York, 1995); andA.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995).
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85037183137
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12, 1998 (1971).
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(1971)
, vol.12
, pp. 1998
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27
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85037178440
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cannot lead to the relevance of their nonlinear terms at (Formula presented) with a conservative noise source obeying (Formula presented) This is the reason why the conservative random noise arising as a result of the derivation of the Navier-Stokes equation from the microscopic equations of motion can safely be neglected in hydrodynamic calculations above two dimensions In contrast, the relevant nonlinear coupling between the (macroion) density fluctuations and the associated electrohydrodynamic flow that we have exhibited in this conservative system, is nonlocal (see, e.g., (Formula presented) in Appendix B)
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In contrast, the relevant nonlinear coupling between the (macroion) density fluctuations and the associated electrohydrodynamic flow that we have exhibited in this conservative system, is nonlocal (see, e.g., (Formula presented) in Appendix B).
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85037177783
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Although we can imagine other more traditional instabilities to occur from the purely deterministic dynamical equations if we consider, for instance, the possibility of variation of the electrophoretic mobilities (e.g., (Formula presented)), such mechanisms cannot explain, however, the experimentally observed differences between hydrodynamically screened and unscreened length scales as they do not involve hydrodynamics
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Although we can imagine other more traditional instabilities to occur from the purely deterministic dynamical equations if we consider, for instance, the possibility of variation of the electrophoretic mobilities (e.g., (Formula presented)), such mechanisms cannot explain, however, the experimentally observed differences between hydrodynamically screened and unscreened length scales as they do not involve hydrodynamics.
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addition to the already mentioned changes of stochastic properties of the internal noise under dynamic rescaling, a quantitative study should also allow the ab initio possibility of spatially anisotropic scalings in reference to the observed dynamical patterns with broken symmetry. Such a requirement leads to the unfortunate consequence of multiplying the number of coupling parameters that transform differently under rescaling, and seems to prevent further analytical progress with reasonable calculation work
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In addition to the already mentioned changes of stochastic properties of the internal noise under dynamic rescaling, a quantitative study should also allow the ab initio possibility of spatially anisotropic scalings in reference to the observed dynamical patterns with broken symmetry. Such a requirement leads to the unfortunate consequence of multiplying the number of coupling parameters that transform differently under rescaling, and seems to prevent further analytical progress with reasonable calculation work.
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0003474751
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Cambridge University Press, Cambridge
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W. H. Press, S. A. Teukolsky, W. T. Veterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge University Press, Cambridge, 1992).
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Numerical Recipes
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Press, W.H.1
Teukolsky, S.A.2
Veterling, W.T.3
Flannery, B.P.4
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85037179166
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M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett
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M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. 6.
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