We study the electro-osmotic flow through a T-junction of microchannels whose dielectric walls are weakly polarizable. The present global analysis thus extends earlier studies in the literature concerning the local flow of an unbounded electrolyte solution around nearly insulated wedges. The velocity field is obtained via superposition of an irrotational part associated with the equilibrium zeta potential and the induced-charge electro-osmotic flow originating from the interaction of the externally applied electric field and the charge cloud it induces owing to field leakage through the polarizable dielectric channel walls. Along the channel walls the latter component gives rise to fluid velocities converging toward the corner which dominate the flow in its immediate vicinity. Recent experimental observations in the literature regarding the appearance and subsequent expansion of flow reversal and vortices downstream ͑initially͒ and upstream ͑subsequently͒ of the junction, are both rationalized in terms of the growing relative importance of this induced contribution to the global velocity field with increasing intensity of the externally applied electric field.

Generalized Taylor dispersion theory extends the basic long-time, asymptotic scheme of Taylor and Aris greatly beyond the class of rectilinear duct and channel flow dispersion problems originally addressed by them. This feature has rendered it indispensable for studying flow and dispersion phenomena in porous media, chromatographic separation processes, heat transfer in cellular media, sedimentation of non-spherical Brownian particles, and transport of flexible clusters of interacting Brownian particles, to mention just a few examples of the broad class of non-unidirectional transport phenomena encompassed by this scheme. Moreover, generalized Taylor dispersion theory enjoys the attractive feature of conferring a unified paradigmatic structure upon the analysis of such apparently disparate physical problems. For each of the problems thus treated it provides an asymptotic, macroscale description of the original microscale transport process, being based upon a convective-diffusive ‘model’ problem characterized by a set of constant (position- and time-independent) phenomenological coefficients.The present contribution formally substantiates the scheme. This is accomplished by demonstrating that the coarse-grained (macroscale) transport ‘model’ equation leads to a solution which accords asymptotically with the leading-order behaviour of the comparable solution of the exact (microscale) convective–diffusive problem underlying the transport process. It is also shown, contrary to current belief, that no systematic improvement in the asymptotic order of approximation is possible through the incorporation of higher-order gradient terms into the model constitutive equation for the coarse-grained flux. Moreover, the inherent difference between the present rigorous asymptotic scheme and the dispersion models resulting from Gill–Subramanian moment-gradient expansions is illuminated, thereby conclusively resolving a long-standing puzzle in longitudinal dispersion theory.

We calculate the average swimming velocity and dispersion rate characterizing the transport of swimming gyrotactic micro-organisms suspended in homogeneous (simple) shear. These are requisite effective phenomenological coefficients for the macroscale continuum modelling of bioconvection and related collective-dynamics phenomena. The swimming cells are modelled as rigid axisymmetric dipolar particles subject to stochastic Brownian rotations. Calculations are effected via application of the generalized Taylor dispersion scheme. Attention is focused on finite (as opposed to weak) shear. Results indicate that the largest transverse average swimming velocities (essential to gyrotactic focusing) appear shortly after transition from the ‘tumbling’ mode of motion to cells swimming in the equilibrium direction. At sufficiently large shear rates, dispersivity is not monotonically decreasing with external-field intensity. Exceptional dispersion rates which are unique to non-spherical cells appear in the ‘intermediate domain’ of external fields. These are rationalized in terms of the corresponding deterministic problem (i.e. in the absence of diffusion) when cell rotary motion is governed by the simultaneous coexistence of multiple stable attractors.

We study the induced-charge electro-osmotic flow around a stationary polarizable dielectric spheroid in the presence of a uniform arbitrarily oriented external electric field. A Robin-type condition connecting the respective electric potentials within the dielectric solid and the bulk electro-neutral solution is highlighted in formulating the macroscale description for the limit of thin electric double layers and low potentials. The results illustrate symmetry breaking phenomena in the ensuing flow and demonstrate qualitative differences associated with variations of the dielectric constant. We briefly discuss the potential impact of these differences on the rotation of freely suspended spheroids.The standard description of electro-osmotic flows in the presence of thin electric double layers ͑EDL's͒ utilizes a macroscale approach which avoids the need to resolve the details of the double layer. This, in turn, is effectively represented by appropriate boundary conditions imposed on the electric potential within the bulk electro-neutral fluid. Incorporating the solution of the resulting electrostatic problem with a prescribed electrokinetic surface charge density or, equivalently, a prescribed zeta potential into the HelmholtzSmoluchowski relation 1 yields the fluid slip velocity, thereby providing the appropriate boundary condition for the macroscopic hydrodynamic problem. For a uniform prescribed zeta potential the resulting flow is irrotational. At polarizable surfaces where the external electric field acts on the diffuse ionic charge cloud induced by the field itself, the interaction gives rise to a slip velocity which is nonlinear in the external field. The resulting induced-charge electro-osmosis ͑ICEO, Ref. 2͒ is thus no longer irrotational. This mechanism has been studied extensively for ideally polarizable ͑i.e., conducting͒ solids 2-6 and to a lesser extent for dielectrics. [7][8][9] The present contribution aims at illustrating the combined effects of nonisotropic body shapes and nonideal electrical material properties on the ICEO around a dielectric solid immersed in an unbounded electrolyte solution in the presence of a uniform external electric field. Recent analyses of induced-charge electro-osmosis and electrophoresis ͑ICEP͒ have focused on the hydrodynamic interaction 10 and the translational and rotational motion 11 of rod-like ideally polarizable ͑conducting͒ particles modeled as slender prolate spheroids. The effects of body geometry on the resulting flows have explicitly been presented 6 for nearly symmetric bodies. It has been demonstrated that slight deviations from a perfect ͑spherical or cylindrical͒ symmetry are sufficient for the appearance of symmetry-breaking phenomena. We examine here these features for dielectric prolate spheroids potentially spanning the entire spectrum from spherical through slender rod-like shapes. Spheroidal shapes are common in colloidal science. Thus, they are often used as models in the context of manipulation of biological cells as well as in the electrodynami...

The stability of a capillary jet of an ideal liquid with a linear variation of axial velocity is investigated. Because of the time dependence in the basic extensional flow the evolution of surface perturbations in the jet is an initial-value problem instead of an eigenvalue one (as in the case of non-stretching jets). The amplification of any given peturbation is found to depend on the elative effects of surface tension and intertia terms associated with the extensional flow as well as on the initial wavenumber and the specific time when the perturbation is introduced in the flow field. The simulation of a shaped-charge jet by the present model is discussed. The esults obtained are found to give a good description of the essential features of the breakup phenomenon of such jets.