Heterogeneities streamlines

Figure 7. Eleotroosmotic streamlines at the midplane of a 50pm T-shaped micromixer for the a) homogeneous case with = -42 mV, b) heterogeneous case with six offset patches on the left and right channel walls. All heterogeneous patches are represented by the crosshatched regions and have a = + 42mV. The applied voltage is (baoD = 500 V/cm.

When water flows through the porous medium, the deviation of the local scale advection velocities around the mean advection velocity v induces hydrodynamic dispersion. At the pore scale, streamline density increases from the pore wall to the pore center. For real and irregularly shaped soil pores however, this within pore variability will be more pronounced, as streamline densities change between pore bodies and pore necks. The heterogeneous pore size distribution with larger flow velocities in larger pores leads to an important additional variability of velocities (Fig. 6). 

Lubarskaya Y, Houde D, Woodard J, et al. (2005). Analysis of recombinant monoclonal antibody isoforms by electrospray ionization mass spectrometry as a strategy for streamlining characterization of recombinant monoclonal antibody charge heterogeneity. Anal. Biochem. Available sciencedirect.com. 

Fig. 3 Sequences of a microvalve which is operated by induced-charge electrokinetics using a heterogeneous particle inside it. The flow pattern and vortices are shown by plotted streamlines. The normalized vectors show the direction of the fluid. The diameter of the heterogeneous particle and the microchamber are 20 and 40 pm, respectively. The height of the microchamber is 40 pm. The results are presented at the x-z plane crossing the middle of the 3D microvalve at different time steps. The zeta potential on the nonconducting hemisphere of the heterogeneous particle is set to —50 mV, while the zeta potentials on the nonconducting microchannel and microchamber walls are set to —15 mV...

Fig. 1 Electroosmotic flow near the double layer region for (a) a homogeneous surface (C = -ICol)and(b) a homogeneous surface with a heterogeneous patch (C = + ICoD- Over the heterogeneous patch, the excess cations are attracted to the positive electrode resulting in an electroosmotic flow in the opposite direction to that over the homogeneous regions with an excess anion concentration. Arrows represent streamlines and 1/k refers to the characteristic thickness of the electrical double layer...

Fig. 6 Electroosmotic flow streamlines over a patchwise heterogeneous surface pattern with Oj,omo =...

The three-dimensional streamlines in a microchannel when a nonconducting particle and a heterogeneous particle are suspended in the microchannel are shown (Fig. 4). The fluid follows the boundaries of the nonconducting sphere smoothly and passes this particle without being disturbed (Fig. 4a). Since the local electric... 

Induced-Charge Electrokinetic Motion of Particle in a MicroChannel, Fig. 4 3D streamlines in a straight microchannel with a (a) nonconducting particle and (b) heterogeneous particle suspended in the middle of this microchannel. Vortices are induced around the conducting hemisphere of the heterogeneous particle. 

At low degrees of surface heterogeneity (streamline pattern shown in Fig. 6a was obtained. As can be seen a net counter-clockwise flow perpendicular to the applied electric field is present at the first transition plane (i. e. at the initial discontinuity in the heterogeneous surface pattern) and a clockwise flow at the second transition plane. This flow circulation is a pressure induced effect that arises as a result of the transition from the higher local fluid velocity (particularly in the double layer) over the homogeneous surface on the right hand side at the entrance, to the left hand side after the first transition plane (and vice versa at the second transition plane). To satisfy continuity then there must be a net flow from... 

We discuss streamline traeing and volume flow rate computations in planar flow liquids and gases, however, are both allowed, and a heterogeneous, anisotropic formation is permitted. Let us consider the Darcy velocity... 

As a second example, calculations were repeated with separations between dark streaks doubled. Because the overall averaged permeabilities are decreased relative to the values just considered, lower volume flow rates should result we consistently obtained, 0.62 as opposed to 0.69, 0.67 versus 0.80, 0.70 versus 0.88, and 0.67 versus 0.87, but streamline convergence was again observed. Again, the cumulative effects of locally weak reservoir heterogeneities and nonuniformities turned out to be important in changing streamline orientation. 

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