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A dynamic density functional theory for particles in a flowing solvent
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Image of FIG. 1.
FIG. 1.

(Color) Cross section of the flow field given in Eq. (1) in a plane parallel to the direction of motion around (a) a small spherical colloid and (b) a big one (full circles, radius ). The dashed circles of radius mark the points of closest approach of solute’s centers (point in the center of open circles) to the colloid. The solute’s diameter in its mutual interaction is and, for nonadditive mixtures, not necessarily equal to its diameter (indicated by the dotted circle) in the interaction with the colloid. The component of the flow field normal to the dashed circle is larger for the small colloid (a) than for the large colloid (b). and are the same in both figures.

Image of FIG. 2.
FIG. 2.

Contour plots of the density of ideal polymers for a flow velocity . The white circle at the origin is the colloidal particle with radius , the black circle is the annulus of thickness , and outer diameter which is unaccessible to the polymer centers due to the hard-wall interaction, see Fig. 1. corresponds to a uniform flow (i.e., to ). The maximum density in front of the colloid is . corresponds to . The bow-wave effect is reduced drastically. The maximum density in front of the colloid is .

Image of FIG. 3.
FIG. 3.

Density of ideal polymers at the point , , i.e., right in front of the forbidden zone around the colloid. (a) shows as a function of the colloid size for and . (b) shows as a function of for different values of .

Image of FIG. 4.
FIG. 4.

Plots of defined in Eq. (25) as provided by the numerical solution of dDFT (lines) and as measured in BD simulations (symbols). (a) corresponds to a velocity and (b) to . In each plot the results for both uniform flow and Stokes flow are presented.

Image of FIG. 5.
FIG. 5.

The plot represents , see Eq. (26), in a Stokes flow with upstream (at , triangles up) and downstream (at triangles down) of the colloid, as measured in BD simulations. The inset shows the results for a smaller simulation box.


Generic image for table
Table I.

Mean force exerted by the polymers measured in the BD simulations for different types of flow ( for the uniform flow, and for the Stokes flow), compared to the force exerted by ideal polymers and to the Stokes friction of the colloid. The forces are given in units of .

Generic image for table
Table II.

Mean and variance of the force exerted by the polymers in a Stokes flow measured in BD simulations of different boxsizes (see Sec. III B). The forces are given in units of .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A dynamic density functional theory for particles in a flowing solvent