Drag force on a sphere moving towards an anisotropic super-hydrophobic planeстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sphere and a
textured superhydrophobic plane that contains trapped gas bubbles. A superhydrophobic wall is characterized
by parameters L (texture characteristic length), b1 and b2 (local slip lengths at solid and gas areas), and φ1 and
φ2 (fractions of solid and gas areas). Hydrodynamic properties of the plane are fully expressed in terms of the
effective slip-length tensor with eigenvalues that depend on texture parameters and H (local separation). The
effect of effective slip is predicted to decrease the force as compared with what is expected for two hydrophilic
surfaces and described by the Taylor equation. The presence of additional length scales, L, b1, and b2, implies
that a film drainage can be much richer than in the case of a sphere moving toward a hydrophilic plane. For a
large (compared to L) gap the reduction of the force is small, and for all textures the force is similar to expected
when a sphere is moving toward a smooth hydrophilic plane that is shifted down from the superhydrophobic
wall. The value of this shift is equal to the average of the eigenvalues of the slip-length tensor. By analyzing
striped superhydrophobic surfaces, we then compute the correction to the Taylor equation for an arbitrary gap.
We show that at a thinner gap the force reduction becomes more pronounced, and that it depends strongly on the
fraction of the gas area and local slip lengths. For small separations we derive an exact equation, which relates
a correction for effective slip to texture parameters. Our analysis provides a framework for interpreting recent
force measurements in the presence of a superhydrophobic surface.