Stokes Flow in a Microchannel with Superhydrophobic Walls

Necessary and Sufficient Conditions for the Separability and the R-Separability of the Irrotational Stokes Equation and Applications

“…The "if" part: If Stokes stream equation separates variables, we will prove that the metric coefficients are given by (9) and (10).…”

“…3 Ω ⊆  is the fluid domain, r is the position vector and µ is the shear viscosity. This system of equations has been firstly used in spherical geometry for solving the flow: of the translation of a sphere [2], of two spheres in a viscous fluid [3], past a porous sphere with Brinkman's model [4], inside a porous spherical shell [5], around spherical particles moving along a line perpendicular to a plane wall [6], past a sphere with slip-stick boundary conditions [7], of a rising bubble near a free surface [8], in a plane microchannel in the case that both walls have super hydrophobic surfaces [9] etc.…”

Pulsating Flow of a Viscous Fluid over a Cavity Containing a Compressible Gas Bubble

“…Experimental observations of the flow on the cavity scale show that usually the bubble surface is curved, and the cavity can be only partially filled with gas, i.e., the position of the meniscus may not coincide with the upper corner points of the microcavity. These factors were taken into account in the studies of a steady flow over cavities with gas bubbles in [6][7][8], where an original version of the boundary integral equation method for the Stokes operator was developed, taking into account the alternating boundary conditions (no-slip/zero friction) on the boundaries of the computational domain. Both the shape of the meniscus and its location relative to the cavity corner points affect very substantially the parameters characterizing the average fluid velocity slip and the friction reduction.…”

“…For solving Stokes equations (2.2) at a given instantaneous fluid velocity profile and a meniscus position, we use the boundary integral equation method [16]. To be more specific, we use a variant of an algorithm of this method developed earlier in [6][7][8]. This method has substantial advantages as compared to finite-difference methods of solving the Stokes equations, since it makes it possible to reduce the original problem by one dimension and to avoid the difficulties associated with the finite-difference approximation of infinite derivatives of the parameters near the points of matching the no-slip boundary conditions on the solid wall and zero shear stress on the bubble surface.…”

Исследование Гидродинамического Сопротивления Щелевого Микроканала С Текстурированной Стенкой

“…Также в настоящее время продолжают разрабатываться различные микрофлюидные приборы: микромасштабные теплофизические устройства, био-МЭМС и " лаборатории на чипе" [2,3], использующие ультрагидрофобные свойства. Поэтому в последние годы проявляется огромный интерес к исследованию высоко-и супергидрофобных микротекстурированных поверхностей как за рубежом [1][2][3][4][5], так и в России [6][7][8][9][10].…”