Stokes flow over a cavity on a superhydrophobic surface containing a gas bubble

Агеев, А. И.; Осипцов, А. Н.

doi:10.1134/s0015462815060046

Cited by 9 publications

(6 citation statements)

References 22 publications

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“…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.…”

Section: Doi: 101134/s001546282106001xmentioning

confidence: 99%

“…At each instant of time, the pressure inside the bubble is assumed to be uniform over the space. The pressure variation along the phase interface in the cavity, attributable to the fluid motion, is much smaller than the difference of the static pressures in the fluid over the cavity and in the gas bubble [6]; this is why, as in statics, the bubble surface can be approximated by a circle arc. The dimensional radius of curvature of the bubble surface meniscus r* is determined by the angle of wetting at the points of touching the meniscus with the cavity walls.…”

Section: Flow On the Scale Of A Cavitymentioning

confidence: 99%

“…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.…”

Section: E P T K H P a Tmentioning

confidence: 99%

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

Агеев

Осипцов

2021

Fluid Dyn

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A two-dimensional pulsating flow of a viscous fluid in a plane channel whose wall has rectangular microcavities partially or completely filled with a compressible gas is investigated. This problem formulation can clarify the friction reduction mechanism in a laminar sublayer of a turbulent viscous boundary layer flow over a textured stripped superhydrophobic surface containing periodically arranged rectangular micro-cavities filled with gas. It is assumed that the dimensions of the cavities are much smaller than the channel thickness. On the macroscale, the problem of one-dimensional unsteady viscous flow in a plane channel with no-slip conditions on the walls and a harmonic variation of the pressure difference is solved. The solution obtained in this way is used for formulating non-stationary in time and periodic in space boundary conditions for the flow on the scale of a chosen cavity (microscale), with the instantaneous volume of the gas bubble in the cavity depending on the instantaneous pressure over the cavity. The flow on the microscale near a cavity with a gas bubble occurs in the Stokes regime. The numerical solution is obtained using an original version of the boundary element method. A parametric numerical study of the flow field in a pulsating shear flow over a cavity with a compressible gas bubble is performed. The averaged parameters characterizing the effective ‘velocity slip’ of viscous fluid and the friction reduction in a pulsating flow over a stripped superhydrophobic surface are calculated.

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Section: Doi: 101134/s001546282106001xmentioning

confidence: 99%

Section: Flow On the Scale Of A Cavitymentioning

confidence: 99%

Section: E P T K H P a Tmentioning

confidence: 99%

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

Агеев

Осипцов

2021

Fluid Dyn

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“…An original numerical procedure based on the BEM was developed to solve the boundary integral equations by the collocation method. Some aspects of the numerical procedure developed for the 2D problem of the flow normal to the stripes can be found in [4]. A similar technique was used to solve the integral equation for the 1D problem of the flow along the stripes.…”

mentioning

confidence: 99%

“…We calculated the flow patterns over the considered striped texture and performed a parametric numerical study of the dimensionless (scaled to L) values of b p,l , which are the principal values of the effective (averaged) slip length tensor of the striped SHS [1]. averaged Navier slip boundary condition [4]. We studied the averaged slip length as the function of geometrical parameters of the surface texture: the gaseous phase area d/L, the dimensionless curvature radius R/c, and the shift s = δ/L of the phase interface into the cavity.…”

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Slow viscous flow near a superhydrophobic surface with trapped gas bubbles

Агеев

Голубкина

Осипцов

2017

Proc Appl Math and Mech

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The Boundary Element Method (BEM) is used to solve the problem of Stokes flow of a viscous fluid over a periodic striped texture of a superhydrophobic surface (SHS), partially filled with frictionless gas bubbles. The shape of the bubble surfaces and the position of the meniscus pinning points relative to the cavity walls are taken into account in the study. Two kinds of flows important for practical applications are considered: a pressure-driven flow in a thin channel with a bottom superhydrophobic wall and a shear-driven flow over a periodic texture. We study the flow pattern in the fluid over a single cavity containing a bubble with a curved phase interface shifted into the cavity. A parametric numerical study of the averaged slip length of the SHS is performed as a function of the geometric parameters of the texture. It is shown that the curvature of the phase interface and/or its shift into the cavity both result in the decrease in the average slip length. It is demonstrated that the BEM can be an efficient tool for studying Stokes flows over textured superhydrophobic surfaces with different geometries of microcavities and phase interfaces. We consider a steady-state Stokes flow of a viscous fluid over a periodic striped texture (with period length L) of a superhydrophobic surface (SHS) containing rectangular microcavities (of width d) partially filled with gas bubbles on the surface of which the shear stress is neglected. The gas bubbles are stably trapped in the cavities by the surface tension force. For a Stokes flow regime, the shape of the gas bubbles is the same as in statics and can be approximated by a circle arc with the curvature radius determined by the static angle of wettability at the pinning points of the meniscus on the cavity walls. The dimensional position of the pinning points δ is assumed to be known. We consider the most general case when the fluid velocity vector is directed at an arbitrary angle to the stripes of the SHS. Due to the linearity of the Stokes equations for the 3D flow, the problem of the flow over a striped SHS is split in two problems corresponding to the flows perpendicular to the stripes (2D problem) and along the stripes (1D problem). These flow directions correspond to the principal directions of the slip-length tensor of the striped SHS [1]. Let L be the length scale of the problem, and U and µU/L be the velocity and pressure scales, respectively. In dimensionless form, the equations of fluid motion in the principal directions over a single cavity of a periodic striped SHS are written as follows:Here, u p = (u p , v p ) is the velocity field for the flow normal to the stripes, u l is the fluid velocity along the stripes, p is the dimensionless pressure in the fluid; j = 1 and 0 in the cases of a pressure-driven flow and a shear-driven flow, respectively. We specify the following boundary conditions at all points of the boundary of the 2D flow domain containing phase interface. On the solid walls, the no-slip condition for the velocity is specified; the upper bounda...

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Application of boundary element method to Stokes flows over a striped superhydrophobic surface with trapped gas bubbles

2018

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A slow steady flow of a viscous fluid over a superhydrophobic surface with a periodic striped system of 2D rectangular microcavities is considered. The microcavities contain small gas bubbles on the curved surface of which the shear stress vanishes. The general case is analyzed when the bubble occupies only a part of the cavity, and the flow velocity far from the surface is directed at an arbitrary angle to the cavity edge. Due to the linearity of the Stokes flow problem, the solution is split into two parts, corresponding to the flows perpendicular and along the cavities. Two variants of a boundary element method are developed and used to construct numerical solutions on the scale of a single cavity with periodic boundary conditions. By averaging these solutions, the average slip velocity and the slip length tensor components are calculated over a wide range of variation of governing parameters for the cases of a shear-driven flow and a pressure-driven channel flow. For a sufficiently high pressure drop in a microchannel of finite length, the variation of the bubble surface shift into the cavities induced by the streamwise pressure variation is estimated from numerical calculations.

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Stokes flow over a cavity on a superhydrophobic surface containing a gas bubble

Cited by 9 publications

References 22 publications

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

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

Slow viscous flow near a superhydrophobic surface with trapped gas bubbles

Application of boundary element method to Stokes flows over a striped superhydrophobic surface with trapped gas bubbles

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