Superhydrophobic annular pipes: a theoretical study

Crowdy, Darren

doi:10.1017/jfm.2020.795

Cited by 15 publications

(23 citation statements)

References 29 publications

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“…Crowdy (2021) provides an analytical flow field solution for annular superhydrophobic pipes of radius , with , and no-shear boundary slits on the inner wall. The velocity field is given as where the subscript indicates the Crowdy annular flow field (Crowdy 2021). Like (2.5), this solution consists of a rotationally symmetric Poiseuille flow and a superposed asymmetric second term with the real part of an analytic function .…”

Section: Mathematical Description Of the Flow Field And Effective Sli...mentioning

confidence: 99%

“…Reconstructing the effective slip length of the no-shear solution derived by Crowdy (2021), we must first identify the average of at along the inner wall: Although not given explicitly in Crowdy (2021), it is readily determined to be with the aforementioned scaling factor from (2.31), and where is any closed circle inside the annulus enclosing the origin (Crowdy 2021). Accordingly, the averaged velocity for the no-shear solution along the inner wall is given by and the associated normalized effective slip length for the no-shear case is with from (2.32), as is given in Crowdy (2021). Determining the effective slip for the superposed annular flow is performed similarly.…”

Section: Mathematical Description Of the Flow Field And Effective Sli...mentioning

confidence: 99%

“…The outer wall is set to be the unit disk. Also, is a scaling constant, and is the coefficient in a Laurent expansion performed by Crowdy (2021), both dependent solely on geometric parameters. For further details, see § 2.2.3.…”

Section: Introductionmentioning

confidence: 99%

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Analytical models for pressure-driven Stokes flow through superhydrophobic and liquid-infused tubes and annular pipes

Zimmermann,

Schönecker

2024

J. Fluid Mech.

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Analytical expressions for the velocity field and the effective slip length of pressure-driven Stokes flow through slippery pipes and annuli with rotationally symmetrical longitudinal slits are derived. Specifically, the developed models incorporate a finite local slip length and constant shear stress along the slits, and thus go beyond the assumption of perfect slip employed commonly for superhydrophobic surfaces. Thereby, they provide the possibility to assess the influence of both the viscosity of the air or other fluid that is modelled to fill the slits as well as the influence of the micro-geometry of these slits. First, expressions for tubes and annular pipes with superhydrophobic or slippery walls are provided. Second, these solutions are combined to a tube-within-a circular-pipe scenario, where one fluid domain provides a slip to the other. This scenario is interesting as an application to achieve stable fluid–fluid interfaces. With respect to modelling, it illustrates the specification of the local slip length depending on a linked flow field. The comparison of the analytically calculated solutions with numerical simulations shows excellent agreement. The results of this paper thus represent an important instrument for the design and optimization of slippage along surfaces in circular geometries.

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Section: Mathematical Description Of the Flow Field And Effective Sli...mentioning

confidence: 99%

Section: Mathematical Description Of the Flow Field And Effective Sli...mentioning

confidence: 99%

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Analytical models for pressure-driven Stokes flow through superhydrophobic and liquid-infused tubes and annular pipes

Zimmermann,

Schönecker

2024

J. Fluid Mech.

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“…[1][2][3] Inspired by an unusual bounce behavior of water droplets on lotus leaves, superhydrophobic surfaces (SHSs) have been long explored to reduce flow drag. [4][5][6][7] Due to the presence of micro-and nanostructures and relatively low surface energy of SHSs, air can be trapped within these structures when SHSs are submerged under water. As water is prevented from a direct contact with a solid wall, a gas-liquid interface (GLI) is formed to form an apparent slip, which makes SHSs useful for applications that require drag reduction.…”

Section: Introductionmentioning

confidence: 99%

Two local slip modes at the liquid–liquid interface over liquid-infused surfaces

Ren

Bao

et al. 2022

Physics of Fluids

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A liquid-liquid interface (LLI) at liquid-infused surfaces (LISs) plays a significant role in promoting slip flow and reducing frictional drag. By employing the transverse many-body dissipative particle dynamics simulations, the behavior of local and effective slip at a flat LLI for shear flows over periodically grooved LISs has been studied. With increasing viscosity ratio between the working fluid and lubricant fluid, two local slip modes are identified. For a small viscosity ratio, the local slip length remains finite along the LLI, while a hybrid local slip boundary condition holds along the LLI for large viscosity ratios, i.e., the local slip length is finite near the groove edge and unbounded in the central region of the LLI. The vortical flow inside the groove can be enhanced by increasing viscosity ratio due to the change in the local slip mode from the finite state to the hybrid one. Moreover, the results suggest two scenarios for the variation of the effective slippage. For LISs with a large LLI fraction, the effective slip length increases significantly with increasing viscosity ratio, while for a small LLI fraction, the effective slippage is rather insensitive to the viscosity ratio. The underlying mechanism for the relationship between the effective slip length and the viscosity ratio for different LLI fractions is revealed based on the two slip modes. These results elucidate the effect of LLI on slip boundary conditions and might serve as a guide for the optimal design of LISs with enhanced slip properties.

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“…Incidentally, Philip's pipe flow solutions have recently been extended by Crowdy (15) who found generalized analytical solutions for flow in superhydrophobic pipes with an annular cross-section and no-shear patterning on one of the two boundary walls. The heat transfer properties of those flows are also of interest and will be studied in future work.…”

Section: Introductionmentioning

confidence: 99%

Superhydrophobicity Can Enhance Convective Heat Transfer in Pressure-Driven Pipe Flow

Rodriguez-Broadbent

Crowdy

2022

The Quarterly Journal of Mechanics and Applied Mathematics

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Summary Theoretical evidence is given that it is possible for superhydrophobicity to enhance steady laminar convective heat transfer in pressure-driven flow along a circular pipe or tube with constant heat flux. Superhydrophobicity here refers to the presence of adiabatic no-shear zones in an otherwise solid no-slip boundary. Adding such adiabatic no-shear zones reduces not only hydrodynamic friction, leading to greater fluid volume fluxes for a given pressure gradient, but also reduces the solid surface area through which heat enters the fluid. This leads to a delicate trade-off between competing mechanisms so that the net effect on convective heat transfer along the pipe, as typically measured by a Nusselt number, is not obvious. Existing evidence in the literature suggests that superhydrophobicity always decreases the Nusselt number, and therefore compromises the net heat transfer. In this theoretical study, we confirm this to be generally true but, significantly, we identify a situation where the opposite occurs and the Nusselt number increases thereby enhancing convective heat transfer along the pipe.

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Superhydrophobic annular pipes: a theoretical study

Abstract: Abstract

Cited by 15 publications

References 29 publications

Analytical models for pressure-driven Stokes flow through superhydrophobic and liquid-infused tubes and annular pipes

Analytical models for pressure-driven Stokes flow through superhydrophobic and liquid-infused tubes and annular pipes

Two local slip modes at the liquid–liquid interface over liquid-infused surfaces

Superhydrophobicity Can Enhance Convective Heat Transfer in Pressure-Driven Pipe Flow

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