Modeling of Hydrophobic Surfaces by the Stokes Problem With the Stick–Slip Boundary Conditions

Kučera, Radek; Šátek, Václav; Haslinger, Jaroslav; Fialová, Simona; Pochylý, František

doi:10.1115/1.4034199

Cited by 6 publications

(5 citation statements)

References 10 publications

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“…In a mathematical model describing the flow between two parallel walls, a layer of air near the hydrophobic surface [1], [8] was considered. Both laminar and turbulent models were derived.…”

Section: New Mathematical Modelmentioning

confidence: 99%

“…This condition has been enhanced for the liquid motion on a general curvilinear surface [4]. Another upgrade of the mathematical model was made by Tesca [8], who assumed that the movement of the liquid on the hydrophobic surface would not occur until a certain value of shear stress was overcome. These models put the size of the contact angle in correlation with the angle of the inclined plane, when the droplet detaches from the surface and moves.…”

Section: Introductionmentioning

confidence: 99%

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Practical aspects of the wettability

Fialová

Pochylý²,

Волков³

et al. 2022

EPJ Web Conf.

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A new knowledge of fluid flow on hydrophobic surface will be presented. The boundary condition will be refined considering the effects of air adhering to the rough, hydrophilic surface. Possibilities of turbulent viscosity effects as a result of liquid slippage on the hydrophobic surface will also be considered. These effects will be demonstrated on the basis of performed experiments. The experimental study will be focused on the determination of the pressure difference in the tube, whose surface is provided with an ultrahydrophobic coating with a contact angle higher than 140 °. Results will be reported based on Reynolds number. In addition to the results of the experiment, the thesis will also include a theoretical study aimed at refining the boundary condition, expressing the interaction of the liquid with the hydrophobic surface. In conclusion, the dissipation function will be derived, expressing the effects of liquid slippage on the hydrophobic surface and compared with its value taking into account the hydrophilic properties of the surface.

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Section: New Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Practical aspects of the wettability

Fialová

Pochylý²,

Волков³

et al. 2022

EPJ Web Conf.

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“…According to the simplified model (11) applied to the liquid flow in a circular cross-section tube, the relationship for turbulent viscosity can be derived. On the basis of the definition of the mixing length l, we can say:…”

Section: Simplified Turbulence Model For a Tube Of Circular Cross Secmentioning

confidence: 99%

New boundary conditions for fluid interaction with hydrophobic surface

2018

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Solution of both laminar and turbulent flow with consideration of hydrophobic surface is based on the original Navier assumption that the shear stress on the hydrophobic surface is directly proportional to the slipping velocity. In the previous work a laminar flow analysis with different boundary conditions was performed. The shear stress value on the tube walls directly depends on the pressure gradient. In the solution of the turbulent flow by the k-ε model, the occurrence of the fluctuation components of velocity on the hydrophobic surface is considered. The fluctuation components of the velocity affect the size of the adhesive forces. We assume that the boundary condition for ε depending on the velocity gradients will not need to be changed. When the liquid slips over the surface, non-zero fluctuation velocity components occur in the turbulent flow. These determine the non-zero value of the turbulent kinetic energy K. In addition, the fluctuation velocity components also influence the value of the adhesive forces, so it is necessary to include these in the formulation of new boundary conditions for turbulent flow on the hydrophobic surface.

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“…In the past few decades, the need for such analysis has grown steadily [8][9][10]. Moreover, non-Newtonian fluids, such as the Bingham fluid [11,12], make the solution to this equation even more intricate.…”

mentioning

confidence: 99%

“…It follows from continuity equation ( 5) that (12) Integration of equation ( 12) over the entire region V (see Fig. 1) yields ( )…”

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confidence: 99%

Methods for Simplification of the Mathematical Model for the Calculation of Flows in the Flow Path of Hydraulic Turbines

et al. 2021

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The main concern of this paper is fundamental research into an acute problem arising in the operation of hydraulic turbines, namely, the formation of a vortex core downstream of the impeller. It is noted that, at present, the operating range of these machines has to be extended due to the change in power network loads in daily and seasonal cycles, thereby increasing the time of hydraulic turbines' operation under offdesign or undesirable conditions, including those involving the risk of formation of a vortex of varying intensity. To describe this complex fluid flow, a mathematical model of the vortex core flow downstream of the hydraulic turbine's impeller was developed. This paper focuses on the fundamental issues encountered in developing the mathematical model. The methods are presented for simplifying the formulation of equations describing the structure of vortex rope formed in the flowpath. In this case, the equations of mathematical physics containing a dependent variable and taking the form of the Navier-Stokes equations when applied fluids flows were employed. They describe the time changes of the selected parameters in a controlled volume induced by the flow through the volume boundaries. The boundary conditions have been demonstrated to considerably affect the unsteady vortex structures. A special case is formulated for a potential force field using the stress tensor that governs the equilibrium. This makes it possible to describe complex motion in liquids without using an intricate form of the Navier-Stokes equations for vortex structures.

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Modeling of Hydrophobic Surfaces by the Stokes Problem With the Stick–Slip Boundary Conditions

Cited by 6 publications

References 10 publications

Practical aspects of the wettability

Practical aspects of the wettability

New boundary conditions for fluid interaction with hydrophobic surface

Methods for Simplification of the Mathematical Model for the Calculation of Flows in the Flow Path of Hydraulic Turbines

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