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تسجيل مستخدم جديدEffective slip over superhydrophobic surfaces in thin channels
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Superhydrophobic surfaces reduce drag by combining hydrophobicity and roughness to trap gas bubbles in a micro- and nanoscopic texture. Recent work has focused on specific cases, such as striped grooves or arrays of pillars, with limited theoretical guidance. Here, we consider the experimentally relevant limit of thin channels and obtain rigorous bounds on the effective slip length for any two-component (e.g. low-slip and high-slip) texture with given area fractions. Among all anisotropic textures, parallel stripes attain the largest (or smallest) possible slip in a straight, thin channel for parallel (or perpendicular) orientation with respect to the mean flow. For isotropic (e.g. chessboard or random) textures, the Hashin-Strikman conditions further constrain the effective slip. These results provide a framework for the rational design of superhydrophobic surfaces.
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Superhydrophobic surfaces demonstrate promising potential for skin friction reduction in naval and hydrodynamic applications. Recent developments of superhydrophobic surfaces aiming for scalable applications use random distribution of roughness, such
as spray coating and etched process. However, most of previous analyses of the interaction between flows and superhydrophobic surfaces studied periodic geometries that are economically feasible only in lab-scale experiments. We conduct direct numerical simulations of turbulent flows over randomly patterned interfaces considering a range of texture widths $w^+approx 4-26$, and solid fractions $phi_s=11%$ to $25%$. Slip and no-slip boundary conditions are implemented in a pattern, modeling the presence of gas-liquid interfaces and solid elements. Our results indicate that slip of randomly distributed textures under turbulent flows are about $30%$ less than those of surfaces with aligned features of the same size. In the small texture size limit $w^+approx 4$, the slip length of the randomly distributed textures in turbulent flows is well described by a previously introduced Stokes flow solution of randomly distributed shear-free holes. By comparing DNS results for patterned slip and no-slip boundary against the corresponding homogenized slip length boundary conditions, we show that turbulent flows over randomly distributed posts can be represented by an isotropic slip length in streamwise and spanwise direction. The average pressure fluctuation on gas pocket is similar to that of the aligned features with the same texture size and gas fraction, but the maximum interface deformation at the leading edge of the roughness element is about twice larger when the textures are randomly distributed.
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number Ha and the magnetic field strength manifested through the magnetic Bond number Bom. For a fixed We 60, we observed that at moderately low Bom 300, droplet rebound off the SH surface is suppressed. The noted We is chosen to observe various impact outcomes and to reveal the consequent ferrohydrodynamic mechanisms. We also show that ferrohydrodynamic interactions leads to asymmetric spreading, and the droplet spreads preferentially in a direction orthogonal to the magnetic field lines. We show analytically that during the retraction regime, the kinetic energy of the droplet is distributed unequally in the transverse and longitudinal directions due to the Lorentz force. This ultimately leads to suppression of droplet rebound. We study the role of Bom at fixed We 60, and observed that the liquid lamella becomes unstable at the onset of retraction phase, through nucleation of holes, their proliferation and rupture after reaching a critical thickness only on SH surfaces, but is absent on hydrophilic surfaces. We propose an analytical model to predict the onset of instability at a critical Bom. The analytical model shows that the critical Bom is a function of the impact We, and the critical Bom decreases with increasing We. We illustrate a phase map encompassing all the post impact ferrohydrodynamic phenomena on SH surfaces for a wide range of We and Bom.
Superhydrophobic surfaces have been shown to produce significant drag reduction in both laminar and turbulent flows by introducing an apparent slip velocity along an air-water interface trapped within the surface roughness. In the experiments present
ed within this study, we demonstrate the existence of a surface tension gradient associated with the resultant Marangoni flow along an air-water interface that causes the slip velocity and slip length to be significantly reduced. In this study, the slip velocity along a millimeter-sized air-water interface was investigated experimentally. This large-scale air-water interface facilitated a detailed investigation of the interfacial velocity profiles as the flow rate, interfacial curvature and interface geometry were varied. For the air-water interfaces supported above continuous grooves (concentric rings within a torsional shear flow) where no surface tension gradient exists, a slip velocity as high as 30% of the bulk velocity was observed. However, for the air-water interfaces supported above discontinuous grooves (rectangular channels in a Poiseuille flow), the presence of a surface tension gradient reduced the slip velocity and in some cases resulted in an interfacial velocity that was opposite to the main flow direction. The curvature of the air-water interface in the spanwise direction was found to dictate the details of the interfacial flow profile with reverse flow in the center of the interface for concave surfaces and along the outside of the interface for convex surfaces. The deflection of the air-water interface was also found to greatly affect the magnitude of the slip. Numerical simulations imposed with a relatively small surface tension gradient along the air-water interface were able to predict both the reduced slip velocity and back flow along the air-water interface.
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