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Register a new userEffect of texture randomization on the slip and interfacial robustness in turbulent flows over 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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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.
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 presented 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.
The study reports the aspects of postimpact hydrodynamics of ferrofluid droplets on superhydrophobic SH surfaces in the presence of a horizontal magnetic field. A wide gamut of dynamics was observed by varying the impact Weber number We, the Hartmann 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.
Phoresis, the drift of particles induced by scalar gradients in a flow, can result in an effective compressibility, bringing together or repelling particles from each other. Here, we ask whether this effect can affect the transport of particles in a turbulent flow. To this end, we study how the dispersion of a cloud of phoretic particles is modified when injected in the flow, together with a blob of scalar, whose effect is to transiently bring particles together, or push them away from the center of the blob. The resulting phoretic effect can be quantified by a single dimensionless number. Phenomenological considerations lead to simple predictions for the mean separation between particles, which are consistent with results of direct numerical simulations. Using the numerical results presented here, as well as those from previous studies, we discuss quantitatively the experimental consequences of this work and the possible impact of such phoretic mechanisms in natural systems.
Transport phenomena involving condensate liquids generated from the phase change heat transfer in microchannels and in engineered superhydrophobic surfaces require consideration of slip effects. In this study, the laminar film condensation over upward facing flat slabs and circular disks of finite sizes with free edges in the presence of wall slip effects is investigated. By considering the Navier slip model and extending the classical Nusselt analysis, the mass, momentum, and energy of the liquid film in two-dimensional and axisymmetric coordinates are solved for the film thickness and the heat transfer rate in non-dimensional form. Numerical solution yields the local structure of the condensate film profile and the Nusselt number for different values of the slip coefficient. Investigation of the results reveals that the condensate film on horizontal surfaces becomes thinner and the overall heat transfer rate is enhanced with an increase in the slip coefficient. In particular, a regression analysis of the results indicates a power law dependence of the Nusselt number on the non-dimensional slip coefficient with an exponent close to 0.5. Significant enhancement in phase change heat transfer follow from the modification of the local velocity profiles within the condensate film, especially in resulting from the additional momentum gain near the wall surfaces due to increases in slip effects.
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