The gas–liquid interface (GLI) over superhydrophobic surfaces (SHSs), where the flow slips, is the key to reduce frictional drag in underwater applications. Many-body dissipative particle dynamics simulations are used to explore the slip behavior of a shear flow over a rectangular grooved SHS, and a flat GLI is obtained by tuning the contact angle of the GLI. Due to the slip, the normal profiles of the local velocity, which are perpendicular to the GLI, are curved and shifted away from the linear form near the GLI. Then, a polynomial function is proposed to fit the velocity profile to extract the local shear rate and calculate the slip length. Based on this fitting method, a hybrid slip boundary condition is derived for both longitudinal and transverse flows. That is, the shear stress and slip length are finite near the groove edge, and the stress is nearly zero and the slip length is infinite in the center region of the GLI. This new hybrid slip boundary condition not only explains the inconsistent slip conditions reported in the literature under different groove length scales, but also unifies the existing exclusive slip assumptions.

Abstract

Fluid viscosity plays an important role in multiphase flows, and the many-body dissipative particle dynamics (MDPD) method is an efficient means of simulating such flows at the mesoscopic scale. As the viscosity of the standard MDPD (S-MDPD) fluid cannot be efficiently adjusted, a transverse MDPD (T-MDPD) scheme is newly proposed to tune the viscosity of an MDPD fluid over a large range. With a lateral friction coefficient added to the S-MDPD form, the viscosity of the T-MDPD fluid is higher than that of an S-MDPD fluid, and the viscosity is about five times larger than that of an S-MDPD fluid with a friction coefficient of 40.5. In a T-MDPD fluid, the viscosity is much more sensitive to the new transverse friction coefficient, as it increases about five times higher when this coefficient increases from 4.5 to 40.5, while the viscosity only increases two times higher with the same variation of the original coefficient. By increasing the repulsive coefficient, the liquid particle number density, or the cutoff radius, the viscosity of the T-MDPD fluid is enhanced as well. Based on this extension of the MDPD scheme, a quantitative expression for the variation of the viscosity in the current T-MDPD fluid is derived. In future simulations of multiphase flows using an MDPD scheme, the transverse effect can be extended to effectively tune the viscosity, and this empirical expression will be useful to predict the viscosity of the T-MDPD fluid.

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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.