Effective slip for flow through a lubricant-impregnated grooved channel

Abstract

Lubricant-impregnated surface has been reported as a kind of non-wetting slippery surface of great potential in practical applications. In this study, flow through a lubricant-impregnated grooved channel under different conditions is investigated, analytically and numerically, to show the performance of this kind of surface on drag reduction.

In the first part, pressure-driven flow through a slit channel bounded by lubricant-impregnated grooved surfaces is considered, where the applied pressure gradient can be in a direction parallel or normal to the grooves. For flow parallel to the grooves, the interface between the lubricating fluid and the working fluid is assumed to be flat and the problem is solved analytically using the methods of domain decomposition and eigenfunction expansion. For flow normal to the grooves, the interface is no longer flat and the front tracking method is used to track the location of the interface. Finite volume method and staggered grids are adopted to numerically solve the transverse flow. The effective slip length, which is a measure for the drag reduction capability of the surface, is determined as a function of geometrical parameters and properties of the fluids.

In the second part, a numerical study is presented for transverse flow through a slit channel bounded by lubricant-impregnated surfaces under the combined action of pressure and thermocapillary forcings. Classical theory shows that the pressure needed to drive a flow through a channel will increase dramatically as the lateral dimension of the channel decreases. Thermocapilalry action, which is caused by a thermally induced surface tension gradient along an interface between two fluids, can be considered as an efficient way to aid the pressure forcing in driving the flow. This work aims to find out how thermocapillary action may contribute to the pumping of fluid through a channel bounded by lubricant-impregnated surfaces by looking into how the effective slip length may change under various conditions.

In the third part, flow through a lubricant-impregnated grooved surface with a curved interface is numerically studied. This work considers the case where the lubricating fluid will protrude into the working fluid and the interface has the form of a meniscus. A matched interface boundary (MIB) method is used to solve the interface conditions and obtain the velocities near the interface. The work shows how effective slip length depends on the geometry of the groove, flow direction, protrusion angle and viscosity ratio between the lubricating and working fluids.

In the fourth part, a semi-analytical model is presented for pressure-driven flow through a channel, where local pressure loss is incurred at a sudden change in the boundary condition: from no-slip to partial-slip. Assuming low-Reynolds-number incompressible flow and periodic stick-slip wall patterning, the problems for parallel-plate and circular channels are solved using the methods of eigenfunction expansion and point match. The work in this part aims to examine in detail how the flow will evolve, on passing through the cross section at which the change in the slip condition occurs, from a no-slip parabolic profile to a less sheared profile with boundary slip.