|Superhydrophobicity is resulted from the ability of a submerged rough hydrophobic surface to trap air in its surface pores, and thereby reduce the area of contact between the water and the solid surface. A reduced contact area can result in a reduction in the skin friction drag exerted on a submerged object, such as an underwater vehicle or a boat or even the inside of a water pipe. A submerged surface can only remain superhydrophobic (SHP) as long as it retains the trapped air in its pores. SHP surfaces have a short underwater life, and their longevity depends strongly on the hydrostatic pressure at which they operate. Our group was the first to develop a mathematical framework to predict the longevity of a submerged superhydrophobic surface [Emami et al. 2013, Hemeda and Tafreshi 2014]. Longevity of a submerged SHP surface depends strongly on the rate at which the air trapped in the surface pores dissolve into the surrounding water. The rate of dissolution of the trapped air depends on its pressure, which in turn, is a function of the hydrostatic pressure on the surface and the capillary pressure of the pore (dependent on the pore geometry and contact angle with water) as shown schematically in the figure below. Solving the integro-partial differential equation given below results in the 3-D shape of the air−water interface inside the pores of the surface as a function of time. This information can then be used to determine the moment at which the surface drag reduction benefits diminishes.
Balance of forces acting on the air-water interface formed over the pores of a submerged superhydrophobic surface. The 3-D shape of the air-water interface can be obtained by solving the above differential equation, and can be used to predict the longevity (life span) of the surface under different hydrostatic pressures [Emami et al., 2013, or Hemeda and Tafreshi 2014].
|Depending on the hydrostatic/hydrodynamic conditions and the surface morphology, the Wenzel state (fully wetted), the Cassie state (fully dry), or a series of transition states in between these extreme states can be expected to prevail over a submerged SHP surface. The hydrostatic pressure at which a SHP surface starts departing from the Cassie state is referred to as the critical hydrostatic pressure. Manmade superhydrophobic surfaces are often manufactured via microfabrication of hydrophobic grooves or posts, and so we started our work on SHP surfaces by first predicting the critical pressure at which the capillary pressure provided by the surface pores can no longer counter the hydrostatic pressure on the air-water interface. We conducted such calculations for microfabricated SHP surfaces comprised of dissimilar pores, posts, or grooves (see figure below).
The above figures show the 3-D shape of the air-water interface for submerged superhydrophobic surfaces comprised of sharp-edged microfabricated posts of different geometries in ordered and/or random configurations [Hemeda et al., 2016].
|However, microfabrication, is a costly process and cannot easily be applied to large surfaces (or to surfaces with arbitrary shapes). An alternative approach to produce a superhydrophobic surface is by depositing hydrophobic fibers (e.g., polystyrene) or particles (e.g., aerogel particles) on a substrate. The definition of the critical hydrostatic pressure is less clear when the pore entrance is round (the case of SHP surface comprised of smooth fibers or round particles). This is because in this case, the AWI cannot anchor itself to any sharp corner, and has to conform to a shape that maintains the Young-Laplace contact angle (YLCA) at any point along the curved wall of the pore. Therefore, even at a zero hydrostatic pressure, it is hard to define a fully dry (Cassie) state as the AWI has already entered the pore, as can be seen in the figure below.
|The above figure shows the 3-D shape of the air-water interface over a submerged superhydrophobic surface comprised spherical particles (pulverized aerogel) [Ameri et al., 2015]. The resulting air-water interface was then used as the “slip” boundary to predict the drag force reduction for a shear flow over such superhydrophobic surfaces [Aziz and Tafreshi 2018].
|The figure below shows the SEM image of an electrospun polystyrene (superhydrophobic) coating along with its numerical counterpart generated to simulate the shape and stability of the air-water interface over the coating under submerged condition. Such information is particularly important for designing superhydrophobic nanofiber coatings for underwater applications where resistance against elevated hydrostatic pressure is crucial, or when manufacturing separation membranes (e.g., distillation membranes used for water desalination).
Figure to the left shows the 3-D shape of the air-water interface over a virtual electrospun polystyrene coating [Emami el al. 2012]. For these simulations, the air-water interface was assumed to be pinned to the fibers. Figure on the right shows a similar results but for when the air-water interface was allowed to slide along the sides of the fibers (maintaining a slope corresponding the YLCA of the fibers). In the latter, the fibers were assumed to be orthogonal to one another to simplify the problem [Bucher et al., 2015].
|To experimentally measure the longevity (life span) of the above-mentioned submerged electrospun polystyrene coatings, Samaha et al. (2011 and 2012) fabricated a novel test rig in which light scattering was used to measure the time-dependent loss of entrapped air in a SHP coating. The loss of trapped air resulted in a measurable decrease in surface reflectivity and the results were compared with measurements of skin-friction drag, under different hydrostatic pressures.
The figure on the left shows the experimental setup used to measure the longevity of submerged SHP coatings under different hydrostatic or flow conditions. The figure on the right shows drag reduction percentage obtained for electrospun polystyrene coatings using a rheometer [Samaha et al., 2011 and 2012].
|As mentioned earlier, SHP surfaces are prone to failure under elevated pressures or because of the air-layer dissolution into the surrounding water. Slippery liquid-infused porous surfaces (SLIPS) or liquid-infused surfaces (LIS) in which the trapped air is replaced with a lubricant have been proposed in the literature as a way of eliminating the air dissolution problem. LIS or SLIPS surface however do not provide significant reduction in drag force (especially for low-viscosity fluids like water). In this concern, we hypothesize a design in which a layer of air is trapped underneath the infused lubricant to reduce the frictional forces preventing the LIS to provide drag reduction for water or any fluid with a viscosity less than that of the lubricant. Drag reduction performance of such a surface (referred to as liquid-infused surface with trapped air, LISTA), is predicted by solving the biharmonic equation for the water−oil−air three-phase system in transverse grooves. For the arbitrary dimensions considered in our proof-of-concept study, LISTA designs showed 20−37% advantage over their LIS counterparts.
|The figure on the left illustrates our LISTA design in which a layer of air is trapped underneath the lubricant layer to enhance drag reduction benefits of the surface. The figure on the right compares the flow field inside a LIS surface with that of its LISTA counterpart. Velocity scales are given above the figure for each case [Hemeda and Tafreshi 2016].