Design principles for superamphiphobic surfaces

Abstract

To predict the properties of superamphiphobic layers we analyzed the wetting of a square and a hexagonal array of vertical pillars composed of spheres (radius R) partially sintered together. Apparent contact angles above 150° are obtained by pinning of a non-polar liquid surface at the underside of the top sphere resulting in a Fakir or Cassie state. Analytical equations are derived for the impalement pressure in the limiting case A₀ ≫ R², where A₀ is the area of the regular unit cell containing a single pillar. The case of close pillars is investigated numerically. By balancing forces at the rim of a drop, we calculate the apparent receding contact angle. To describe drag reduction of a flowing liquid we calculate the apparent slip length. When considering pressure-induced flow through cylindrical capillaries of radius r_c, significant drag reduction occurs only for thin capillaries. The mechanical stability with respect to normal forces and shear is analyzed. Nanoscopic silica glass pillars would be able to sustain the normal and shear stresses caused by capillary and drag forces. For a high impalement pressure and good mechanical stability A₀ should be small and R (respectively the neck diameter) should be large, whereas a large A₀ and a small R imply low contact angle hysteresis and high slip length.