B. Emami

Predicting shape and stability of air–water interface on superhydrophobic surfaces with randomly distributed, dissimilar posts

A mathematical framework developed to calculate the shape of the air–water interface and predict the stability of a microfabricated superhydrophobic surface with randomly distributed posts of dissimilar diameters and heights is presented. Using the Young–Laplace equation, a second-order partial differential equation is derived and solved numerically to obtain the shape of the interface, and to predict the critical hydrostatic pressure at which the superhydrophobicity vanishes in a submersed surface. Two examples are given for demonstration of the method’s capabilities and accuracy.

Effect of fiber orientation on shape and stability of air-water interface on submerged superhydrophobic electrospun thin coatings

To better understand the role of fiber orientation on the stability of superhydrophobic electrospun coatings under hydrostatic pressures, an integro-differential equation is developed from the balance of forces across the air–water interface between the fibers. This equation is solved numerically for a series of superhydrophobic electrospun coatings comprised of random and orthogonal fiber orientations to obtain the exact 3D shape of the air–water interface as a function of hydrostatic pressure. More important, this information is used to predict the pressure at which the coatings start to transition from the Cassie state to the Wenzel state, i.e., the so-called critical transition pressure. Our results indicate that coatings composed of orthogonal fibers can withstand higher elevated hydrostatic pressures than those made up of randomly orientated fibers. Our results also prove that thin superhydrophobic coatings can better resist the elevated pressures. The modeling methodology presented here can be used...

Predicting shape and stability of air–water interface on superhydrophobic surfaces comprised of pores with arbitrary shapes and depths

An integro-differential equation for the three dimensional shape of air–water interface on superhydrophobic surfaces comprised of pores with arbitrary shapes and depths is developed and used to predict the static critical pressure under which such surfaces depart from the non-wetting state. Our equation balances the capillary forces with the pressure of the air entrapped in the pores and that of the water over the interface. Stability of shallow and deep circular, elliptical, and polygonal pores is compared with one another and a general conclusion is drawn for designing pore shapes for superhydrophobic surfaces with maximum stability.

Modeling resistance of nanofibrous superhydrophobic coatings to hydrostatic pressures: The role of microstructure

In this paper, we present a numerical study devised to investigate the influence of microstructural parameters on the performance of fibrous superhydrophobic coatings manufactured via dc and ac electrospinning. In particular, our study is focused on predicting the resistance of such coatings against elevated hydrostatic pressures, which is of crucial importance for submersible applications. In our study, we generate 3D virtual geometries composed of randomly or orthogonally oriented horizontal fibers with bimodal diameter distributions resembling the microstructure of our electrospun coatings. These virtual geometries are then used as the computational domain for performing full morphology numerical simulations to establish a relationship between the coatings’ critical pressure (pressure beyond which the surface may depart from the Cassie state) and their microstructures. For coatings with ordered microstructures, we have also derived analytical expressions for the critical pressure based on the balance o...

Predicting longevity of submerged superhydrophobic surfaces with parallel grooves

A mathematical framework is developed to predict the longevity of a submerged superhydrophobic surface made up of parallel grooves. Time-dependent integro-differential equations predicting the instantaneous behavior of the air–water interface are derived by applying the balance of forces across the air–water interface, while accounting for the dissolution of the air in water over time. The calculations start by producing a differential equation for the initial steady-state shape and equilibrium position of the air–water interface at t = 0. Analytical and/or numerical solutions are then developed to solve the time-dependent equations and to compute the volume of the trapped air in the grooves over time until a Wenzel state is reached as the interface touches the grooves bottom. For demonstration, a superhydrophobic surface made of parallel grooves is considered, and the influence of the grooves dimensions on the longevity of the surface under different hydrostatic pressures is studied. It was found that ...

Optimizing fiber cross-sectional shape for improving stability of air-water interface over superhydrophobic fibrous coatings

In this letter, a mathematical force-balance formulation is developed that can be used to predict the critical pressure, the hydrostatic pressure above which the surface starts to depart from the non-wetting state, for superhydrophobic surfaces comprised of highly aligned fibers (e.g., biased AC-electrospun coatings) with arbitrary cross-sectional shapes. We have also developed a methodology for optimizing the fiber cross-sections to maximize the critical pressure of the surface, using the Euler–Lagrange equation. A case study is presented to better demonstrate the application of our method.