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 hydrostaticpressure above which the surface starts to depart from the non-wetting state, for superhydrophobicsurfaces 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

On applications and limitations of one-dimensional capillarity formulations for media with heterogeneous wettability

Force-balance-based one-dimensional algebraic formulations that are often used in characterizing the capillarity of a multi-component system (e.g., predicting capillary height rise inporous media) are discussed. It is shown that such formulations fail to provide accurate predictions when the distribution of wetting (or non-wetting) surfaces is not homogeneous. A more general mathematical formulation is suggested and used to demonstrate that for media with heterogeneous wettability, hydrophilic (or hydrophobic) surfaces clustered in groups will have less contribution to the overall capillarity of the system

A realistic modeling of fluid infiltration in thin fibrous sheets

In this paper, a modeling study is presented to simulate the fluid infiltration in fibrous media. The Richards’ equation of two-phase flow in porous media is used here to model the fluid absorption in unsaturated/partially saturated fibrous thin sheets. The required consecutive equations, relative permeability, and capillary pressure as functions of medium’s saturation are obtained via fiber-level modeling and a long-column experiment, respectively. Our relative permeability calculations are based on solving the Stokes flow equations in partially saturated three-dimensional domains obtained by imaging the sheets’ microstructures. The Richards’ equation, together with the above consecutive correlations, is solved for fibrous media inclined with different angles. Simulation results are obtained for three different cases of upward, horizontal, and downward infiltrations. We also compared our numerical results with those of our long-column experiment and observed a good agreement. Moreover, we establish empirical coefficients for the semianalytical correlations previously proposed in the literature for the case of horizontal and downward infiltrations in thin fibrous sheets

Effects of roughness on droplet apparent contact angles on a fiber

This paper reports on our investigation of the effects of surface roughness on the equilibrium shape and apparent contact angles of a droplet deposited on a fiber. In particular, the shape of a droplet on a roughened fiber is studied via the energy minimization method implemented in the surface evolver finite element code. Sinusoidal roughness varying in both the longitudinal and radial directions is considered in the simulations to study the effects of surface roughness on the most stable shape of a droplet on a fiber (corresponding a global minimum energy state). It is found that surface roughness delays droplet shape transition from a symmetric barrel to a clamshell or an asymmetric barrel profile. A phase diagram that includes the effects of fiber roughness on droplet configurations-symmetric barrel, clamshell, and asymmetric barrel-is presented for the first time. It is also found that droplet apparent contact angle tends to decrease on rough fibers. Likewise, roughness tends to increase the force required to detach a droplet from a fiber but the effect diminishes as droplet size increases relative to the size of surface roughness. The results presented in our study have been compared with experimental data or those from prior studies whenever possible, and good agreement has been observed

Geometrical modeling of fibrous materials under compression

Many fibrous materials such as nonwovens are consolidated via compaction rolls in a so-called calendering process. Hot rolls compress the fiber assembly and cause fiber-to-fiber bonding resulting in a strong yet porous structure. In this paper, we describe an algorithm for generating three dimensional virtual fiberwebs and simulating the geometrical changes that happen to the structure during the calendering process. Fibers are assumed to be continuous filaments with square cross sections lying randomly in the x or y direction. The fibers are assumed to be flexible to allow bending over one another during the compression process. Lateral displacement is not allowed during the compaction process. The algorithm also does not allow the fibers to interpenetrate or elongate and so the mass of the fibers is conserved. Bending of the fibers is modeled either by considering a constant “slope of bending” or constant “span of bending.” The influence of the bending parameters on the propagation of compression through the material’s thickness is discussed. In agreement with our experimental observations, it was found that the average solid volume fraction profile across the thickness becomes U shaped after the calendering. The application of these virtual structures in studying transport phenomena in fibrous materials is also demonstrated

Simulation and Analysis of Unbonded Nonwoven Fibrous Structures

In this work we report on our algorithm for generating 3-D virtual structures resembling un-bonded fibrous webs. The paper discusses short and infinitely long fibers, each emulating a category of nonwoven fibrous medium. The structure Solid Volume Fraction (SVF), being the most important characteristic of a fibrous porous medium, is calculated for different fiberwebs and discussed in details. It is shown that the SVF of the fibrous structures generated by our algorithm is independent of the basis weight. In other words, the porosity of the medium is only a function of the fiber properties – this is as expected. It is also demonstrated that by decreasing the fiber diameter while keeping other properties of the virtual fiberweb constant causes the SVF to decrease almost linearly. The same is not observed for the fiber rigidity. The capability of our algorithm for generating fibrous webs made up of layers of different fibers is demonstrated and their properties are discussed. The application of such virtual fibrous structures in modeling transport phenomena in nonwoven materials and their potential applications in load-deformation studies are discussed

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 superhydrophobicsurface 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 superhydrophobicelectrospun coatings under hydrostaticpressures, 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 superhydrophobicelectrospun coatings comprised of random and orthogonal fiber orientations to obtain the exact 3D shape of the air–water interface as a function of hydrostaticpressure. 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 hydrostaticpressures 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 to design nanofibrous superhydrophobic coatings for underwater applications

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 superhydrophobicsurfaces 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 superhydrophobicsurfaces with maximum stability