Superhydrophobic surfaces often incorporate roughness on both micron and nanometer length scales, although a satisfactory understanding of the role of this hierarchical roughness in causing superhydrophobicity remains elusive. We present a two-dimensional thermodynamic model to describe wetting on hierarchically grooved surfaces by droplets for which the influence of gravity is negligible. By creating wetting phase diagrams for droplets on surfaces with both single-scale and hierarchical roughness, we find that hierarchical roughness leads to greatly expanded superhydrophobic domains in phase space over those for a single scale of roughness. Our results indicate that an important role of the nanoscale roughness is to increase the effective Young's angle of the microscale features, leading to smaller required aspect ratios (height to width) for the surface structures. We then show how this idea may be used to design a hierarchically rough surface with optimally high contact angles.
The findings indicate that tongue ROM is reduced in individuals with more severe dysarthria when estimated using a standardized paragraph containing all American English phonemes. The articulatory working space measure could be useful for estimating speech dysfunction in ALS. ROM of the tongue decreases, but ROM of the lower lip and jaw each increase in individuals with severe dysarthria. Differential involvement of the articulators in the anterior-posterior dimension needs to be further investigated.
Wetting of solid surfaces is important for many potential applications, including the design of low-drag and antifouling/self-cleaning surfaces, and it is usually quantified by the contact angle and by contact angle hysteresis. Both the chemistry and the physical patterning of the surface are known to affect the contact angle. In studying the wetting of such surfaces, most models focus on the small Bond number (Bo) limit in which the effect of gravity is negligible, which simplifies free energy calculations. In this work, we employ a thermodynamic model for surfaces patterned with two-dimensional asperities, which remains applicable for nonzero Bo. We employ two versions of the model: one in which we require the liquid-vapor interface to remain a circular cap, and another in which we allow the liquid-vapor interface to deform. We find that the effects of gravity are twofold. First, drops with larger Bo tend to flatten and spread across the surface relative to the same size drops with Bo = 0. Second, gravity makes it more favorable for drops to penetrate surface asperities compared to the case of Bo = 0, which also tends to lower the contact angles. The main effect of droplet deformation is to produce larger contact angles for the same wetting configuration. Finally, we compare our model predictions with relevant experimental observations. We find very close agreement with the experiments, thereby validating our theoretical model.
The Wenzel model, commonly used for predicting the equilibrium contact angle (CA) of drops which penetrate the asperities of a rough surface, does not account for the liquid volume stored in the asperities. Interestingly, many previous experimental and molecular dynamics studies have noted discrepancies between observed CAs and those predicted by the Wenzel model because of this neglected liquid volume. Here, we apply a thermodynamic model to wetting of periodically patterned surfaces to derive a volume-corrected Wenzel equation in the limit of small pattern wavelength (compared to drop size). We show that the corrected equilibrium CA is smaller than that predicted by the Wenzel equation and that the reduction in CA can be significant when the liquid volume within the asperities becomes non-negligible compared to the total droplet volume. In such cases, the corrected CAs agree reasonably well with experimental observations and results of molecular dynamics simulations reported in previous studies.
Double-slit interference is a difficult phenomenon for students to grasp in an introductory physics course. A thorough understanding of constructive and destructive interference is critical, but even with such an understanding, visualizing exactly how an interference pattern is formed by light passing through two slits can still be a challenge for students. Here, we describe a simple demonstration that seems to have improved our students’ understanding of this phenomenon. The required materials are readily available in nearly any physics classroom or lab, and the demonstration can easily be constructed in 5 to 10 minutes.
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