We find solutions that describe the levelling of a thin fluid film, comprising a non-Newtonian power-law fluid, that coats a substrate and evolves under the influence of surface tension. We consider the evolution from periodic and localized initial conditions as separate cases. The particular (similarity) solutions in each of these two cases exhibit the generic property that the profiles are weakly singular (that is, higher-order derivatives do not exist) at points where the pressure gradient vanishes. Numerical simulations of the thin film equation, with either periodic or localized initial condition, are shown to approach the appropriate particular solution.

The surface thermodynamic properties of a series of n-alkylammonium and quaternary ammonium treated clay films were determined by contact angle measurement of drops of test liquids using the Young equation for polar materials. The two clays were a Wyoming montmorillonite (SWy-1) and Laponite RD. For a series of primary n-alkyl (6 ≤ n ≤ 15) and several quaternary organic cations, the organo-clay (both SWy-1 and Laponite RD) showed very little change in the value of γLW compared to the equivalent ammonium-saturated clay. Also, γ⊕ remained small or increased slightly compared to the ammonium-saturated clay. For SWy-1 exchanged by both quaternary ammonium and primary n-alkylammonium cations, the value of γ⊖ was smaller (0.1 ≤ γ⊖ ≤ 15.8 mJ/m2) than for the ammonium-saturated clay (γ⊖ = 36.2 mJ/m2) and decreased linearly with the number of carbon atoms. The γ⊖ values for the organic cation-exchanged Laponite RD samples (24.2 ≤ γ⊖ ≤ 31.2 mJ/m2) were smaller than or comparable to the ammonium saturated clay (γ⊖ = 30.7 mJ/m2), and were relatively insensitive to the number of carbon atoms in the organic cation. Thus, for both clays the increased adsorption of organic molecules resulting from replacement of inorganic cations by organic cations is due primarily to the decrease in the value of the Lewis base parameter, γ⊖.

Current methods for fabricating lenses rely on mechanical processing of the lens or mould, such as grinding, machining and polishing. The complexity of these fabrication processes and the required specialized equipment prohibit rapid prototyping of optical components. This work presents a simple method, based on free-energy minimization of liquid volumes, which allows us to quickly shape curable liquids into a wide range of spherical and aspherical optical components, without the need for any mechanical processing. After the desired shape is obtained, the liquid can be cured to produce a solid object with nanometric surface quality. We provide a theoretical model that accurately predicts the shape of the optical components, and demonstrate rapid fabrication of all types of spherical lenses (convex, concave, meniscus), cylindrical lenses, bifocal lenses, toroidal lenses, doublet lenses and aspheric lenses. The method is inexpensive and can be implemented using a variety of curable liquids with different optical and mechanical properties. In addition, the method is scale invariant and can be used to produce even very large optical components, without a significant increase in fabrication time. We believe that the ability to easily and rapidly create optical components, without the need for complex and expensive infrastructure, will provide researchers with new affordable tools for fabricating and testing optical designs.

The surfaces of quartz crystals that were partially dissolved in superheated, H2O-saturated rhyolite melt are covered with hemispherical embayments; each embayment is judged to have formed where a gas bubble in the melt approached the crystal. ‘Flux-line attack’ and ‘upward-drilling’ of the refractory lining of glass tanks are analogous processes. As a bubble nears a dissolving solid it enters a compositional boundary layer in the melt, resulting in melt of variable surface tension surrounding the bubble. This unstable situation results in small-scale convection of the melt about the bubble (Marangoni convection) which can cause locally enhanced dissolution rate of the solid. It is suggested that this mechanism could cause round embayments to form in quartz phenocrysts in acid volcanic and sub-volcanic rocks. Criteria by which embayed phenocrysts formed by dissolution can be distinguished from those formed by unstable growth are reviewed briefly.

The addition of surfactant (trimethylnonylpolyethoxyethanol) at 0.5% (v/v) of the spray solution caused a twofold increase in the deposit of clopyralid (3,6-dichloro-2-pyridinecarboxylic acid) applied at 0.14 or 0.28 kg ae/ha on greenhouse-grown honey mesquite (Prosopis glandulosa Torr. # PRCJG) and increased transport into the plants compared to clopyralid applied alone. Application of equal rates of benazolin [4-chloro-2-oxo-3(2H)-benzothiazoleacetic acid] with clopyralid at 0.28 + 0.28 kg/ha enhanced transport of clopyralid into honey mesquite. Spray deposit, absorption, and translocation of clopyralid was unaffected by addition of 0.5% (v/v) of d'limonene (4-isopropenyl-1-methyl-cyclohexane). Greater spray deposit of clopyralid on plant surfaces after addition of surfactant was associated with reduced liquid surface tension and greater percentage of spray volume in small droplets (<204-μm diam).

Greenhouse studies were conducted to investigate the effects of adjuvant and rainfall on bentazon spray retention, efficacy, and foliar washoff in hemp sesbania, sicklepod, smooth pigweed, and velvetleaf. Bentazon was applied at 0.28 to 2.24 kg ai/ha with Agri-Dex, a crop oil concentrate (COC) or Kinetic, an organiosilicone-nonionic surfactant blend (OSB) when weeds were at the three- to five-leaf stage. Plants were subjected to 2.5 cm simulated rainfall for 20 min at 1 and 24 h after application of bentazon. Shoot fresh weight reduction assessed 2 wk after treatment was similar with either adjuvant on velvetleaf and smooth pigweed. OSB enhanced bentazon efficacy in hemp sesbania and sicklepod as compared to COC. Rainfall at 1 h after application generally reduced bentazon activity in all weeds. OSB maintained bentazon activity in hemp sesbania when subjected to rainfall at 1 h after application as compared to COC. Overall, bentazon spray retention on plants was 9 to 550% higher with OSB as compared to COC among the species at 1 h after application. Amount of bentazon residue washed off from the foliage by rainfall within a weed species was relatively similar for both adjuvants except in smooth pigweed and ranged from 39 to 98% among the four weed species at 1 h after application. OSB exhibited specificity for certain weed species and the potential to minimize bentazon spray reaching the soil by increasing deposition.

Greenhouse studies were conducted to evaluate the effectiveness of Kinetic, a silicone adjuvant that appeared to increase the efficacy and rainfastness of the isopropylamine salt of glyphosate on velvetleaf, sicklepod, barnyardgrass, guineagrass, yellow foxtail, and yellow nutsedge. Simulated rainfall of 1.3 cm in 5 min at 15 and 60 min after herbicide treatment reduced glyphosate efficacy on all weeds. Kinetic enhanced glyphosate efficacy when yellow nutsedge and guineagrass were subjected to post-spray rainfall at 60 min. On velvetleaf, sicklepod, and yellow foxtail, Kinetic improved glyphosate efficacy when the critical rain-free period was reduced to 15 min. Kinetic failed to provide rainfastness for barnyardgrass, thereby indicating a specificity of Kinetic for certain weed species.

The effect of oxyethylene (OE) chain length of three homologous series of nonionic surfactants (allinol, nonoxynol, octoxynol) on glyphosate uptake was markedly affected by the leaf surface fine-structure of sugarbeet and kohlrabi. Adaxial leaf surfaces of sugarbeet were covered with a layer of amorphous wax, whereas the adaxial surface of kohlrabi leaves was covered with fine crystalline wax. Foliar uptake of glyphosate (1 mM glyphosate, 20 mM glycine, pH 3.2) averaged 4% for sugarbeet without surfactant, but droplets were not retained by kohlrabi leaves in the absence of a surfactant. Glyphosate absorption with octoxynol (9 to 10 OE units, 0.5 g L−1) was rapid initially (0 to 2 h) and leveled off about 2 h after application in both species. Absorption by sugarbeet decreased from 12 to 3% as OE content of octoxynol was increased from 5 to 30 OE units. In contrast, surfactants of intermediate OE content (octoxynol, 16 OE units) induced the greatest uptake (17%) on kohlrabi. Leaf wetting was markedly affected by surfactant and leaf surface. As OE content of octoxynol increased from 5 to 30 OE units, droplet/leaf interface areas of 1-μl droplets decreased from 4 to 3 mm2 on the adaxial leaf surface of sugarbeet and from 61 to 2 mm2 on kohlrabi. Concurrently, the rate of droplet evaporation (1 μl) decreased from 1.0 to 0.7 nl s−1 on sugarbeet and 4.2 to 0.5 nl s−1 on kohlrabi leaves. The effect of OE content on enhancement of glyphosate uptake and wetting characteristics of spray solutions was similar within species for different hydrophobic moieties but differed markedly between species.

This article is presented the surface tension effect on the two-dimensional blade section of the partially submerged propeller (PSP). In this regard, blade is entered to the water that causes to splash the water due to the impact and free surface. Also, because of the blade's angle of attack suction side is vented by air and pressure side is wetted and gripped the water to generate thrust. The Reynolds-Averaged Navier-Stokes (RANS) method is used in order to predict the hydrodynamic flow from entering to the exit. Present paper is numerically investigated the effect of free surface and surface tension i.e. related to the Weber number. So, many numerical results are presented and discussed that are included volume fraction, ventilation zones, pressure distributions, vertical and horizontal forces at various Weber numbers.

The steady, axisymmetric flow induced by a point sink (or source) submerged in an inviscid fluid of infinite depth is computed and the resulting deformation of the free surface is obtained. The effect of surface tension on the free surface is determined and is the new component of this work. The maximum Froude numbers at which steady solutions exist are computed. It is found that the determining factor in reaching the critical flow changes as more surface tension is included. If there is zero or a very small amount of surface tension, the limiting factor appears to be the formation of small wavelets on the free surface; but, as the surface tension increases, this is replaced by a tendency for the lowest point on the free surface to descend sharply as the Froude number is increased.

We examine a problem in which a line sink causes a disturbance to an otherwise uniform flowing stream of infinite depth. We consider the fully non-linear problem with the inclusion of surface tension and find the maximum sink strength at which steady solutions exist for a given stream flow, before examining non-unique solutions. The addition of surface tension allows for a more thorough investigation into the characteristics of the solutions. The breakdown of steady solutions with surface tension appears to be caused by a curvature singularity as the flow rate approaches the maximum. The non-uniqueness in solutions is shown to occur for a range of parameter values in all cases with non-zero surface tension.

We consider a two-layer fluid of finite depth with a free surface and, in particular, the surface tension at the free surface and the interface. The usual assumptions of a linearized theory are considered. The objective of this work is to analyse the effect of surface tension on trapped modes, when a horizontal circular cylinder is submerged in either of the layers of a two-layer fluid. By setting up boundary value problems for both of the layers, we find the frequencies for which trapped waves exist. Then, we numerically analyse the effect of variation of surface tension parameters on the trapped modes, and conclude that realistic changes in surface tension do not have a significant effect on the frequencies of these.

This note presents an elasto-capillary model of a cantilever subject to capillary stiction during drying process of removing sacrificial layers in MEMS. Similar to the dynamic analysis of the electrostatic pull-in of electrostatic micro actuators, the cantilever beam tends to be pulled down to the substrate due to the nonlinear capillary force with respect to the gap. The critical one-half gap deformation and the corresponding critical wetting area for pulling down a micro cantilever by surface tension are analytically found herein. The instability situation of a generalized critical deformation for power-law surface force with respect to gap is also predicted accordingly. Some prior MEMS works are exemplified to justify this critical one-half gap deformation for capillary stiction.

Two-phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines. We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate. The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking level) and allows for moving contact lines and contact angle hysteresis and pinning through a variational inequality. Moreover, the formulation can be extended to include non-linear contact line motion models. We prove the well-posedness of the time semi-discrete system and fully discrete method using appropriate choices of finite element spaces. A formal energy law is derived for the semi-discrete and fully discrete formulations and preliminary error estimates are also given. Simulation results are presented for a droplet in multiple configurations to illustrate the method.