Homogeneous Solid Substrate Research Articles

Hysteresis of Contact Angle of Sessile Droplets on Smooth Homogeneous Solid Substrates via Disjoining/Conjoining Pressure.

A theory of contact angle hysteresis of liquid droplets on smooth, homogeneous solid substrates is developed in terms of the shape of the disjoining/conjoining pressure isotherm and quasi-equilibrium phenomena. It is shown that all contact angles, θ, in the range θr < θ < θa, which are different from the unique equilibrium contact angle θ ≠ θe, correspond to the state of slow "microscopic" advancing or receding motion of the liquid if θe < θ < θa or θr < θ < θe, respectively. This "microscopic" motion almost abruptly becomes fast "macroscopic" advancing or receding motion after the contact angle reaches the critical values θa or θr, correspondingly. The values of the static receding, θr, and static advancing, θa, contact angles in cylindrical capillaries were calculated earlier, based on the shape of disjoining/conjoining pressure isotherm. It is shown now that (i) both advancing and receding contact angles of a droplet on a on smooth, homogeneous solid substrate can be calculated based on shape of disjoining/conjoining pressure isotherm, and (ii) both advancing and receding contact angles depend on the drop volume and are not unique characteristics of the liquid-solid system. The latter is different from advancing/receding contact angles in thin capillaries. It is shown also that the receding contact angle is much closer to the equilibrium contact angle than the advancing contact angle. The latter conclusion is unexpected and is in a contradiction with the commonly accepted view that the advancing contact angle can be taken as the first approximation for the equilibrium contact angle. The dependency of hysteresis contact angles on the drop volume has a direct experimental confirmation.

Hysteresis of Contact Angle of Sessile Droplets

A theory of contact angle hysteresis on smooth, homogeneous solid substrates is developed in terms of shape of disjoining/conjoining pressure isotherm and quasi-equilibrium phenomena. It is shown that all contact angles, θ , in the range θ r a , which are different from the unique equilibrium value θ e , correspond to the state of slow “microscopic” advancing or receding motion of the liquid if θ e a or θ r e , respectively. This “microscopic” motion almost abruptly becomes fast “macroscopic” advancing or receding motion after the contact angle reaches the critical values θ a or θ r , correspondingly. The values of the static receding, θ r , and static advancing,θ a , contact angles in cylindrical capillaries were calculated earlier, based on the shape of disjoining/conjoining pressure isotherm. It is shown that both advancing contact and receding contact angles of a droplet on a solid substrate depends on the drop volume and are not a unique characteristic of the liquid-solid system. The suggested mechanism of the contact angle hysteresis of droplets has direct experimental confirmation.

Static contact angle hysteresis on smooth, homogeneous solid substrates

A theory of contact angle hysteresis on smooth, homogeneous solid substrates is developed in terms of shape of disjoining/conjoining pressure isotherm and quasi-equilibrium phenomena. It is shown that all contact angles, θ, in the range θ r < θ < θ a, which are different from the unique equilibrium contact angle θ ≠ θ e, correspond to the state of slow “microscopic” advancing or receding motion of the liquid if θ e < θ < θ a or θ r < θ < θ e, respectively. This “microscopic” motion almost abruptly becomes fast “macroscopic” advancing or receding motion after the contact angle reaches the critical values θ = θ a or θ r = θ, correspondingly. The values of the static receding, θ r, and static advancing, θ a, contact angles in cylindrical capillaries were calculated earlier, based on the shape of disjoining pressure isotherm. It is shown that an advancing contact angle of a droplet on a solid substrate depends on the drop volume and is not a unique characteristic of the liquid–solid system. The suggested mechanism of contact angle hysteresis has direct experimental confirmation.

Fluidized-bed column method for automatic dynamic extraction and determination of trace element bioaccessibility in highly heterogeneous solid wastes

Dynamic flow-through extraction/fractionation methods have recently drawn much attention as appealing alternatives to the batchwise steady-state counterparts for the evaluation of environmentally available pools of potentially hazardous trace elements in solid matrices. The most critical weakness of flow-based column approaches lies in the small amount of solid that can be handled, whereby their applicability has been merely limited to date to the extraction of trace elements in highly homogeneous solid substrates; otherwise the representativeness of the test portion might not be assured. To tackle this limitation, we have devised an automated flow-through system incorporating a specially designed extraction column with a large volume capacity, wherein up to 2 g of solid sample could be handled without undue backpressure. The assembled flow setup was exploited for fast screening of potentially hazardous trace elements ( namely, Cd, Cr, Cu, Pb, and Zn) in highly inhomogeneous municipal solid waste incineration (MSWI) bottom ashes. The pools of readily mobilizable metal forms were ascertained using the Toxicity Characteristic Leaching Procedure (TCLP) based on the usage of 0.1 mol L −1 CH 3COOH as leachant and analysis of extracts by inductively coupled optical emission spectrometry. The application of a two-level full factorial (screening) design revealed that the effect of sample fluidization primarily but other experimental factors such as the solid to liquid ratio and extractant flow rate significantly influenced the leachability of given elements in raw bottom ashes at the 0.05 significance level. The analytical performance of the novel flow-based method capitalized on fluidized-bed extraction was evaluated in terms of accuracy, through the use of mass balance validation, reproducibility and operational time as compared to batchwise extraction and earlier flow injection/sequential injection microcolum-based leaching tests.

Pattern Formation in Unstable Thin Liquid Films

The problem of spontaneous evolution of morphological patterns in thin ( $l100\mathrm{nm}$) unstable liquid films on homogeneous solid substrates is resolved based on a 3D nonlinear equation of motion. Initially, a small amplitude bicontinuous structure emerges, which either grows and fragments into a collection of microdroplets (for relatively thinner films), or leads directly to isolated circular holes (for thicker films) which dewet the surface. The characteristics of a pattern, and its pathway of evolution, thus depend crucially on the form of the intermolecular potential in an extended neighborhood of the initial thickness. The linear and 2D nonlinear analyses used hitherto fail completely in prediction of morphological patterns, but can predict their length scales rather well.

Plane-wave reflection from a solid layer with nonuniform density, sound speed, and shear speed

This paper considers the problem of calculating the reflection coefficient of a plane wave incident on an inhomogeneous elastic solid layer of finite thickness, overlying a semi-infinite, homogeneous solid substrate. The physical properties of the inhomogeneous layer, namely the density, compressional (sound) speed, shear speed, and attenuation, are all assumed to vary with depth. It is shown that, provided terms involving the gradient of the shear speed and of the shear modulus are ignored, and volume coupling between compressional and shear waves is neglected, analytical solutions of the resulting equations can be obtained. The assumptions made are justified at most frequencies of practical interest in underwater acoustics. In the case of a solid whose density and shear speed are constant, the results obtained are exact solutions of the full equations of motion, and may usefully be compared with numerical solutions in which the variation in sound speed through the layer is represented by a number of homogeneous sublayers. It is concluded that, with realistic sediment and substrate properties, a surprisingly large number of sublayers can be needed to give accurate results.

Molecular dynamics of a microscopic droplet on solid surface.

The spreading of a microscopic nonvolatile liquid drop on a homogeneous solid substrate has been studied by molecular dynamics simulations of Lennard-Jones systems. The substrate is assumed to be continuous without atomic structure and exerting a long-range Lennard-Jones potential on liquid particles in the drop. A molecular precursor film is observed to spread initially with nearly constant speed, crossing over later to diffusive spreading. These results are compared with recent molecular dynamics results of a volatile liquid on a structured substrate.

A plane wave reflection loss model based on numerical integration

A method is developed for computation of the complex plane‐wave reflection coefficient for a class of geoacoustic models of the ocean bottom, consisting of an arbitarary number of inhomogeneous (fluid) sediment layers overlying a a semi‐infinite homogeneous solid substrate (basement). Within the sediment layers the density, sound speed, and attenuation are permitted to vary arbitrarily with depth. An appropriate formulation of the problem permits the reflection coefficient to be constructed using the results obtained from the direct numerical integration of the depth separated wave equation. The entire computation is thus reduced to that of an initial value problem to which established methods can be applied. The Runge–Kutta method which was chosen permits user selected local error tolerances. Extensive application of the resulting computer code has shown that for a wide class of physically reasonable models global error is bounded, and accuracy far in excess of the minimum required is easily obtained. Requirements imposed on computer word size and available core are modest, and the model can be implemented on any modern general purpose computer and perhaps on a minicomputer.

Influence of surface waves on plane wave bottom reflection loss for realistic ocean sediments

Plane-wave reflection coefficients have been computed for several cases of fluid sediments, containing a constant sound-speed gradient, overlying a homogeneous solid substrate. It is shown that for realistic sediment descriptions, a pronounced maximum in bottom loss can occur at low grazing angles (well below the shear-wave critical angle). This maxima is well defined in angle and can occur only for special combinations of sound-speed gradient, frequency, and sediment thickness. It is shown that this phenomena is due to Stoneley waves propagating in the neighborhood of the sediment-substrate interface. These surface waves can become excited only when their phase velocity equals the parallel component of the phase velocity equals the parallel component of the phase velocity of the incident plane waves. Calculations are presented showing excellent agreement between the location of the bottom loss maxima and the predictions of a simplied theory based upon the excitation of Stoneley waves. The frequency, layer thickness, and sound speed gradient dependence are all adequately accounted for.