Spreading of Polydimethylsiloxane Drops on Solid Horizontal Surfaces

Effect of the volume of drops, surface energy and roughness of substrate together with temperature and viscosity on the spreading velocity of polydimethylsiloxane (PDMS) drops on solid horizontal surfaces was studied. Spreading velocity was shown to grow with decreasing drop volume, the effect being more pronounced at high viscosities of polymer. The deviation of shape of the spreading drop from that of a spherical segment is more pronounced the higher the surface energy of substrate, the higher the polymer viscosity and the smaller the drop volume. Spreading on a rough surface is slower than on a smooth one owing to the energy barrier created by surface inhomogeneities: the barrier is to be overcome by the spreading liquid. Based on the experimental results a mechanism of spreading of polymer drops is proposed. Changes in potential energy of a drop and in the free surface energy of the system during spreading were compared, allowing a theoretical evaluation of the influence of gravity on the spreading velocity of drops. A theoretical analysis of spreading kinetics of viscous drops is given. The equation proposed agrees well with the experimental results at 90° > θ > 0°.     

Numerical simulations of drop impact and spreading on horizontal and inclined surfaces

The phenomenon of drop spreading is important to several process engineering applications. In the present work, numerical simulations of the dynamics of drop impact and spreading on horizontal and inclined surfaces were carried out using the volume of fluid (VOF) method. For the horizontal surfaces, the dynamics of impact and spreading of glycerin drops on wax and glass surfaces was investigated for which the experimental measurements were available [Šikalo, Š., Tropea, C., Ganic, E.N., 2005a. Dynamic wetting angle of a spreading droplet. Experimental Thermal and Fluid Science 29, 795-802; Šikalo, Š., Tropea, C., Ganic, E.N., 2005b. Impact of droplets onto inclined surfaces. Journal of Colloid and Interface Science 286, 661-669]. The influence of surface wetting characteristics was investigated by using static contact angle (SCA) and dynamic contact angle (DCA) models. The dynamics of drop impact and spreading on inclined surfaces and the different regimes of drop impact and spreading process were also investigated. In particular, the effects of surface inclination, surface wetting characteristics, liquid properties and impact velocity on the dynamics of drop impact and spreading were investigated numerically and the results were verified experimentally. It was found that the SCA model can predict the drop impact and spreading behavior in quantitative agreement with the experiments for less wettable surfaces (SCA>90^°). However, for more wettable surfaces (SCA<90^°), the DCA observed at initial contact times were order of magnitude higher than SCA values and therefore the DCA model is needed for the accurate prediction of the spreading behavior.     

Spontaneous spreading of emulsions on solid surfaces: Morphology and dynamics

The spontaneous spreading of emulsions of water dispersed in silicone oil onto glass surfaces is examined using differential interference contrast (DIC) microscopy. Spreading occurs via a precursor film from which the emulsion droplets are excluded. The radius of the interline of the bulk drop is found to vary as (time)^1/10, as is commonly observed for the spontaneous spreading of pure liquids. The spreading rate constant decreases linearly with the volume percent of the dispersed phase, but drops suddenly to zero at approximately 73% dispersed phase. The width and spreading rate of the precursor film also is found to decrease with dispersed phase concentration. A fingering type of instability is evident at the leading edge of the precursor film, yet has little effect on the spreading rate of either the precursor film or the droplet interline. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 1817–1825, 2001     

Characterization of polydihydrosilane by SEC-MALLS and viscometry

Silicon hydride compounds consisting of silicon and hydrogen constitute a fascinating class of silicon-based polymers because of their ability to form high-quality silicon film by solution-based process. In this study, we synthesize polydihydrosilane by photo-induced ring-opening polymerization of cyclopentasilane, and determine the molar mass, radius of gyration, and intrinsic viscosity of it in cyclohexene by size-exclusion chromatography combined with multi-angle laser light scattering and viscometry. It was found that the molar mass of polydihydrosilane ranges broadly from 10² to 10⁶ g/mol. Both the intrinsic viscosity and radius of gyration exhibited a scaling behavior with respect to the molar mass with the intrinsic viscosity exponent α = 0.206 and radius of gyration exponent ν = 0.410. Classification of the polymer structure based on the α value suggests that the polydihydrosilane forms a branched-chain structure with a particle-like compact shape rather than a straight chain.     

Thickness-dependent crystal orientation in poly(trimethylene 2,6-naphthalate) films studied with GIWAXD and RA-FTIR methods

The thickness dependence of the crystal orientation of poly(trimethylene 2,6-naphthalate) (PTN) films was clearly demonstrated using the methods of two-dimensional grazing incidence wide angle X-ray diffraction (2D GIWAXD) and grazing incidence reflection absorption FTIR (RA-FTIR) spectroscopy. The 2D GIWAXD results showed that for films thicker than 200 nm, the “c” axis (main chain direction) and “b” axis of crystal unit cell are almost parallel to the sample surface, whereas for thin films the “c” axis is preferentially perpendicular to the film plane in the crystalline phase of isothermally crystallized PTN films. The anisotropic orientation of the naphthalene rings in the isothermally crystallized PTN film was also confirmed. By analyzing the relative absorbance of the parallel band (1602 cm⁻¹) to the one of perpendicular band (917 cm⁻¹), the thickness dependence of the crystal orientation suggested by the GIWAXD results was also confirmed. Furthermore, the naphthalene rings in the isothermally crystallized thick films were found to lie flat on the film plane. The chain orientations derived from the GIWAXD and RA-FTIR results in this work were found to be consistent with the “flat-on” and “edge-on” lamellar orientation for the thin and thick films, respectively, which has previously been reported in many polymer systems.     

Impedance spectroscopy of oxidized polyaniline and poly(o-ethoxyaniline) thin film modified Pt electrodes

Impedance spectra of potentiodynamically formed polyaniline (PANI) and poly(o-ethoxyaniline) (POEA), thin film modified Pt electrodes measured at potentials of conductive, emeraldine form in H₂SO₄ electrolyte solution were reported. Specific features of spectra obtained for films of different voltammetric charge densities were modelled and interpreted according to “homogeneous” and “distributed” impedance models. The values of charging capacitances of different PANI and POEA films were found independent of the model used. Charging of polymer films was in terms of both models controlled by charge transport processes being ion diffusion and migration in the first case, and polymer film and ionic conductivities in the second case. Distortion from Warburg-like response observed for both polymer films was explained by either differences in relaxation times of diffusion and migration processes, or by impedance of ionic channels with “anomalous” frequency dispersion. There were some discrepancies between theories and results suggesting that “homogeneous” model was more appropriate for POEA films while “distributed” model was more appropriate for PANI films, at least if both films were formed and measured in presently described conditions.     

Equation of state for polymer solution

The flow pattern through a cloud of polymer segments is obviously different from the flow pattern around a solid object. It can be shown theoretically, however, that the partial viscosity due to the cloud can take the same value as for a solid sphere with the radius of gyration of the cloud as its radius. The specific viscosity of polymer solution has been derived as 2.5(c/c_I), with c_I being the internal concentration associated with a polymer molecule. The internal concentration is the ratio of mass over the volume of gyration of segments in a polymer chain. A radius of gyration exists for any type of polymers, flexible or rigid, exhibiting different kinds of dependence on the molecular weight. From the expression of the specific viscosity, the intrinsic viscosity is shown to be equal to 2.5/c^∗, c^∗ being the (minimum) internal concentration for the state of maximum conformational entropy. The equation for the specific viscosity, thus obtained, is expanded into a polynomial in c[η]. This formula is shown to agree with data for several kinds of polymers, with flexible, semi-rigid and rigid.The quantity 1/c_I can be interpreted as an expression for the chain stiffness. In polyelectrolytes, coulombic repulsive potentials affect the chain stiffness. The dependence of c_I on the effective population of polyions in the polyelectrolyte molecule is discussed.An equation of state for the polymer solution is formulated that included the internal concentration. The virial coefficients emerge as a result of c_I not always being equal to c^∗, and they are molecular weight dependent.     

Factors Affecting the Collision of Aerosol Particles with Small Water Drops

The factors influencing the collision of aerosol particles with small water drops at low collision efficiencies are examined. The gravitational force and velocity slip of air on the drop surface are found to affect the collision efficiency in the range of values of 10^?4–^?2. The efficacies of the different computational models are compared for ratios of particle radius to drop radius of less than 0.1. The accuracy of the numerical scheme in the trajectory model can be verified by comparing the efficiencies obtained for submicrometer particles with the convective-diffusion model.     

A new approach for computation of drop terminal velocity in stagnant medium

A new approach for solving the drop motion problem in a continuous medium is presented in this work. The classical curve of the terminal velocity was divided into two parts, named “A” left side and “B” right side. Such a division was done with respect to drop of minimal size with a maximal terminal velocity. In a first step, we focus on the large drops moving in air (part B), in which some approximation schemes can be used by taking advantage of the region's properties. An expression of the terminal velocity is derived using an analytic approach to the study of the motion of large liquid drops falling in air. Our formula agrees well with experiments for drops falling in air of part B. However, for drops of the part A, large differences are observed. In an attempt to deal with this shortcoming, our formula was extended to liquid drops falling in air in both parts. The equation is also tested on drops moving in water. We observe that it is only applicable to the drops of the part A. As far as the part B liquid drops in water are concerned, an analogy between the surface waves of an infinite medium and the free fall of drops is made and a more generalized formula is proposed. Good agreement was found between the present model and experimental data from the literature. An extension of the expression for air and water to other continuous media is attempted.     

Dehydration of red bell-pepper (Capsicum annuum L.): Change in drying behavior, colour and antioxidant content

The sun, oven (50 and 70 °C) and microwave oven (210 and 700 W) drying behaviors of red bell-pepper slices were investigated. Effects of these drying methods in terms of colour indices and antioxidant activity of pepper slices were also studied. “Midilli and Küçük” model exhibited high coefficient of determination (R²) values for all the drying methods used in the assay, ranging between 0.994-0.999, while “Page” and “Modified Page” models fit better for oven drying at 70 °C. The calculated effective diffusivity (D_eff) values (m²/s) of pepper slices for the drying processes ranged between 0.31 and 87.39 × 10⁻⁹. Sun dried and followed by microwave oven (700 W) dried samples revealed the highest L^*, a^* and b^* colour values than the other dried samples. Microwave oven dried (210 W) and oven dried (50 °C) samples exhibited the lowest TEAC and DPPH radical scavenging activities among the dried samples.     

Calculating liquid transport into high-performance concrete during wet freeze/thaw

A method for calculation of the liquid transport into high-performance concrete (HPC) during wet freeze/thaw exposure is proposed. This transport, or pumping effect, which is larger than absorption above 0 °C, is in the present calculation assumed to be caused by diffusion of water from the wet surface, through hardened cement paste (HCP) where water in nonfreezable, to large voids with very low vapour content. Saturated flow is assumed between the wet concrete surface and the active voids. Cranks solution for stationary transport into a hollow sphere of mean radius r? is combined with Powers spacing factor. The shell thickness is the mean void spacing factor (L?). The flow into voids was calculated (“good” vs. “bad” void system) for various maximum possible moisture potentials between wet surface, saturated HCP and active void (at 263 K and 1 atm; Δp=saturation pressure=260 Pa or Δv=moisture content=0.00215 kg/m³ in void, etc.). Realistic voids and diffusivity were used. The calculation fits with liquid uptake measured in wet freeze/thaw of HPC with exposed surface equal to the surface of the active voids. The lower the void content, the lower is the pumping effect. Nonstationary transport, further experiments and simulations are discussed briefly.     

A molecular dynamics study of short-chain ordering in crystalline LiPF6·PEO6

Molecular dynamics (MD) simulations have been made of the crystalline short-chain LiPF₆·PEO₆ system to probe structural ordering for different chain-end arrangements for a methyl-terminated monodisperse poly(ethylene oxide) (EO₂₃M_w = 1059) host polymer. Five different start structures have been studied, two “smectic” and three “nematic”, to represent different types of relative alignment of the end-groups between adjacent PEO chains, and different chain-end coordination situations to the Li-ions. One particular situation is found to result effectively in Li-ion bridging between PEO chains along the chain axes, thereby creating continuous ion transport pathways across the chain breaks. This situation is also found to give rise to Li⁺-PF₆⁻ ion-pairing and Li-O coordination instabilities in the end-group regions, where coordination to Li-ions would appear to have a more radical influence on local structure than the issue of smectic vs. nematic end-group alignment. It could be that such structural situations involving bridging Li-ions (in both smectic and nematic arrangements) are a necessary condition for the promotion of Li-ion transport in the chain direction. Comparison of simulated and experimental XRD profiles is concluded to be an inappropriately crude and uncertain technique for distinguishing between possible short-chain ordering models.     

Dispersion of water into oil in a rotor–stator mixer. Part 2: Effect of phase fraction

In Part 1 (Rueger and Calabrese, 2013), we monitored dilute water-in-oil dispersions in a batch Silverson L4R rotor–stator mixer to establish breakage mechanisms and develop a mechanistic basis for correlation of equilibrium mean drop size. In this study (Part 2) we consider the effect of water phase fraction under similar processing conditions, thereby requiring consideration of coalescence. Most of the work on the effect of phase fraction in stirred vessels was done with a low-viscosity continuous phase in turbulent flow with inertial subrange scaling (d > η). For that case drop size increases linearly with phase fraction, ?. In this study, viscous oils comprised the continuous phase, with water as the drop phase. The equilibrium DSD was measured in both laminar and turbulent flow conditions. The diameter of the largest drops was always less than the Kolmogorov microscale (d < η). A much greater increase (than the aforementioned linear relationship) in drop size with phase fraction was observed for ? ≤ 0.05; including cases where an oil soluble surfactant was present and where metal mixing head surfaces were rendered hydrophobic by treatment with silane functional groups. It is argued that this significantly greater dependence on ? is due to the flow field being locally laminar near the drops with coalescence rate being strongly affected by the collision efficiency, which depends on the viscosity of both phases. The presence of surfactant decreased drop size. The silane treatment decreased drop size; possibly by altering water drop interactions with mill head surfaces. Additional experiments were performed at higher phase fraction, where surfactant was required to stabilize the emulsion. The equilibrium drop size was found to plateau for 0.10 < ? < 0.50. The high phase fraction behavior is attributed to the competing rates of coalescence and breakage and their dependence on ? and drop size.     

Synthesis and characterization of well-defined poly(l-lactide) functionalized graphene oxide sheets with high grafting ratio prepared through click chemistry and supramolecular interactions

Two simple and effective methods, “click” chemistry and supramolecular interactions, are demonstrated here to synthesize well-defined poly(l-lactide) (PLLA) functionalized graphene oxide (GO) sheets. We provide a simple method to introduce azide groups on GO sheets by the ring opening reaction of sodium azide with the epoxide groups of GO. The GO-N₃ sheets can easily undergo “click” reaction with alkyne-terminated PLLA by “grafting onto” method to produce GO/PLLA composites with high grafting ratio and exfoliated structure. Interestingly, GO-N₃ can be grafted with oxygen-containing polymers such as PLLA, polymethyl methacrylate (PMMA) or polyethylene oxide (PEO) via supramolecular interactions between the azide groups and these oxygen atoms on polymers, producing GO/polymer composites with low grafting ratio and intercalated structure. These “grafting onto” methods are useful to produce a variety of GO/polymer composites with different structure via “click” reaction or supramolecular interactions, which have potential applications in material science.     

Break-up of a drop in a stirred tank

The drop break-up mechanism was studied in a stirred tank containing two immiscible liquids. The daughter drops formed by break-up of a single drop of known size were recorded photographically. From the experiments at constant agitator speed the following results were obtained. There is a critical drop size under which drops do not break up under given conditions. The break-up frequency increases approximately linearly with increase in drop volume. The number of daughter drops, v, is a random variable with a mean v > 2 which increases with the volume of the mother drop. The relative volume of a daughter drop has a β-distribution.     

The Rheology of Wetting By Polymer Melts

Theoretically, the rate of capillary penetration of a polymer melt into a slit, a model for a surface irregularity, has been shown to depend on γcosθ/η) where γ refers to the surface tension of the liquid, η its viscosity and θ a time-dependent contact angle. Analytical expressions relating the depth of penetration with time have been experimentally verified by observations of the penetration of molten polyethylene and poly-(ethylene-vinyl acetate) into aluminum channels. Values of η, calculated from the observed data, agree closely with independent determinations of this material parameter. A theoretical treatment has also been developed which describes the velocity of spreading of a liquid drop over a flat surface. Flow equations for the flow of free films were adapted for this purpose. The spreading velocity is predicted to depend on the product of three factors (1) a scaling factor, (γ/η1R_o), where R_o is the initial radius of curvature, (2) cosθ_∞. (l-cosθ/cosθ_∞) where θ_∞ refers to the equilibrium value of θ, and (3) geometric terms. After demonstrating that a drop of molten polymer may be treated as a spherical cap, the predicted dependence of spreading rate on drop size, cosθ_∞ (nature of the substrate) and the scaling factor was experimentally verified. Some discrepancies noted at long times and high temperatures are discussed.     

Constrained nonlinear optimization for solubility parameters of poly(lactic acid) and poly(glycolic acid)—validation and comparison

An optimization technique has been proposed to determine Hansen solubility parameters (HSP) and radius of interaction (R) of PLA and PGA; objective function to be minimized being radius of interaction (R), and the constraints being that the solvents should be within and nonsolvents outside the interaction sphere. The proposed method has been validated and found to be most reliable. The values of HSP (δ_d, δ_p, δ_h) and R for PLA have been obtained as ((18.50, 9.70, 6.00) and 10.50) (J/cc)^0.5 at 25 °C; and those of PGA as ((17.70, 6.21, 12.50) and 1.92) (J/cc)^0.5 at 80 °C. For formulating the nonlinear inequality constraints known HSP data for 20 solvents and seven nonsolvents have been used for PLA at 25 °C; similarly HSP data for three newly found solvents (phenol, m-cresol and 4-chlorophenol), and five nonsolvents have been used for PGA at 80 °C. Established methods have been used for comparison. HSP and R have been directly compared using the 3D intrinsic viscosity and classical methods. Indirectly the total solubility parameter δ has been compared with the values obtained from the intrinsic viscosity 1D approach and group contribution method using Fedors and van Krevelen correlations. The 1D approach has led to an empirical correlation for intrinsic viscosities of PLA and PGA.     

Dispersion of high-viscosity liquid-liquid systems by flow through SMX static mixer elements

The pressure drop and the dispersed phase drop size distribution have been measured for flow through SMX static mixer elements, in columns of diameter 41.18 and 15.75 mm, for a continuous phase of aqueous corn syrup and a dispersed phase of silicone oil. For single-phase flow the pressure drops were consistent with known literature correlations. In the presence of the dispersed phase the pressure drops were increased about 20% above the expected single-phase values, showing more short-term fluctuations but with no significant effect of the flow fraction of the dispersed phase. Droplet size distributions were measured by the computer-aided analysis of images from a digital camera. For shorter lengths of packing the distributions showed a significant “tail” at the large-diameter end, but as the packing length was increased the tail decreased or became non-existent. The mean drop sizes have been compared with a new model based on drop formation at equivalent point sources within the packing.