Adhesion of solid particles to gas bubbles. Part 2: Experimental

In slurry bubble columns, the adhesion of solid catalyst particles to bubbles may significantly affect the G-L mass transfer and bubble size distribution. This feature may be exploited in design by modifying the hydrophilic or hydrophobic nature of the particles used. Previously we have proposed a generalised model, describing the adhesion of particles to G-L interface under stagnant conditions. In this work, we studied the adhesion of particles characterised by different degree of hydrophobicity and porosity: non-porous polystyrene and glass beads, unmodified and hydrophobised mesoporous silica, and activated carbon particles. Images recorded at high optical magnification show the particles adhering to gas bubbles individually or as aggregates. In aqueous media, higher liquid surface tension and particle surface hydrophobicity increase the adhesion strength and the tendency of particles to agglomerate, in agreement with the model. The adhesion of non-porous rough-surface particles to gas bubbles can be characterised by the receding contact angle. The advancing contact angle represents better the adhesion of the same particles to liquid droplets. We found that the “effective” contact angle of porous particles is much lower than an “intrinsic” contact angle calculated from the heat of immersion in water, or measured by sessile drop method. An equivalent contact angle derived from the Cassie rule explains the wetting behaviour of particles having the pores filled with liquid.     

Equilibrium shape and contact angle of sessile drops of different volumes—Computation by SPH and its further improvement by DI

Equilibrium shapes of sessile liquid drops over horizontal substrates are modeled using smoothed particle hydrodynamics (SPH). The model can predict the variations of shape and contact angle of drops as a function of drop volume. In the model, a scheme of repositioning the particle at the triple line has been incorporated to attain the in situ contact angle. The simulations show a reasonable match with available analytical results. However, some mismatch of the drop shape near the three-phase contact line is observed. To improve the predictability, combined diffused interface smoothed particle hydrodynamics model (Das and Das, 2009b) is employed. The developed hybrid simulations improve the prediction. Estimated drop shapes and contact angle agree with experimental data reasonably well over a wide range of fluid properties and drop volume. The technique establishes the suitability of a particle-based hydrodynamic simulation for the modeling of complex interfaces and three-phase contact lines.     

Some surface tension and contact angle problems in industry

Contact angle, surface tension and wetting properties are of fundamental importance in many industrial processes, e.g. coating of television screens and fluorescent lights. In addition, different stages of many processes may involve immersion cleansing and subsequent drying. We consider two different problems: one being very practical and involving cleansing and drying of silicon substrates in the semiconductor industry, and the other being theoretical whereby the problem of the shape of scssile and pendant drops is addressed with a possible practical application for making contact angle and surface tension measurements. In the case of cleansing of silicon substrates, we model a process whereby dirt particles are removed as a result of the surface tension forces exerted on a particle passing through a water/air interface and give a possible explanation as to why the efficiency of the process is vclocity dependent. For the case of small liquid drops, a new formulation of the governing equation yields solutions for multiple pendant and extended sessile drops.     

Anisotropic Wetting of Liquids on Finely Grooved Surfaces

A photolithographically-prepared, parallel-grooved surface on silica has been employed as a model to study the influence of roughness on the spreading equilibrium of liquid drops. The equations generated by Oliver, Huh and Mason for cylindrically shaped drops were extended to account for wetting by liquid crystals. The observed drop shapes were dependent upon surface roughness. The equilibrium contact angles on a smooth surface can be calculated from the roughness, contact angles both parallel and perpendicular to the grooves, and the drop shape. Reasonably good agreement with experimental contact angles was obtained.     

Use of NMR imaging to measure interfacial properties of asphalts

An NMR imaging method that allows for direct calculation of interfacial surface tensions of asphalts is described. The method is based upon acquiring NMR images of water drops on the surface of asphalt as a function of time. By expressing the contact angle for the water drop either in terms of Young's equation, or the liquid lens equation for the initial placement of the water drop on the asphalt surface, and for a later time when the water drop has penetrated below the asphalt surface, two equations that incorporate the asphalt-air surface and asphalt-water interfacial tensions are obtained which can be solved analytically. The NMR imaging method was used to determine the surface tensions of the eight Strategic Highway Research Program (SHRP) core asphalts at 25 °C. Asphalt-water interfacial tension values ranged from 25 to 40 dynes/cm, and asphalt-air surface tension values ranged from about 38-50 dynes/cm. These results are in general agreement with other asphalt surface tension measurements that have been made using the du Noüy ring tensiometer, or the Wilhelmy Plate method. Spreading coefficients and capillary numbers derived from the surface tension calculations are also reported.     

Determination of the peripheral contact angle of sessile drops on solids from the rate of evaporation

A method was developed to determine the initial peripheral contact angle of sessile drops on solid surfaces from the rate of drop evaporation for the case where ₁ < 90°. The constant drop contact radius, the initial weight, and the weight decrease with time should be measured at the ambient temperature for this purpose. When water drops are considered, the relative humidity should also be known. The peripheral contact angle so obtained is regarded as the average of all the various contact angles existing along the circumference of the drop. Thus, each determination yields an average result not unduly influenced by irregularities at a given point on the surface. In addition, the error in personal judgment involved in drawing the tangent to the curved drop profile at the point of contact can be eliminated. The application of this method requires the use of the product of the vapor diffusion coefficient with the vapor pressure at the drop surface temperature. This product can be found experimentally by following the evaporation of fully spherical liquid drops.     

A revised surface tension model for macro-scale particle methods

A simple treatment for surface tension in immiscible fluids is proposed for macro-scale particle methods such as smoothed particle hydrodynamics (SPH) and macro-scale pseudo-particle modeling (MaPPM). By introducing a repulsion between the neighboring particles of different fluids, surface tension arises automatically, while simple equations of state are still possible for each phase. This treatment is validated by comparative simulations on the deformation of a square liquid drop in suspension using the volume of fluid (VOF) method. The relationship between surface tension and the repulsion intensity parameter in our model is obtained by the sessile drop method.     

Interfacial tension from the height and diameter of sessile drops and captive bubbles with an arbitrary contact angle

A method has been developed to calculate the interfacial tension of sessile drops and captive bubbles of arbitrary contact angle by measuring the drop diameter and vertical distance to the apex at arbitrary horizontal planes within the drop. The procedure works in theory for any contact angle with an accuracy on the order of 0.1%. However, practical limitations reduce the range of angles to roughly 50°–180° but do not restrict the range of interfacial tensions (at least 0.01 mJ/m² to 72.0 mJ/m²). The optimal strategy is to use the method at several points on a single drop and to calculate the mean and standard deviation of the resulting interfacial tensions.     

Phenomenological theory of depth membrane filtration

A phenomenological theory of depth membrane filtration (DMF), in which outside-in hollow fiber membranes are used as collectors of colloidal particles, is developed to study the performance of a hollow fiber membrane filter with two product streams, permeate (clarified liquid that passed through semipermeable membrane) and filtrate (clarified liquid due to the collection of suspended particles on the external surface of hollow fibers). The theory is based on the general phenomenological expression for the rate of particle deposition on the membrane surface, in which the deposition rate is proportional to the product of the particle deposition coefficient and the concentration of suspended particles, with the deposition coefficient being an arbitrary function of the mass of deposited particles and permeate velocity. The system of governing equations is solved by the generalized Crank-Nicholson finite-difference method and the approximate method using the averaging of the permeate velocity in the mass conservation equation. The effect of membrane permeability on the filter productivity is studied. It is shown that the approximate solution can be used as a relatively simple and accurate tool to study and design hollow fiber filters for DMF.     

粗糙固体平面上液滴的接触角滞后的简单流体静力学模型

The phenomenon of hysteresis of contact angle is an important topic subject to a long time of argument.A simple hydrostatic model of sessile drops under the gravity in combination with an ideal surface roughness model is used to interpret the process of drop volume increase or decrease of a planar sessile drop and to shed light on the contact angle hysteresis and its relationship with the solid surface roughness. With this model, the advancing and receding contact angles are conceptually explained in terms of equilibrium contact angle and surface roughness only,without invoking the thermodynamic multiplicity. The model is found to be qualitatively consistent to experimental observations on contact angle hysteresis and it suggests a possible way to approach the hysteresis of three-dimensional sessile drops.     

Influence of Polymeric Suspension Characteristics on the Particle Coating in a Spouted Bed

Abstract

The influence of the coating suspensions and particle properties on the coating process in a conventional spouted bed is presented. Glass beads were coated at fixed operating conditions with different formulations of aqueous polymeric coating suspensions in a spouted bed of laboratory scale. The wettability of the solids by the liquid was quantified by the contact angle and surface tension of the coating suspensions. The coating efficiency and particle growth were correlated with the adhesion of the coating suspension to the solid particle, which is a function of the solids and liquid characteristics. The physical properties of the coated particles—particle mean diameter, sphericity, bulk, absolute and apparent densities, porosity and flow velocity—were determined and compared to the properties of uncoated particles.     

Particle Adhesion to Drops

The adhesion of spheroidal particles to spherical drops is calculated and discussed in terms of an equilibrium-penetration index. The present study emphasizes the case of particles that are sufficiently large to affect the drop volume upon penetration. It is shown that the more elongated the particles, the steeper the dependence of the penetration index on the contact angle. The effect of line tension on nanoscale particles is considered. Positive line tensions increase the steepness of the dependence of penetration index on contact angle whereas negative line tensions decrease this dependence. In addition, the energy barrier caused by positive line tensions is presented and discussed.     

Particle Adhesion to Drops

The adhesion of spheroidal particles to spherical drops is calculated and discussed in terms of an equilibrium-penetration index. The present study emphasizes the case of particles that are sufficiently large to affect the drop volume upon penetration. It is shown that the more elongated the particles, the steeper the dependence of the penetration index on the contact angle. The effect of line tension on nanoscale particles is considered. Positive line tensions increase the steepness of the dependence of penetration index on contact angle whereas negative line tensions decrease this dependence. In addition, the energy barrier caused by positive line tensions is presented and discussed.     

Experimental determination of capillary forces by crushing strength measurements

Mechanisms that lead to powder agglomeration are in many cases controlled by capillary forces. Indeed, in the earliest stage of agglomeration, minute amounts of liquid join solid particles by liquid bridges. Spontaneous formation of the bridge at contact points is caused by capillary condensation. Depending on solid/liquid interactions, particularly contact angle and spreading, liquid bridges may attract or repel individual particles. Undesired agglomeration may appear during storage and is called caking. On the other hand, powder agglomeration process is often required, for example, in enlargement of the particle size, i.e. granulation. A simple experimental device, designed from usual caking tests, was developed in order to estimate capillary forces transmitted by attracting liquid bridges joining particles. Crushing strength of wet cylindrical agglomerates was estimated. Influence of the low saturations of the void space (0<S<25%) and the surface tension of a liquid have been investigated. A normalised force which does not depend on the surface tension contribution has been calculated from experimental measurements and compared to Rumpf's model. It is possible to roughly estimate the solid/liquid contact angle by comparison with the model.     

The Apparent Contact Angle of Liquids on Finely-Grooved Solid Surfaces-A SEM Study

A finely parallel-grooved nitrocellulose surface has been employed as a model to study by scanning electron microscopy the influence of roughness on the spreading equilibrium of liquid drops. The Cassie and Baxter equation for spherical drops on a composite interface was experimentally confirmed with mercury and a similar equation derived for a cylindrical drop has also been shown to be approximately valid for liquid polyphenylether. The observed drop shapes have been explained and the importance of groove edges demonstrated.

Direct measurements of the microscopic contact angle of mercury locally on the grooved surfaces were found to be approximately the same for the smooth ungrooved surface.     

Evaluation of surface energy of solid polymers using different models

In the present work, contact angles formed by drops of diethylene glycol, ethylene glycol, formamide, diiodomethane, water, and mercury on a film of polypropylene (PP), on plates of polystyrene (PS), and on plates of a liquid crystalline polymer (LCP) were measured at 20°C. Then the surface energies of those polymers were evaluated using the following three different methods: harmonic mean equation and geometric mean equation, using the values of the different pairs of contact angles obtained here; and Neumann's equation, using the different values of contact angles obtained here. It was shown that the values of surface energy generated by these three methods depend on the choice of liquids used for contact angle measurements, except when a pair of any liquid with diiodomethane was used. Most likely, this is due to the difference of polarity between diiodomethane and the other liquids at the temperature of 20°C. The critical surface tensions of those polymers were also evaluated at room temperature according to the methods of Zisman and Saito using the values of contact angles obtained here. The values of critical surface tension for each polymer obtained according to the method of Zisman and Saito corroborated the results of surface energy found using the geometric mean and Neumann's equations. The values of surface energy of polystyrene obtained at 20°C were also used to evaluate the surface tension of the same material at higher temperatures and compared to the experimental values obtained with a pendant drop apparatus. The calculated values of surface tension corroborated the experimental ones only if the pair of liquids used to evaluate the surface energy of the polymers at room temperature contained diiodomethane. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 1831–1845, 2000     

Influence of Polymeric Suspension Characteristics on the Particle Coating in a Spouted Bed

The influence of the coating suspensions and particle properties on the coating process in a conventional spouted bed is presented. Glass beads were coated at fixed operating conditions with different formulations of aqueous polymeric coating suspensions in a spouted bed of laboratory scale. The wettability of the solids by the liquid was quantified by the contact angle and surface tension of the coating suspensions. The coating efficiency and particle growth were correlated with the adhesion of the coating suspension to the solid particle, which is a function of the solids and liquid characteristics. The physical properties of the coated particles—particle mean diameter, sphericity, bulk, absolute and apparent densities, porosity and flow velocity—were determined and compared to the properties of uncoated particles.     

La flottation de spheres et de cylindres

A study is made of the maximum weight of spherical and cylindrical particles which can be supported by a pendant bubble and at an infinite fluid/liquid interface. The maximum weight increases with the radius, the contact angle (measured through the lower fluid), the density difference between the two fluids and the interfacial tension. It follows that to ensure good flotation suface active agents must be added to increase the contact angle. The maximum particle weight which can be supported at an infinite interface is always greater than that which can be transported there by the pendant bubble.     

On the Predominant Electron-Donicity of Polar Solid Surfaces

The reasons for the predominant electron-donicity of almost all solid polar surfaces and its implications are discussed in this paper. By contact angle or interfacial tension measurements, the electron-accepting as well as the electron-donating properties of polar liquids can be ascertained, through the interplay between their energies of adhesion and cohesion. For the solid-liquid interface, direct interfacial tension measurements are not possible, but indirectly, solid/liquid interfacial tensions of polar systems can be obtained by contact angle measurement. However, as the energy of cohesion of a solid does not influence the contact angle formed by a liquid drop placed upon its surface, one can only measure the solid surface'ks residual polar property, manifested by the energy of adhesion between solid and liquid. This residual polar property is of necessity the dominant component; in most cases this turns out to be its electron donicity. When, by means of contact angle measurements with polar liquids, both electron-accepting and electron-donating potentials are found on a polar solid, it is most likely still partly covered with a polar liquid: usually water. The amount of residual water of hydration of a polar solid follows from its polar (Lewis acid-base) surface tension component (γ^AB). The degree of orientation of the residual water of hydration on a polar solid can be expressed by the ratio of the electron-donating to electron-accepting potentials (γ^⊖/γ^⊕), measured on the hydrated surface.