Model calculations for capillary condensation

Melrose, J.C.

doi:10.1002/aic.690120526

Cited by 164 publications

(88 citation statements)

References 23 publications

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“…The meniscus force between two spheres has been calculated numerically [136,[140][141][142] and with the toroidal approximation [120,143,144]. For a sphere of radius R which is a distance D away from a planar surface the meniscus forces is [145] …”

Section: Calculation Of Meniscus Force For Fundamental Geometriesmentioning

confidence: 99%

On the Adhesion between Fine Particles and Nanocontacts: An Atomic Force Microscope Study

et al. 2006

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To optimize the handling of fine powders in industrial applications, understanding the interaction forces between single powder particles is fundamental. The forces between colloidal particles dominate the behavior of a great variety of materials, including paints, paper, soil, and many industrial processes. With the invention of the atomic force microscope (AFM), the direct measurement of the interaction between single micron-sized particles became possible. The adhesional contact between a particle and a substrate is a parameter for analyzing pull-off force data generated by AFM. The aim of this study was to understand surface interactions between fine particles. I measured the adhesion forces between AFM tips or particles attached to AFM cantilevers and different solid samples. Smooth and homogeneous surfaces such as silicon wafer, mica, or highly oriented pyrolytic graphite (HOPG), and more rough and heterogeneous surfaces such as iron particles or patterns of TiO 2 nanoparticles on silicon wafer were used. First, I addressed to the wellknown issue that AFM adhesion experiment results show wide distributions of adhesion forces rather than a single value. My experimental results show that variations in adhesion forces comprise fast (i.e., from one force curves to the next) random fluctuations and slower fluctuations, which occur over tens or hundreds of consecutive measurements. Slow fluctuations are not likely to be the result of variations in external factors such as lateral position, temperature, humidity, and so forth because those were kept constant. Even if two solid bodies are brought into contact under precisely the same conditions (same place, load, direction, etc.) the result of such a measurement will often not be the same as for the previous contact. The measurement itself will induce structural changes in the contact region which can change the value for the next adhesion force measurement.In the second part I studied the influence of humidity on the adhesion of nanocontacts. Humidity was adjusted relatively fast to minimize tip wear during one experiment. For hydrophobic surfaces, no signification change of adhesion force with humidity was observed. Adhesion force-versus-humidity curves recorded with hydrophilic surfaces either showed a maximum or continuously increased. I demonstrate that the results can be interpreted with simple continuum theory of the meniscus force. The meniscus force is calculated based on a model that includes surface roughness and takes into account different AFM tip (or particle) shapes by a two-sphere-model.Experimental and theoretical results show that the precise contact geometry has a critical influence on the humidity dependence of the adhesion force.Changes of tip geometry on the sub-10-nm length scale can completely change adhesion force-versus-humidity curves. Our model can also explain the differences between earlier AFM studies, where different dependencies of the adhesion force on humidity were observed.Keywords: Atomic force microscopy (AFM), cantile...

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Section: Calculation Of Meniscus Force For Fundamental Geometriesmentioning

confidence: 99%

On the Adhesion between Fine Particles and Nanocontacts: An Atomic Force Microscope Study

et al. 2006

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“…Depending on their interests, they looked at the solutions of the problem in terms of liquid volumes (i.e., liquid contents), meniscal areas, meniscal curvatures, or forces exerted on the solid surfaces by the pendular ring. For instance, volumes were of concern in calculations of water saturation in soils (Haines, 1925;Fisher, 1926); curvatures were crucial to the study of capillary condensation or evaporation in porous materials (Melrose, 1966); forces were of special interest in liquid-phase sintering (Heady and Cahn, 1970), or in the study of deformation of moist soils (Haines, 1925) or in the depen-dence of the bulk mechanical properties of powders upon humidity (Coughlin et al, 1982).…”

Section: Introductionmentioning

confidence: 99%

“…Following routine simplifications, the free energy for a single-component condensate can be written (Melrose, 1966),…”

Section: Introductionmentioning

confidence: 99%

Calculations of the Equilibrium Vapor Pressure of Water over Adhering 50–200-nm Spheres

Crouzet

Marlow

1995

Aerosol Science and Technology

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Treatments of condensation on aerosols generally assume the particles to be spherical implying that the condensate presents a positively curved surface to the surrounding vapor. In contrast, the region between two adhering spheres supports a pendular ring of condensation which may result in a condensate-vapor interface with negative curvature. According to the Kelvin equation, the equilibrium vapor pressure over such surfaces is depressed relative to a planar surface and therefore the substrate particle shows entirely different condensational characteristics than for an isolated sphere of similar size and composition to the adhering spheres. In this paper, literature results are utilized to develop general approaches to the calculation of the curvature of the pendular ring of condensation between two macroscopic spheres (radii > 10 nm) that may differ in size and composition. Results of calculations for specific cases are given for spheres of 50, 100, and 200 nm and for a range of condensate-substrate contact angles. Illustrative examples of critical supersaturations are calculated and dimensionless mean curvature graphs that can be used for computations of the critical supersaturations for adhering spheres of different size and composition are presented. These calculations indicate that even somewhat hydrophobic adhering spheres may be capable of activation as cloud condensation nuclei a t the moderate supersaturations encountered in the atmosphere.

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“…Therefore, they are not applicable in a separation process such as centrifugation where the body force plays an important rule. Moreover, the consideration of liquid bridge volume in previous studies (Simons et al, 1994;Smith et al, 1930;Kruyer, 1958;Mehrotra and Sastry, 1980;Mason and Clark, 1965;Rose, 1958;Melrose, 1966) was just the liquid holdup volume for the given filling angle and not the maximum liquid hold up at equilibrium.…”

Section: Brazilian Journal Of Chemical Engineeringmentioning

confidence: 99%

Capillary holdup between vertical spheres

Heris¹,

Mosavian²,

White

2009

Braz. J. Chem. Eng.

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-The maximum volume of liquid bridge left between two vertically mounted spherical particles has been theoretically determined and experimentally measured. As the gravitational effect has not been neglected in the theoretical model, the liquid interface profile is nonsymmetrical around the X-axis. Symmetry in the interface profile only occurs when either the particle size ratio or the gravitational force becomes zero. In this paper, some equations are derived as a function of the spheres' sizes, gap width, liquid density, surface tension and body force ( gravity/centrifugal) to estimate the maximum amount of liquid that can be held between the two solid spheres. Then a comparison is made between the result based on these equations and several experimental results.

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Model calculations for capillary condensation

Cited by 164 publications

References 23 publications

On the Adhesion between Fine Particles and Nanocontacts: An Atomic Force Microscope Study

On the Adhesion between Fine Particles and Nanocontacts: An Atomic Force Microscope Study

Calculations of the Equilibrium Vapor Pressure of Water over Adhering 50–200-nm Spheres

Capillary holdup between vertical spheres

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