Drag force acting on an evaporating particle immersed in a rarefied plasma flow

Analytical expressions are presented for the drag force acting on an evaporating or nonevaporating particle immersed in a plasma flow for the extreme case of free-molecule flow regime and thin plasma .sheath. It is shown that the drag force on a spherical particle is proportional to the square of the particle radius and to the relative velocity between the particle and the bulk plasma at low speed ratios. The existence of a relative velocity between the particle and the plasma results in a nonuniform heat flux distribution with its rnaximum value at the frontal stagnation point of tire sphere. This nonuniform distribution of the local heat fux density causes a nonuniforrn distribution of the local evaporated-mass flux and vapor reaction force around the surface of an evaporating particle, and thus induces an additional force on the particle. Consequently, the drag force acting on art evaporating particle is always greater than that on a nonevaporating one. This additional drag force due to particle evaporation is more significant for nonmetallic particles and for particle materials with lower latent heat of evaporation and lower vapor molecular mass. It increases with increasing plasma temperature and with decreasing gas pressure at the high plasma temperatures associated with appreciable gas ionization. The drag ratio increases with increasing electron/heavy-particle temperature ratio at high electron temperatures for a two-temperature plasma.     

Modeling local flotation frequency in a turbulent flow field

Despite the significance of turbulent fluid motion for enhancing the flotation rate in several industrial processes, there is no unified approach to the modeling of the flotation rate in a turbulent flow field. Appropriate modeling of the local flotation (bubble-particle attachment) rate is the basic constituent for global modeling and prediction of flotation equipment efficiency. Existing approaches for the local flotation rate are limited to specific set of conditions like high or low turbulence. In addition, the combined effects of buoyant bubble rise and/or particle gravity settling are usually ignored. The situation is even vaguer for the computation of collision and attachment efficiencies which are usually computed using the gravity induced velocities although the dominant mode of flotation is the turbulent one. The scope of this work is clear: the development of a general expression for the flotation rate in a turbulent flow field which will cover in a unified and consistent way all possible sets of the problem parameters. This is achieved by using concepts from statistical approach to homogeneous turbulence and gas kinetic theory.     

Molecular interactions at the solid liquid interface with special reference to flotation and solid particle stabilized emulsions

Colloid and Polymer Science - The experiments carried out with a variety of pure surface active agents, employed in flotation of ores as either collectors or frothers, show that (a) long chain...     

Forces on a porous particle in an oscillating flow

We investigate theoretically forces acting on a porous particle in an oscillating viscous incompressible flow. We use the unsteady equations describing the creeping flow, namely the Stokes equations exterior to the particle and the Darcy or Brinkman equations inside it. The effect of particle permeability and oscillation frequency on the flow and forces is expressed via the Brinkman parameter beta = a/square root(k) and the frequency parameter Y = square root(a(2)omega/2nu) = a/delta, respectively. Here a is particle radius, k is its permeability, omega is the angular frequency, delta is the thickness of Stokes layer (penetration depth) and nu is the fluid kinematic viscosity. It is shown that the oscillations interact with permeable structure of the particle and affect both the Stokes-like viscous drag and the added mass force components.     

Influence of electrical double-layer interaction on coal flotation

In the early 1930s it was first reported that inorganic electrolytes enhance the floatability of coal and naturally hydrophobic minerals. To date, explanations of coal flotation in electrolytes have not been entirely clear. This research investigated the floatability of coal in NaCl and MgCl2 solutions using a modified Hallimond tube to examine the role of the electrical double-layer interaction between bubbles and particles. Flotation of coal was highly dependent on changes in solution pH, type of electrolyte, and electrolyte concentration. Floatability of coal in electrolyte solutions was seen not to be entirely controlled by the electrical double-layer interaction. Coal flotation in low electrolyte concentration solutions decreases with increase in concentration, not expected from the theory since the electrical double layer is compressed, resulting in diminishing the (electrical double layer) repulsion between the bubble and the coal particles. Unlike in low electrolyte concentration solutions, coal flotation in high electrolyte concentration solutions increases with increase in electrolyte concentration. Again, this behavior of coal flotation in high electrolyte concentration solutions cannot be quantitatively explained using the electrical double-layer interaction. Possible mechanisms are discussed in terms of the bubston (i.e., bubble stabilized by ions) phenomenon, which explains the existence of the submicron gas bubbles on the hydrophobic coal surface.     

On the force acting on a horizontal cylinder withdrawn from a liquid

Summary Analyses, reported in the literature on the capillary force resulting from the formation of a liquid meniscus, are examined in the light of a new rigorous mathematical treatment. Formal aspects are pointed out, emphasizing the consideration that surface mechanical properties should preferably be conceived as originating by virtue of the existence of a surface free energy rather than of a contractile skin.With 1 figure     

The force of interaction in a monomolecular film at low surface pressure

Summary The London-van der Waals attractive constant between methylene groups is experimentally determined from measurements of the constant and small surface pressure of a monomolecular film, assuming the formation of two dimensional micelles. Electrostatic repulsion is eliminated by subtracting the surface pressures for two surface active materials having the same polar groups but hydrocarbon chains of different lengths. Experimental values of the London-van der Waals attractive constant assuming a solid film are about 5 × 10^–59 erg cm⁶ which agrees well with the theoretical value.

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Zusammenfassung Die London-van der Waals-Anziehungskonstante zwischen Methylengruppen wird experimentell über Messungen des konstanten Oberflächendruckes eines monomolekularen Films bestimmt, wobei man die Bildung von zweidimensionalen Micellen annimmt. Die elektrostatische Abstoßung wird eliminiert, indem man die Oberflächendrucke von zwei grenzflächenaktiven Substanzen, welche sich nur durch die verschieden langen Kohlenstoffketten unterscheiden, voneinander subtrahiert. Experimentelle Werte der London-van der Waals-Anziehungskonstanten ergeben bei der Annahme eines festen Films ungefähr 5 × 10^–59 erg cm⁶, in guter Übereinstimmung mit theoretischen Werten.

     

Thermophoretic force acting on an evaporating particle suspended in a rarefied plasma

Analytical results of the thermophoretic force on an evaporating spherical particle immersed in a rarefied plasma with a large temperature gradient are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the existence of a temperature gradient in the plasma causes a nonuniform distribution of the local heat flux density on the sphere surface with its maximum value at the fore-stagnation point of the sphere, although the total heal flux to the whole particle is independent of the temperature gradient existing in the plasma. This nonuniform-distribution of the local heat flux density causes a nonuniform distribution of the. local evaporated-mass flux and related reaction force around the surface of an evaporating particle, and thus causes an additional force on the particle. Calculated results show that the thermophoretic force on an evaporating particle may substantially exceed that on a nonevaporating one, especially for the case of a metallic particle (with infinite electric conductivity). The effect of evaporation on the thermophoretic force is more pronounced as the evaporation latent heat of the particle material is comparatively low and as high plasma temperatures are involved.     

Drag force on a rigid spheroidal particle in a cylinder filled with Carreau fluid

The boundary effect on the drag acting on a rigid particle is investigated by considering a spheroid on the axis of a cylinder filled with a Carreau fluid. The result of numerical simulation reveals that the ratio (drag coefficient in Carreau fluid/drag coefficient in Newtonian fluid) has a maximum as the ratio (semiaxis in radial direction/radius of cylinder) varies. The presence of a wall has the effect of enhancing the convective motion in the rear part of a particle, and therefore, the formation of wakes. The influence of the shape of a particle on the drag force acting on it can be decreased either by increasing the shear-thinning effect of the fluid or by increasing the Reynolds number. The Reynolds number at which flow separation occurs is found to increase roughly linearly with the increase in the power-law exponent of the Carreau fluid.     

Calculation of the diffusion coefficient in a liquid based on the force covariance function

Methods of optimal use of statistical information on the Brownian motion of molecules in a liquid for calculating the diffusion coefficient are considered. Relationships between covariance functions for the displacement of a molecule, its velocity, and the force acting on the molecule are established. It is proposed the method of calculation of the diffusion coefficient estimates should be made using the force covariance function, which enables to reduce the time of simulation of the molecular motion. The proposed method is used for callculating diffusion coefficients for some systems.     

The interaction of monosubstituted benzenes with the stationary liquid in gas liquid chromatography

In gas liquid chromatography (GLC), the relative retention values log gamma was mainly expressed by van der Waals energy (the sum of the dispersion E(dis) and repulsive E(rep) energies) to the interactions between monosubstituted benzene derivatives and the nonpolar stationary liquid as squalane. The single exception was that of anilines, and it was corrected by the electrostatic energy (E(ES)) due to C-H/pi hydrogen bond. When the stationary liquid changed from the nonpolar to polar, log gamma was estimated by the inductive interaction energy (included in E(ES)) in addition to the sum of E(dis) and E(rep). In the benzene solution, the relative equilibrium values log K/K(o) introduced from the interactions between phenol and substituted benzene derivatives were estimated by E(ES). The E(ES) of COCH(3), CO(2)C(2)H(5) groups is especially originated in the excited dipole moments micro(e). The relative frequency values log nu/nu(o) derived from O-H or O-D stretching vibration of phenol or methanol-D gave the correlation to E(ES) as well as log K/K(o). That of anilines-methanol-D however had been out of a linear relation to E(ES). The cause is concluded that the aniline-methanol-D is making the proton transfer structure from the discussion about the proton affinity (PA) of the base.     

The influence of wettability on the equilibrium wall flow of liquid in a packed column

It is well known that when a packed column is irrigated by a liquid and is operated in the trickle flow regime, part of the liquid flows preferentially along the column wall. The liquid distribution reaches equilibrium if the column is tall enough. In the present study the equilibrium wall flow in a column packed with rasching rings was studied experimentally. The effects of the wettability of the wall and the packing, and the total liquid flow rate on the equilibrium wall flow were investigated. It was found that the equilibrium wall flow depends strongly on the wettability of the wall, but is almost independent of the wettability of the packing. These results were used to gain some insight into the mechanism of the development of wall flow in packed columns.     

Drag on a nanotube in uniform liquid argon flow

In this work, nonequilibrium molecular dynamics (MD) simulations were performed to investigate uniform liquid argon flow past a carbon nanotube. In the simulation, nanotubes were modeled as rigid cylinders of carbon atoms. Both argon-argon and argon-carbon interactions were calculated based on Lennard-Jones potential. Simulated drag coefficients were compared with (i) published empirical equation which was based on experiments conducted with macroscale cylinders and (ii) finite element (FE) analyses based on Navier-Stokes equation for flow past a circular cylinder using the same dimensionless parameters used in MD simulations. Results show that classical continuum mechanics cannot be used to calculate drag on a nanotube. In slow flows, the drag coefficients on a single-walled nanotube calculated from MD simulations were larger than those from the empirical equation or FE analysis. The difference increased as the flow velocity decreased. For higher velocity flows, slippage on the surface of the nanotube was identified which resulted in lower drag coefficient from MD simulation. This explains why the drag coefficient from MD dropped faster than those from the empirical equation or FE simulation as the flow velocity increased. It was also found that the drag forces are almost equal for single- and double-walled nanotubes with the same outer diameter, implying that inner tubes do not interact with fluid molecules.     

Thermophoretic force on a metallic or nonmetallic particle immersed into a rarefied Plasma

Analytical results of the thermophoretic force on a metallic or nonmetallic spherical particle immersed into a rarefied plasma with a heat flux within the plasma are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the thermophoresis is predominantly caused by atoms at low plasma temperatures with negligible gas ionization, while it is mainly due to ions and electrons at high plasma temperatures with great degree of ionization. The ion flux incident to a particle is constant on the whole sphere surface, while the electron flux to the metallic sphere is dependent on the -position with slightly greater value at the fore stagnation point. Consequently, there is a small difference between the metallic and nonmetallic spheres in their -distributions of the floating potential on the surface, which causes the thermophoretic force on a nonmetallic sphere to be appreciably greater than that on a metallic sphere at high plasma temperatures. Expressions for the total thermophoretic force on a metallic sphere and its components due to, respectively, atoms, ions, and electrons have been given in a closed form. Calculated results are also presented on the effects of pressure and of electron/heavy-particle temperature ratio. These results can be understood based on the variation of atom, ion, and electron thermal conductivities with the gas pressure, the temperature, and the temperature ratio.     

Paper on a disc: balancing the capillary-driven flow with a centrifugal force

This paper describes the active control of the capillary-driven flow in paper using a centrifugal device.     

The rupture of a liquid layer by solutocapillary flow

The development of a strong deformation of the surface of a thin viscous liquid layer on a horizontal wettable substrate is experimentally studied. The deformation develops owing to a concentration-induced surface tension gradient that appears as a result of the deposition of a droplet of a soluble surface-active liquid onto the free surface of the layer. The conditions under which the viscous liquid layer is ruptured and the place beneath which the spreading droplet becomes partly uncovered are studied. For different pairs of liquids, the dependences of the radius of the dry spot on time, on the volume of a deposited droplet, on the horizontal sizes and thickness of the layer, and on the difference between the surface tensions of the droplet and the layer are obtained. It is shown that the rupture occurs at an appreciably larger initial thickness of the liquid layer than in the case of thermocapillarity. The critical thickness of the layer, at which its deformation reaches the substrate, is virtually independent of the amount of the deposited surfactant and is determined mainly by the surface tension gradient on the surface.     

Single particle force distributions in simple fluids

The distribution function, W(F), of the magnitude of the net force, F, on particles in simple fluids is considered, which follows on from our previous publication [A. C. Bran?ka, D. M. Heyes, and G. Rickayzen, J. Chem. Phys. 135, 164507 (2011)] concerning the pair force, f, distribution function, P(f), which is expressible in terms of the radial distribution function. We begin by discussing the force on an impurity particle in an otherwise pure fluid but later specialize to the pure fluid, which is studied in more detail. An approximate formula, expected to be valid asymptotically, for W(F) referred to as, W(1)(F) is derived by taking into account only binary spatial correlations in the fluid. It is found that W(1)(F) = P(f). Molecular dynamics simulations of W for the inverse power (IP) and Lennard-Jones potential fluids show that, as expected, W(F) and P(f) agree well in the large force limit for a wide range of densities and potential forms. The force at which the maximum in W(F) occurs for the IP fluids follows a different algebraic dependence with density in low and high density domains of the equilibrium fluid. Other characteristic features in the force distribution functions also exhibit the same trends. An exact formula is derived relating W(F) to P(x)(F(x)), the distribution function of the x-cartesian components of the net force, F(x), on a particle. W(F) and P(x)(F(x)) have the same analytical forms (apart from constants) in the low and high force limits.     

Direct measurement of the force between solid surfaces in a polar liquid

The force between mica sheets in a polar liquid (propylene carbonate) with various electrolyte concentrations is found to be the sum of an electrostatic double-layer force, accurately described by Gouy—Chapman theory, and a short-range oscillatory salvation force, qualitatively similar to that found in non-polar liquids.     

The characterisation of rough particle contacts by atomic force microscopy

An Atomic Force Microscopy (AFM) reverse imaging technique has been used to determine the contact zone topography of glass and UO3 particles in contact with flat mica substrates. A method is proposed that uses this topography to determine an effective asperity radius of curvature for the contacting particle. Application of the method has been found to be consistent with established contact mechanics models, for both glass and UO3 particle probes that present significantly different surface roughness. The method proposed is straightforward to apply and offers a greater insight into the influence of particle micro- and nano-roughness on adhesion. This is important for applications that rely on the control of granular flow such as pellet or tablet manufacture.     

Drag force of a particle moving axisymmetrically in open or closed cavities

Hydrodynamic resistance to particle transport arising from the solid mass in porous media is of fundamental importance. We investigate an axisymmetric creeping flow caused by a spherical particle migrating in a spherical cavity or connected cavities of equal size by a boundary element method. Each cavity has either one or two circular apertures, through which a sufficiently small particle can pass. Drag force on the particle is calculated to determine the correction factor to the Stokes law. It is found that when passing through an aperture, the particle experiences a local maximum drag force larger than that located in the cavity center. This force is also greater than that for the particle near the closed end at the same smallest surface-to-surface distance. For connected cavities open to the exterior fluid, the drag force is smaller than that in the corresponding closed system.