K. Malysa

Creeping flow over a composite sphere: Solid core with porous shell

Abstract Creeping flow past a solid sphere with a porous shell has been solved using the Stokes and Brinkman equations. The dimensionless solid core and shell radii, normalized by the square root of the shell permeability, are the two parameters that govern the flow. In the limiting cases, the analytical solution describing the flow past the composite sphere reduces to that for flow past a solid sphere and a homogeneous porous sphere. The settling rates of a solid sphere with attached threads are measured experimentally. This system can be considered a model for rigid linear molecules anchored or adsorbed onto a colloidal particle. The analytical solution for the composite sphere is in excellent agreement with the experimental results.

Wet foams: Formation, properties and mechanism of stability

Abstract Overall picture of phenomena occuring during formation and existence of the wet foams is presented. Properties and mechanism of stability are discussed on the example of the wet foams obtained from solutions of two homologous series of surface active substances; the fatty acids and n-alkanols. In general three physical processes which contribute to foam stability can be distinguished: drainage of liquid out of the foam, coalescence and/or rupture of bubbles, and disproportionation (which may be called Ostwald ripening or gas diffusion from one bubble to another). Dynamic and non-equilibrium character of the wet foams is stressed. Motion of a bubble through the solution causes disequilibration of the surface concentration alongside the bubble surface. The surface concentration on the upstream part of the bubble is much smaller than the equilibrium concentration. Thus, the bubbles arrive at the solution surface with non-equilibrium surface concentration, and these actual non-equilibrium surface coverages determine possibility of formation and properties of the foams. Solution content ϕ in the volume of wet foam is high (of an order 307.), while in top foam layer it is much smaller (ϕ≅5%) . It shows that rupture of the wet foam takes place practically only in the top layer of bubbles and durability of these top foam films determine stability and volume of the whole foam column. On the basis of measurements of liquid content ϕ and lifetimes of bubbles in the top foam layer it was estimated that thicknesses of rupture of these top films were of an order of a few micrometers. At such thicknesses the force of disjoining pressure do not attain yet any meaningful value. Influence of kinetics of adsorption, frequency of external disturbances, surface activity of the solute and lifetime of the foam films on magnitude of the surface elasticity forces induced in the systems studied is discussed. It is shown that stability of the wet foams can be explained in terms of the effective elasticity farces, i.e. the surface elasticity forces which are induced at an actual non-equilibrium surface coverage. There is agreement between the courses of the dependences of the foamability parameter (retention time, rt) and the effective elasticity forces as a function of the number n of carbon atoms in the fatty acid and n-alkanol molecule. This shows that the effective elasticity forces are decisive parameter in formation and stability of the wet foams. It also explains why the foamability of a substance with a stronger surface activity can be lower than that of a substance with a weaker surface activity. The foamability, especially under dynamic conditions, cannot simply be correlated with the surface activity.

Relationship between foam stability and surface elasticity forces : fatty acid solutions

Abstract The stability of wet foams of fatty acid solutions (n-pentanoic to n-decanoic acid) in 0.005 N HCl was studied. Retention time values, being a measure of the stability of foams under steady-state conditions, equilibrium surface tension - concentration isotherms σ(log c0), values of the surface dilational modulus, and effective elasticity forces Eeff were determined. The mechanism of foam formation is discussed and the importance of dynamic effects in foam stability is stressed. It is shown that stabilizing forces are connected with actual non-equilibrium coverages of interfaces, and changes in foamability can be correlated with values of the effective elasticity forces. Reasons why the foamability of solutions of the higher members of a homologous series of fatty acids starts to decrease even though their surface activity is successively increasing are also explained.

Surface elasticity and frothability of n-octanol and n-octanoic acid solutions

Abstract The importance of surface elasticity forces in frothability under steady state conditions is discussed. The surface dilatational modulus of n-octanol and n-octanoic acid solutions was determined using the pulsation bubble method. The frothing properties of solutions are described in terms of retention time values — the foaminess parameter whose values supply information concerning the average time necessary for the average gas bubble to pass through the system studied, that is, the solution + foam. A linear relation between retention time and the Marangoni dilatational modulus values was found. This result should not, however, be overestimated since values of the Marangoni dilatational modulus refer to the insoluble behaviour of the fully established adsorption layer. Nevertheless, the results obtained indicate the decisive role of surface elasticity forces in frothability of the solutions studied under steady state conditions.

Influence of the Impact Velocity and Size of the Film Formed on Bubble Coalescence Time at Water Surface

Phenomena occurring during bubble collisions with a water/air interface were studied. The bubble impact velocity was tuned by the following: (i) changing the bubble diameter and (ii) adjusting the distance between the bubble formation point and the water free surface (at the bubble acceleration stage). It was found that the bubble bouncing and the coalescence time, i.e., the time from the moment of the bubbles first collision to its rupture, increased with the impact velocity. The coalescence time varied from a few to ca. 120 ms when the bubble impact velocity was changed from 8.0 to 36.7 cm/s. It was found that a prolongation of the coalescence time was related to size of the liquid film formed during the bubble collision. Higher impact velocity means larger deformation of the bubble shape and larger radius of the liquid film formed. It was shown that the bubble bounces when the thinning water film between the bubble and the air/water interface does not reach its rupture thickness during the collision time.

Surface elasticity and dynamic stability of wet foams

Abstract Solutions of n-butanol, n-pentanol, n-hexanol, n-heptanol, n-octanol, n-nonanol and n-decanol were studied. The frothability of the solutions was determined by a pneumatic method, surface elasticity forces were measured using the oscillating bubble technique, and the average lifetimes of gas bubbles in a top foam layer were determined by cinephotography. The frothability of solutions was described in terms of the retention time ( rt ) values. The rt values depend strongly on the kind of surface-active substance and on its concentrations. The frothabilities of the various n-alkanols were compared at the same values of their reduced concentrations c 0 / a , where a is the concentration of the half surface coverage. The rt values initially increase with increasing number ( n ) of carbon atoms in n-alkanol molecules, reach a maximum for C 6 C 8 , and then rapidly decrease for n-nonanol and n-decanol. The surface activity of the solute, its adsorption kinetics, the lifetime of the foam films, and the frequency of the external disturbances are the main factors determining the magnitude of the effective elasticity forces ( E eff ). Similar to the rt values, the E eff values initially increase with increasing n , reach a maximum for C 6 C 8 , and then rapidly decrease for higher members of the n-alkanol homologous series. The magnitude and the position of these maxima are a function of the solute concentration, adsorption times, and frequency of external disturbances. The results obtained show that the effective elasticity forces are the major factors determining the stability of wet dynamic foams.

A method of comparison of the frothing and collecting properties of frothers

Abstract It is commonly acknowledged that various n-alkanols differ in their flotation properties. Usually, the flotation properties of n-alkanols are estimated by comparing flotation yields at a chosen alcohol concentration. However, the final result of a flotation test depends on the reagent action at liquid/gas, liquid/solid, and solid/gas interfaces. Thus, the comparison and evaluation of flotation collectors and frothers would be more reliable if done in terms of a parameter characterizing surface properties of the system. Frothing properties of solutions were measured by a pneumatic method and described in terms of retention time ( rt ) and dynamic frothability index (DFI) values. DFI characterizes solely the frothing properties of the reagent itself and can thus be considered as a material constant. The product of DFI and the given solution concentration ( c ) gives information about the frothability of the solution. Flotation tests, for coals of ranks 32, 33, and 34 were carried out in a laboratory Denver-type cell. Comparison of the flotation results as a function of DFI. c showed that the flotation yields were not dependent on the kind of n-alkanol used. This means that n-butanol, n-pentanol and n-hexanol showed the same collecting properties.

The influence of surface oxidation of chalcocite on its floatability and ethyl xanthate sorption

Abstract The results obtained from measurements of potassium ethyl xanthate (EtXK) sorption by synthetic chalcocite (Cu 2 S) and the results of chalcocite floatability measurements are presented. Five chalcocite samples, denoted as Cu 2 S A, B, C, D and E, were used for the measurements. Chalcocite samples of 60–75 μm were prepared in the same manner but were kept under conditions which differed in their degree to prevent surface oxidation by atmospheric oxygen. Chalcocite surface oxidation has a strong effect both on xanthate sorption and on chalcocite floatability. The maximal amount of xanthate abstracted ( Q max ) by chalcocite samples from deoxygenated solutions after a long sorption period increases with increasing oxidation of the samples. The Q max values give information concerning the total amount of surface oxidation products. Chalcocite decreases its floatability with increasing surface oxidation. Most oxidized chalcocite samples required an about 100 times greater collector consumption to obtain the same flotation results than the least-oxidized samples studied.

Steady-state foaming and the properties of thin liquid films from aqueous alcohol solutions

Abstract The role of individual foam films in the stabilization of steady-state foams (froths) obtained under dynamic conditions was studied. n -Amyl alcohol (AmOH) was chosen as the frothing agent. It was assumed that the stability of such foams is determined by the stability of the bubbles in the top layer, because the liquid content in the foam volume is high and the gas bubbles do not contact one another. The role of the foam films was found through parallel investigations of steady-state foams, single foam films, and foam bubbles at the surface of a solution at appropriately chosen geometrical parameters and at the same composition of the solution. The results showed that the bubbles in the surface layer of the stationary froths rupture at relatively large thickness (larger than 300 nm) where the specific thermodynamic and kinetic properties of the foam films are not yet operative.

Steady-state foams: Influence of the type of liquid films

Abstract Properties of “dry” steady-state foams formed from sodium lauryl sulphate (NaLS) solutions containing various amounts of electrolyte have been investigated. The results of the foamability measurements performed under dynamic steady-state conditions are described in terms of retention time (rt) values. Upper limits of NaLS concentrations, for which the measurements of steady-state foamability could be performed were found to depend strongly on the amounts of electrolyte added. Investigations of the action of α-particle showed that three types of foam film were formed in the highest layers of the foams studied. Newton black, common black and normal thin liquid films were formed in the presence of 0.5, 0.1 and 10−4M NaCl, respectively. The properties of these three types of film determined the observed behaviour of the steady-state foam formed.