Surface bubble

Defoamers. Foam is a common problem in papermaking systems (27). It is caused by surface-active agents which are present in the pulp slurry or in the chemical additives. In addition, partially hydrophobic soHd materials can function as foam stabilizers. Foam can exist as surface foam or as a combination of surface foam and entrained air bubbles. Surface foam usually can be removed by water or steam showers and causes few problems. Entrained air bubbles, however, can slow drainage of the stock and hence reduce machine speed. Another serious effect is the formation of translucent circular spots in the finished sheet caused by permanently entrained air. 

Even if the interfacial tension is measured accurately, there may be doubt about its applicability to the surface of bubbles being rapidly formed in a solution of a surface-active agent, for the bubble surface may not have time to become equihbrated with the solution. Coppock and Meiklejohn [Trans. Instn. Chem. Engrs., 29, 75 (1951)] reported that bubbles formed in the single-bubble regime at an orifice in a solution of a commercial detergent had a diameter larger than that calculated in terms of the measured surface tension of the solution [Eq. (14-206)]. The disparity is probably a reflection of unequihbrated bubble laminae. 

For any adsubble method, if the material to be removed (termed the colligend) is not itself surface-active, a suitable surfactant (termed the collector) may be added to unite with it and attach or adsorb it to the bubble surface so that it may be removed (Sebba, Ion Flotation, Elsevier, New York, 1962). The union between colligend and collector may be by chelation or other complex formation. Alternatively, a charged colhgend may be removed through its attraction toward a collector of opposite charge. 

Adsorption The separation achieved depends in part on the selectivity of adsorption at the bubble surface. At equihbrium, the adsorption of dissolved material follows the Gibbs equation (Gibbs, Collected Works, Longmans Green, New York, 1928). 

The major surfactant in the foam may usually be considered to be present at the bubble surfaces in the form of an adsorbed monolayer with a substantially constant F, often of the order of 3 X 10" (g mol)/ cm", for a molecular weight of several hundred. On the other hand, trace materials follow the linear-adsorption isotherm Tj = KiCj if their concentration is low enough. For a wider range of concentration a Langmuir or other type of isotherm may be applicable (Davies and Rideal, loc. cit.). 

Oxygen transfer rate (OTR) The product of volumetric oxygen transfer rate kj a and the oxygen concentration driving force (C - Cl), (ML T ), where Tl is the mass transfer coefficient based on liquid phase resistance to mass transfer (LT ), a is the air bubble surface area per unit volume (L ), and C and Cl are oxygen solubility and dissolved oxygen concentration, respectively. All the terms of OTR refer to the time average values of a dynamic situation. 

Yet, Eq. (14) does not describe the real situation. It must also be taken into account that gas concentration differs in the solution and inside the bubble and that, consequently, bubble growth is affected by the diffusion flow that changes the quantity of gas in the bubble. The value of a in Eq. (14) is not a constant, but a complex function of time, pressure and bubble surface area. To account for diffusion, it is necessary to translate Fick s diffusion law into spherical coordinates, assign, in an analytical way, the type of function — gradient of gas concentration near the bubble surface, and solve these equations together with Eq. (14). 

Calderbank et al. (C6) studied the Fischer-Tropsch reaction in slurry reactors of 2- and 10-in. diameters, at pressures of 11 and 22 atm, and at a temperature of 265°C. It was assumed that the liquid-film diffusion of hydrogen from the gas-liquid interface is a rate-determining step, whereas the mass transfer of hydrogen from the bulk liquid to the catalyst was believed to be rapid because of the high ratio between catalyst exterior surface area and bubble surface area. The experimental data were not in complete agreement with a theoretical model based on these assumptions. 

For chemical reaction-rate constants greater than 10 sec-1, NT increases linearly with the total bubble surface area, i.e., linearly with the gas holdup. In other words, the agitation rate only affects the total bubble surface area and has almost no effect on the rate of absorption per unit area. This result is in accordance with the work of Calderbank and Moo-Young (C4), discussed in Section II. 

Characteristic length [Eq. (121)] L Impeller diameter also characteristic distance from the interface where the concentration remains constant at cL Li Impeller blade length N Impeller rotational speed also number of bubbles [Eq, (246)]. N Ratio of absorption rate in presence of chemical reaction to rate of physical absorption when tank contains no dissolved gas Na Instantaneous mass-transfer rate per unit bubble-surface area Na Local rate of mass-transfer per unit bubble-surface area Na..Average mass-transfer rate per unit bubble-surface area Nb Number of bubbles in the vessel at any instant at constant operating conditions N Number of bubbles per unit volume of dispersion [Eq. (24)] Nb Defined in Eq. (134)... 

The study of flotation kinetics relates to a number of mass transfer processes and these are listed in Table 2.8. The term, entrainment which figures in the mass transfer process statements made in Table 2.8 may be elaborated. It is the process by which particles enter the base of a flotation froth and are transferred up and out of the flotation cell suspended in the water between bubbles. Entrainment should be distinguished from true flotation, whereby particles come out of the cell attached to bubble surfaces. True flotation is chemically selective, while the entrainment process recovers both gangue and valuable minerals alike. Entrainment harms the product grade since recovery of the more abundant gangue mineral reduces the quality of the concentrate. This is especially true in the processing of fine ores. Much flotation research has dealt with reducing entrainment in order to improve... 

The Weber-Reynolds number (Re/We) is defined as the ratio of surf ace tension of a bubble to viscous shear on the bubble surface due to bubble motion ... 

Choi and Funayama [19] also measured sodium atom emission from sodium dodecylsulfate (SDS) solutions in the concentration range of 0.1-100 mM at frequencies of 108 kHz and 1.0 MHz. The sodium line intensity observed at 1 MHz was nearly constant in the concentration range from 3 to 100 mM and was considerably higher than that at 108 kHz. This frequency dependence of the intensity is opposite that for NaCl aqueous solution. The dynamical behavior of the absorption and desorption of surfactant molecules onto the bubble surface may affect the reduction and excitation processes of sodium atom emission. This point should be clarified in the future. 

Figure 3. Temporal and Spatial Evolution of Reaction Rates in the Liquid Phase Reaction Zone. Rates were calculated as a function of time and distance from the bubble surface assuming only conductive heat transport from a sphere with radius 150ym at 5200K, embedded in an infinite matrix at 300K.

The chemicals added to the flotation cell assist in separating the ink from the fiber and enhance the ability of the ink particles to adhere to the bubble surface. A common chemical added to the cell is sodium hydroxide (NaOH) which causes the fiber to swell, thus releasing the ink particle... 

When particles approach the gas-liquid interface, the surface-tension force acts on the particles through the liquid film. The bubble-surface-tension induced force can be described by... 

Density in liquid Density in bubble Surface tension Parameter in Eq. (3)... 

W.A. Ducker, Z. Xu, and J.N. Israelachvili Measurements of Hydrophobic and DLVO Forces in Bubble-Surface Interactions in Aqueous Solutions. Langmuir 10, 3279 (1994). 

Bubbles are blown into the inverted funnel. Inside the funnel, the bubble film is transported away and collected. Since the bubble film consists of a surface-active substance and water, it is seen that even very minute amounts (less than milligram per liter) of surface-active substances will accumulate at the bubble surface. As shown previously, it would require a large number of bubbles to remove a gram of substance. However, since one can blow thousands of bubbles in a very short time, the method is found to be very feasible. 

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