Monodisperse system bubbles

Thus far most of the relationships discussed apply to monodisperse systems in which the dispersed species have the same size and shape. Although for a monodisperse system, relative viscosity is often independent of droplet/bubble/particle size, at the high end of the dispersed phase volume fraction range the viscosity will often become influenced by size. The actual range of volume fraction for which this occurs depends strongly on the nature of a particular system, including factors such as surface rigidity [215]. 

For the sedimentation of rarefied monodisperse systems of spherical particles, drops, or bubbles, the mean Sherwood number can be calculated by using formulas (4.6.8) and (4.6.17), where the Peclet number must be determined on the basis of the constrained flow velocity. 

We note that in [421], the cell flow model was used for the investigation of mass and heat transfer in monodisperse systems of spherical drops, bubbles, or solid particles for Re < 250 and 0 < < 0.5. 

In a monodisperse foam the deformation of spherical bubbles and formation of films at the places of their contact starts when the gas content in the system reaches - 50% (vol.) for simple cubic bubble packing or 74% for close (face-centred) cubic or hexagonal packing (foam expansion ratio - 4). In a polydisperse foam the transition to polyhedral structure starts at expansion ratio n - 10-20, according to [ 10] but, as reported in [51], this can occur at n < 4, the latter being more probable. The structure which corresponds to the transition of bubbles from spherical to polyhedral shape is called occasionally honeycomb structure. 

The average foam dispersity in the experiments performed varied within the limits of aVL = 6.10"2-3.5.10 1 mm the degree of polydispersity significantly increased in the process of foam coarsening. It can be seen that curves 1 and 2 fit well at expansion ratio n > 300. At low expansion ratio (20 < n < 40) the difference between rjr (n) and rjrn(n) grows to 15% but if the longitudinal curvature is accounted for then this difference is about 7%. This means that the difference in size of the individual bubbles in a polydisperse foam does not influence strongly the course of the ra lrn (n) dependence as compared to the monodisperse model system. 

Individual structural elements of the foam, such as films and borders, can be under hydrostatic equilibrium and can correspond to a true metastable state. Therefore, when there is no diffusion expansion of bubbles in a monodisperse foam, its state can be regarded as metastable in the whole disperse system. Krotov [5-7] has performed a detailed analysis of the real hydrodynamic stability of polyhedral foam by solving two problems determination of... 

A direct proportionality is expected between k a and e for monodisperse bubble populations in coalescence-inhibited material systems. In fact it was found [617] for three differently sized bubble columns of D = 96 200 300 mm with a perforated plate as sparger (boreholes 0.5 mm in diameter) in the material system 1 N sodium sulfite solution (Cu -catalyzed sulfite method for kbU determination) that ... 

Abstract. The lecture will review the recent advances in the techniques for formation of bubbles of gas and droplets of liquid in two-phase microfluidic systems. Systems comprising ducts that have widths of the order of 100 pm produce suspensions of bubbles and droplets characterized by very narrow size distributions. These systems provide control over all the important parameters of the foams or emulsions, from the volumes of the individual bubbles and droplets, through the volume fraction that they occupy, the frequency of their formation, and the distribution of sizes, including monodisperse, multimodal and non-Gaussian distributions. The lecture will review the fundamental forces at play, and the mechanism of formation of bubbles and droplets that is responsible for the observed monodispersity. 

The mechanisms of formation of discrete segments of fluids in microfiuidic flow-focusing and T-junction devices, that we outlined above point to (i) strong effects of confinement by the walls of the microchannels, (ii) importance of the evolution of the pressure field during the process of formation of a droplet (bubble), (iii) quasistatic character of the collapse of the streams of the fluid-to-be-dispersed, and (iv) separation of time scales between the slow evolution of the interface during break-up and last equilibration of the shape of the interface via capillary waves and of the pressure field in the fluids via acoustic waves. These features form the basis of the observed - almost perfect -monodispersity of the droplets and bubbles formed in microfiuidic systems at low values of the capillary number. 

Surfactants are either present as impurities that are difficult to remove from the system or are added deliberately to the bulk fluid to manipulate the interfacial flows [24]. Surfactants may also be created at the interface as a result of chemical reaction between the drop fluid and solutes in the bulk fluid [25, 26]. Surfactants usually reduce the surface tension by creating a buffer layer between the bulk fluid and droplet at the interface. Non-uniform distribution of surfactant concentration creates Marangoni stress at the interface and thus can critically alter the interfacial flows. Surfactants are widely used in numerous important scientific and engineering applications. In particular, surfactants can be used to manipulate drops and bubbles in microchannels [2, 25], and to synthesize micron or submicron size monodispersed drops and bubbles for microfluidic applications [27]. 

Foam is a disperse system in which the dispersed phase is a gas (most commonly air) and the dispersion medium is a liquid (for aqueous foams, it is water). Foam structure and foam properties have been a subject of a number of comprehensive reviews [6, 17, 18]. From the viewpoint of practical applications, aqueous foams can be, provisionally, divided into two big classes dynamic (bubble) foams which are stable only when gas is constantly being dispersed in the liquid 2) medium and high-expansion foams capable of maintaining the volume during several hours or even days. In general, the basic surface science rules are established in foam models foam films, monodisperse foams in which the dispersed phase is in the form of spheres (bubble foams) or polyhedral (high-expansion foams). Meanwhile, real foams are considerably different from these models. First of all, the main foam structure parameters (dispersity, expansion, foam film thickness, pressure in the Plateau-Gibbs boarders) depend... 

Another complication arises when strong attractive forces operate between the drops or bubbles. This may lead to a finite contact angle, 6, between the intervening film (of reduced tension) and the adjaeent bulk interfaces (21, 24-26). Under those conditions, droplets will spontaneously deform into truncated spheres upon contact and can thus pack to much higher densities. For monodisperse drops, the ideal close-packed density, consistent with minimization of the system s surface free energy, is given (21) by... 

The simplest way to form a nearly ideal foam is to introduce the gas into the liquid through a capillary tube. In that way individual bubbles of equal (almost) size will break off from the capillary tip under the action of surface tension. The process, however, must be slow in order to ensure that interfadal equihbrium is achieved for each bubble otherwise a monodisperse foam will not be produced. A much more rapid, but less controllable, procedure is to bubble gas into the system through a porous plug. In that process a highly polydisperse foam will result since many small bubbles will have the opportunity to coalesce while still attached to the plug. Even less consistent results will be obtained for foams produced by agitation. 

Two types of 2D vertical vibration are possible one with the thin direction perpendicular to the vertical and one with the thin direction parallel. For perpendicular drive, patterns similar to the 3D patterns are observed [34,38,41, 44,48,59,60,63-65,73,81,92,98], although due to the limited dimension not as many pattern types are possible. In systems with air, bubbling occurs for strong excitation [94]. A crystallization transition occurs for systems with monodisperse particles [82,99]. 

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