The drainage and rupture of partially-mobile films between colliding drops at constant approach velocity

Abid, S; Chesters, AK Allen

doi:10.1016/0301-9322(94)90033-7

Cited by 105 publications

(107 citation statements)

References 7 publications

Supporting

Mentioning

102

Contrasting

Unclassified

Order By: Relevance

“…The proportionality constant for the rate of collisions is a rather complex function of the hydrodynamics of multiple interacting drops. For isolated pairs of drops (i.e., very dilute emulsions), the film drainage model is frequently used, which is more suited for non-deformable surfaces (i.e., drops of high viscosity) [18,19].…”

Section: Coalescence In Slow Flowsmentioning

confidence: 99%

“…Given that the capillary number increases for the larger drops, then a maximum size exists, where coalescence dominates and rupture kinetics begin, cancelling each other out. In the work of Grizzuti and Minale, it is suggested that the two processes coexist in the same system [19][20][21][22][23][24][25][26][27]. Therefore, a second critical capillary number should be observed-associated with the transition of coalescence to rupture-and defined when drops increasing in size undergo a breakage process [11,12,23,24].…”

Section: Coalescence In Slow Flowsmentioning

confidence: 99%

See 1 more Smart Citation

Evolution of the Size Distribution of an Emulsion under a Simple Shear Flow

Leiva

Geffroy

2018

Fluids

View full text Add to dashboard Cite

Understanding the rheology of immiscible liquids mixtures, as well as the role played by its micro-structures are important criteria for the production of new materials and processes in industry. Here, we study changes over time of the droplet size distributions of emulsions induced by slow shearing flows. We observe that the initial heterogeneous microstructure may evolve toward more complex structures (such as bimodal distribution) as a result of coalescence and rupture of droplets. These dynamic structures were produced using a flow cell made up of two parallel disks, separated by a gap of 100 µm. The steady rotation of the lower disk generates a simple shear flow of 2 of 15 r rates. Despite the possible relevance of the latter, here, we address f the emulsion at low shear rates and in the relevance to the rheology responds to the low, dimensionless time evolutions induced by slow ork.lished on the effects of the history of the shear rate (e.g., on the rop, or coalescence of quasi-equal size drops). The pioneering work t deformation of a single drop establishes experimentally that two etermine the drop deformation under a linear flow: the capillary rger capillary numbers induce larger drop deformations, and viscous r capillary number in order to deform significantly. n by Equation (1)e viscosity of the fluid matrix, the radius of the drop, the applied ion coefficient between phases, respectively. he two phases is given by Equation (2)perse fluid, and η m is the viscosity of the continuum fluid or matrix. nder flow (besides deformation of drops), other phenomena can alescence of drops [4], break up of drops [6], or capture of a rather larger drop [14]. When applying a larger shear rate to the emulsion, ed and are frequently the main source of the observed dynamical drops; although, each phenomenon depends most likely on different flows, coalescence of small, equal-sized drops is observed, and the rates of deformation, especially with low viscosity fluids. Research tions under shearing flows, even beyond a critical drop size (up droplets), are given in [15][16][17]. The growth of drops through the droplets-by a mechanism that appears to resemble an Oswald produced but requires a rather broad size distribution, including ing distributions of particles induced by flow have been observed as phenomena is less well documented. Here, we attempt to describe a low-shear-flow phenomena, which generally modifies the observed r complex and nonlinear manner.nism occurs mainly in the weakest of flows. During this process, end enough time in close proximity. Thus, a dimensionless time, τ, quired for a high probability of coalescence (or its efficiency) can betion of imposed flow of the experiment, while the shear rate,.γ, ions of drops of a given size. Please note that it is customary to ation measure, but here, we prefer to associate the inverse of this cy or efficiency of coalescence. Dimensionless deformation measures = 0.75 s −1 , during ∼ 400 s. After a brief rest time, this procedure was repeated by applying ...

show abstract

Section: Coalescence In Slow Flowsmentioning

confidence: 99%

Section: Coalescence In Slow Flowsmentioning

confidence: 99%

Evolution of the Size Distribution of an Emulsion under a Simple Shear Flow

Leiva

Geffroy

2018

Fluids

View full text Add to dashboard Cite

show abstract

“…The transitions between the different drainage models follow from the restrictions of the partially mobile interfaces model (35). In essence, for small p ( < 6 hcrit/a), the drops can be considered inviscid, yielding fully mobile interfaces, while for large p (> 3a/hcri,), the drops become rigid with immobile interfaces.…”

Section: Film Drainagementioning

confidence: 99%

Dynamics of liquid‐liquid mixing: A 2‐zone model

Janssen

Meijer

1995

Polymer Engineering & Sci

113

109

View full text Add to dashboard Cite

The development of multiphase liquid-liquid morphologies during mixing at small Reynolds numbers has been modeled. The mixing process is divided into i) stretching of dispersed drops, ii) breakup of the liquid threads formed, and iii) coalescence of the final droplets upon collision. Rules and criteria of the distinct processes are presented and combined to a general 2-zone mixing model simplifying the flow field into a sequence of alternating "strong and weak zones." In a "strong zone," dispersed drops and threads are stretched unless their radius is too small: meanwhile, the stretching threads might break up into droplets. In the subsequent "weak zone," the remaining threads may disintegrate while any drops present may coalesce. After passing a number of zones, stretching, breakup, and coalescence lead to a dynamic equilibrium that could be considered as the "final" morphology. Using the 2-zone mixing model, the influence of material parameters and processing conditions on the morphology has been studied. Interestingly, increasing either viscosity (dispersed or continuous phase) yields a finer morphology due to the delay of thread breakup (allowing for further stretching) and suppression of coalescence.

show abstract

“…Nesse caso, usando coordenadas polares, as variações em z são muito menores que em r. Tomando coordenadas cartesianas x e y, isso implica ∂h ∂x ≪ 1; ∂h ∂y ≪ 1 que é uma condição necessária na teoria da lubrificação [19] e no estudo de filmes finos em geral [13]. A validade dessa condição foi discutida nos trabalhos de Chesters [1,7,20]. Assumimos também que as velocidades de interação são baixas e consideramos que ocorre fluxo de Stokes na qual o número de Reynolds é pequeno, ou seja, Re = 2R o ρV /µ ≪ 1, onde R o é o raio da bolha não deformada e V a velocidade de aproximação da bolha.…”

Section: Equações Governantesunclassified