Continued self-similar breakup of drops in viscous continuous phase in agitated vessels (original) (raw)
Effect of Dispersed-Phase Viscosity on the Maximum Stable Drop Size for Breakup in Turbulent Flow
Journal of Chemical Engineering of Japan, 1977
A formula for the maximumstable drop size has been derived theoretically, by taking into consideration the effect of the dispersed-phase viscosity. The derived formula indicates that the controlling factors of the maximumstable drop size are the WeberNumberand the viscosity group which is defined as the ratio of the viscous stress to the stress of interfacial tension. The validity of the formula was confirmed experimentally over a wide range of dispersed-phase viscosity.
A model of droplet breakup in a turbulent flow for a high dispersed phase holdup
h i g h l i g h t s A model of droplet breakup at a high dispersed phase holdup is developed. Droplet fluctuation velocities are calculated by kinetic theory of granular media. The breakup model developed is incorporated into the STARCCM+ Ò CFD code. The breakup model is validated using experimental data obtained in a Couette device.
Journal of Dispersion Science and Technology, 2005
The breakage of drops or bubbles in isotropic turbulent dispersions has been investigated. Based on the experimental data given in the literature, some new empirical relationships are derived to evaluate the minimum stable drop sizes, the breakup frequencies, and the drop size distribution in turbulent dispersions. The solutions of the stochastic Focker‐Planck equation are used to estimate the particle size
Effect of turbulence on drop breakup in counter air flow
International Journal of Multiphase Flow, 2019
Understanding the factors that lead to breakup of liquid droplets is of interest in many applications. Liquid droplet breakup processes are typically broken into regimes based on a Weber number calculated based on an average flow velocity (Solsvik et al., 2013). In turbulent flows, the instantaneous velocity may differ significantly from the average velocity. Here an experimental investigation on the role of turbulence in the breakup process is undertaken, whose continuous phase is gas. The turbulence is produced by confined counterflow into which the droplets fall. Droplet breakup mode is visualized by high speed camera, and the turbulence of counterflow is measured by Particle Image Velocimetry. The experimental results show that the breakup morphology and mode frequency varies with the turbulence intensity of the counterflow.
Droplet breakup mechanisms: Stepwise equilibrium versus transient dispersion
Journal of Rheology, 1993
In dispersive mixing of immiscible liquids the minimum attainable dropsize is often deduced from the critical value of the Capillary number (the ratio of the shear stress to the interfacial stress) necessary for drop breakup under quasiequilibrium conditions. The critical Capillary number shows a minimum if the viscosity ratio between dispersed and continuous phase is about one. Hence, it is commonly accepted that the finest morphology is obtained if both viscosities match. In practical mixing devices, however, small drops are formed by a transient mechanism of thread breakup during extension rather than by stepwise breakup under equilibrium conditions. For Newtonian liquids, a comparison is made between the dropsizes resulting from a stepwise equilibrium and a transient breakup mechanism. Generally, the transient mechanism yields smaller drops and, more interestingly, a higher viscosity ratio between the dispersed and continuous phases results in a finer morphology, as already indicated by . In the present paper the comparison is elaborated over a broad range of the relevant parameters while a compact illustrative presentation of the results is given to stress the possible consequences for practical blend morphologies.
Drop breakup in turbulent stirred-tank contactors. Part I: Effect of dispersed-phase viscosity
AIChE Journal, 1986
Numerous experiments were conducted in four, baffled cylindrical tanks of standard geometry, equipped with six-blade Rushton turbines, by photographically examining dilute suspensions of silicone oils in water. Five grades of oil, ranging in viscosity from about 0.1 to 10 Pas and exhibiting the same interfacial tension with water ([0.0378 N / m), were employed. The range of variables studied includes 13,000 < Re < 101.000. 44 < We < 1.137, and 0.065 < < 0.50 m2/s3. The objectives of the experimental program were to examine the extent to which dispersed-phase viscosity influences equilibrium mean drop size and drop size distribution at constant interfacial tension, and to determine the relevance of the predicted correlating parameters and the range of applicability of the semiempirical theory.
Breakup time and morphology of drops and bubbles in a high-Reynolds-number flow
Journal of Fluid Mechanics, 2006
The breakup process of a drop or a bubble immersed in a straining flow at high Reynolds numbers, is studied numerically with the aim at comparing the breakup frequencies obtained with those measured in real flows. We assume that both the inner and the outer velocity fields are axisymmetric and irrotational. Under these assumptions the time evolution of the drop's interface is computed with a boundary integral method for a wide range of the inner-to-outer density ratios, Λ. Despite the simplicity of the model, it qualitatively displays some of the features of the turbulent breakup of drops and bubbles observed experimentally. Furthermore, when Λ ∼ O(1), the slender geometry of the droplets observed in the numerical simulations suggests the use of a simplified theoretical analysis that reproduces accurately the time evolution of the drop radius obtained numerically.
Analytical Criterion for Droplet Breakup in Turbulent Flow Fields
The utilisation of high-injection-pressure fuel system in direct diesel injection requires liquid fuel being injected at a very high pressure, which is later converted to a corresponding high velocity by the injector nozzle, which gives rise to a turbulent flow fields around droplets. The fate of a droplet that travels through ambient depends on the droplet velocity, on the droplet thermo-physical properties and on the ambient properties, which are related, in part, by the Weber number. The Weber number is the ratio between disruptive forces and cohesive forces. When a drop travels in ambient, deformation occurs, which may lead to droplet breakup. The droplet breakup will occur only if the Weber number locally exceeds a certain critical value. A new droplet breakup criterion model, which combines energy criterion and dual-timescale, to also account for turbulent shear in droplet dispersion, is suggested for droplet breakup. The suggested analytical breakup criterion is proposed on t...
Chemical Engineering Research and Design, 2013
The study of phase dispersion of two immiscible fluids in different flows requires identifying the relevant breakup mechanisms. We propose here a detailed investigation of droplet breakup in a multifunctional exchanger-reactor of the vortex generator type in which transfer intensification is due to longitudinal vortical structures. We compare the efficiency of the mean gradients and turbulent mechanisms in droplet breakup in this industrial reactor. This efficiency is essentially characterized by the resulting distribution of droplet diameters. Then, the roles of the mean flow and the turbulent field, intensity, energy spectrum, and turbulence scales are examined in relation to the liquid/liquid dispersion in order to explore the governing mechanisms of drop breakup. In the complex flow considered here -nonhomogeneous and anisotropic turbulence at moderate Reynolds numbers (<15,000) -with weak turbulence intensity (about 10%), it can be demonstrated that turbulent breakup mechanisms largely dominate mean flow effects; elongation and shear effects are shown to have minor effects on the breakup mechanisms. Moreover, the global characteristic scales of the flow are not the relevant parameters in predicting the final size of the emulsion, but instead the Kolmogorov microscale, implying that the residence time in the reactor is not a limiting factor. Hence, the local dissipation rate governs the performance of the actual multifunctional reactor. This study provides some insight in the design and scaling-up of multiphase reactors.
Drop breakup modelling in turbulent flows
2015
This paper deals with drop and bubble break-up modelling in turbulent flows. We consider the case where the drop/bubble slip velocity is smaller than or of the order of the turbulent velocity scales, or when the drop/bubble deformation is mainly caused by the turbulent stress (atomisation is not addressed here). The deformation of a drop is caused by continuous interactions with turbulent vortices; the drop responds to these interactions by performing shape-oscillations and breaks up when its deformation reaches a critical value. Following these observations, we use a model of forced oscillator that describes the drop deformation dynamics in the flow to predict its break-up probability. Such a model requires a characterization of the shape- oscillation dynamics of the drop. As this dynamics is theoretically known only under restrictive conditions (without gravity, surfactants), CFD two-phase flow simulations, based on the Level-Set and Ghost Fluid methods, are used to determine the ...
Single drop breakage in turbulent flow: Statistical data analysis
Chemical Engineering Science: X, 2020
To improve breakage models in the population balance framework, single octanol droplet experiments have been performed in a channel flow and recorded by high-speed camera. The study investigates impact of mother drop size on the breakage time, breakage probability, average number of daughters and the daughter size distribution for known turbulence characteristics. Each breakage event is associated with an individual turbulence level, based on the local flow characteristics. A clearly defined statistical analysis is presented. Using 95% confidence intervals, the precision of each of the determined properties is described quantitatively. Furthermore, the confidence intervals are a tool for determining whether an increased number of experiments will yield a significant increase in the precision, considered against the sources of error. It is found that 35-50 breakage events are sufficient to obtain confidence intervals of desired precision.
Drop break-up and coalescence in a stirred tank
It is shown in the paper that drop size distribution in liquid-liquid dispersions is affected by both the fine-scale and the large-scale inhomogeneity of turbulence. Fine-scale inhomogeneity is related to the phenomenon of local intermittency and described using a multifractal formalism. Largescale inhomogeneity is related to inhomogeneous distributions of the locally averaged properties of turbulence, including the rate of energy dissipation and the integral scale of turbulence. Large-scale distributions of the properties of turbulence in a stirred tank are considered with a network of wellmixed zones. CFD methods are used to compute the properties of turbulence in these zones. A model taking into account inhomogeneity of both types explains the effect of the system's scale on drop size; it predicts smaller maximum stable drop sizes than the classic Kolmogorov theory of turbulence. The model predictions agree well with experimental data.
Drop breakup and fragment size distribution in shear flow
Journal of Rheology, 2003
We report a study on the deformation and breakup of drops in an impulsively started shear flow under Stokes flow conditions using boundary-integral simulations and video-microscopy experiments. Two independent techniques are used for determining the physical parameters of the system from the combined use of numerical simulations and experiments. Accurate breakup criteria ͑critical capillary numbers͒ are presented for a range of viscosity ratios. The time required for breakup events has a broad minimum corresponding to moderate shear rates. The size distribution of droplets produced by breakup events is shown to scale with the critical size drop for breakup in shear. A simplified model, based on this finding, is developed for the size distribution in a sheared emulsion. According to the model, the drop size distribution in a given emulsion depends only on the average initial drop size and the shear rate.
Chemical Engineering Journal, 2019
A generalized model for breakage and coalescence kernels valid for the entire spectrum of turbulence is proposed and validated. Most of the available kernels in the literature, indeed, assume that in a turbulent liquid-liquid dispersion, the dispersed droplets have dimension in the inertial subrange and are affected by eddies with size in the same subrange. These kernels are based on the Kolmogorov second-order structure function, which is valid only in the inertial subrange. However, in most industrially encountered situations, many droplets may have a size in the dissipation range, where the Kolmogorov second-order structure function does not apply. Therefore, a more general description of the energy transferred between these droplets and the turbulent eddies is needed to properly model breakage and coalescence events. In this work, the Coulaloglou and Tavlarides breakage and coalescence kernels [1] will be modified through the implementation of the second-order structure function proposed by Davidson [2], along with the Pope energy spectrum [3]. Turbulent liquid-liquid 2 dispersion experiments at high continuous phase viscosity are performed to test and validate the model. The generalized model is able to predict the experimental Sauter mean diameters at different viscosities, turbulent conditions and dispersed-phase volume fraction without any adjustment of the kernel parameters.
Breakup of a drop in a liquid–liquid pipe flow through an orifice
AIChE Journal, 2007
This work addresses the drop fragmentation process induced by a cross-sectional restriction in a pipe. An experimental device of an upward co-current oil-in-water dispersed flow (viscosity ratio ≈ 0.5) in a vertical column equipped with a concentric orifice has been designed. Drop break-up downstream of the restriction has been studied using a high-speed trajectography. The first objective of this work deals with a global analysis of the fragmentation process for a dilute dispersion. In this context, the operating parameters of the study are the orifice restriction ratio , the flow Reynolds number, Re and the interfacial tension, . The break-up domain has been first mapped on a (Re) graph and drop size distributions have been measured for different flow Reynolds numbers. It was observed that the mean drop diameter downstream of the restriction linearly increases as a function of the inverse of the square root of the pressure drop. This behaviour is in agreement with the observations previously made by Percy and Sleicher [A.I.Ch.E. Journal, 1983, 29(1), 161-164]. In addition, experiments based on the observation of single drop break-up downstream of the orifice have allowed the identification of different breakup mechanisms, and the determination of statistical quantities such as the break-up probability, the mean number of fragments and the daughter drop distribution. The drop break-up probability was found to be a monotonous increasing function of the Weber number based on the maximal pressure drop through the orifice. The mean number of fragments is also an increasing function of the Weber number and the reduced mean daughter drop diameter decreases as the Weber number increases. The daughter drop distributions are multimodal at low and moderate Weber numbers as a result of asymmetrical fragmentation processes. The statistical analysis of single drop break-up experiments was implemented in a simple global population balance model in order to predict the evolution of the size distribution across the restriction at different Reynolds numbers, in the limit of dilute dispersions.
Drop-breakage in agitated liquid—liquid dispersions
Chemical Engineering Science, 1974
Experimental data from batch vessels on cumulative volumetric drop-size distributions at various times are shown to yield useful information on probabilities of droplet-breakup as a function of drop-size. Such information is sufficient for a priori prediction of drop-sizes in agitated dispersions in batch and continuous vessels. It may also be useful in predicting heat and/or mass transfer in liquid-liquid dispersions by accounting for the simultaneity of transport processes from individual drops and droplet breakage processes:
Single Droplet Break-up in Controlled Mixed Flows
ACS Applied Materials & Interfaces, 2010
In this work, the break-up dynamics of a single, Newtonian droplet dispersed in an immiscible Newtonian matrix undergoing a controlled mixture of shear and extensional flow is investigated using a homemade eccentric cylinder device. Hereto, different representative supercritical flows with varying shear/elongation balance have been applied. The effect of viscosity ratio is explored using droplets with a viscosity ratio of 0.1 and 1.3, respectively. In all cases, break-up is observed to proceed through an "end-pinching" mechanism. The experimentally obtained break-up times have been compared with scaling relations known from literature for simple shear and purely extensional flow. It is found that the global break-up dynamics is still shear dominated, even for conditions where the elongational contribution comprises a substantial amount (up to 30% on average) of the mixed flow.