Modelling of high viscosity oil drop breakage process in intermittent turbulence

doi:10.1016/j.ces.2005.10.048

Chemical Engineering Science

Volume 61, Issue 9, May 2006, Pages 2986-2993

https://doi.org/10.1016/j.ces.2005.10.048 Get rights and content

Abstract

A multifractal model of the fine-scale structure of turbulence is applied to describe breakage of viscous drops of immiscible liquid immersed in a fully developed turbulent flow. A population of drops whose diameter falls within the inertial subrange of turbulence is considered here. The population balance equation is used to predict the drop size distributions. Calculations are performed for binary and multiple breakage. Several daughter distribution functions are applied and the results of their application are compared with experimental data. Experimental investigations of drop breakup were carried out in a flat bottom stirred tank having the diameter of $T = 0.15 m$ and equipped with Rushton type agitator and four baffles. Silicone oils with viscosity of 10, 100, 500 and 1000 m Pa s were dispersed in the aqueous continuous phase. Measurements were performed using high resolution digital camera. Experimental results as well as numerical simulations show that after the initial period of multiple breakage, the strongly asymmetric type of binary breakage dominates.

Introduction

Drop size distribution in immiscible liquid–liquid dispersion evolves due to drop break-up and coalescence. These phenomena are often encountered in industrial processes such as liquid–liquid extraction, emulsion polymerization, suspension polymerization, oil–water separation and multiphase reactions. In dilute dispersions coalescence can be neglected, so drop size is determined entirely by the breakage process.

Deformation and breakage depend on the flow pattern around the drop. Early studies were focused on the analysis of drop deformation in simple shear and hyperbolic flows (Taylor, 1932; Grace, 1982, Bentley and Leal, 1986) or on estimation of the maximum stable drop size (Kolmogorov, 1949, Hinze, 1955, Shinnar, 1961) in turbulent flows. Bławzdziewicz et al. (1998) presented the first direct numerical simulations of three-dimensional drop break-up in isotropic turbulence, but their work was restricted to drops smaller that Kolmogorov microscale. According to the authors’ knowledge similar analyses have not been performed for drops whose diameters are within the inertial subrange of turbulence. The reason is the highly complicated flow field. Instead, there are many investigations focusing on estimation of the maximum stable drop size, as well as on formulation of the statistical models that enable us to predict transient drop size distributions. Most often it is the systems characterized by low dispersed phase viscosity that are studied. However, the viscosity of the dispersed phase was taken into account in modeling as early as in 1949 by Kolmogorov, and independently by Hinze (1955). They introduced the viscosity group which is the ratio of internal viscosity force to an interfacial tension force. Effects of the dispersed phase viscosity on maximum stable drop size were studied by Arai et al. (1977), Davies (1985), Calabrese et al. (1986), Lagisetty et al. (1986), Kumar et al. (1992).

Most of break-up kernels were proposed for drops of low viscosity. An exception is the model developed by Nambiar et al., 1992, Nambiar et al., 1994 that is based on the concept of Lagisetty et al. (1986). Nambiar et al., 1992, Nambiar et al., 1994 associated the breakage mechanism, frequency and daughter droplet distribution with the size of eddies interacting with a drop.

All breakage models mentioned above were derived using traditional method of description of the turbulent field structure based on the Kolmogorov–Obukhov energy cascade theory. This means that the impact of intermittent character of turbulent flow including the effect of the system scale on the maximum stable drop size (Konno et al., 1983) and the rate of drop breakage or the drift of the exponent on Weber number in time are omitted. The influence of fine scale intermittency on drop break up was considered by Bałdyga and Podgórska (1998).

The aim of this work is to present the improved interpretation of breakage of viscous drops in intermittent turbulent flow. While most papers devoted to breakage of viscous drops are limited to comparison of predicted and measured maximum or mean drop size, the present paper focuses on drop size distribution, which enables better discrimination of models. Drop size distributions predicted while relying on the breakage rate models that are based on multifractal representation of the microstructure of turbulence and while accounting for different breakage mechanisms at different stages of the process will be compared with experimental data.

Section snippets

Experimental

Experiments were performed in a completely filled flat-bottom stirred tank with the diameter of $T = 0.15 m$ and height of $H = T$ equipped with a standard stainless steel six-blade Rushton turbine having the diameter of $D = T / 2$ situated at the mid-plane of the vessel, and with four equally spaced stainless steel baffles. The width of each baffle was equal to $T / 10$ . The vessel was enclosed by stainless steel cover. The high value of the ratio of impeller to tank diameter and bottom clearance equal to the

Model formulation

Drop size distribution and its evolution in time are predicted by solving the population balance equation $\frac{\partial n (υ, t)}{\partial t} = - g (υ) n (υ, t) + \int_{υ}^{\infty} β (υ, υ^{'}) ν (υ^{'}) g (υ^{'}) n (υ^{'}, t) d υ^{'} .$ Here $n (υ, t)$ is number density of drops having volume $υ$ at time $t$ , $β (υ, υ^{'})$ is the daughter drop distribution and $ν (υ^{'})$ represents the number of daughter drops formed during breakage of mother drop of size $υ^{'}$ . In the stirred tank the breakage takes place mainly in the vicinity of the impeller where the locally averaged energy dissipation

Results and discussion

Measured drop size distributions show that drop diameters are within the inertial subrange of turbulence, i.e., they are larger than Kolmogorov scale. The classical Kolmogorov scale, in the impeller zone ( $〈 ε_{imp} 〉 = 5.93 〈 ε 〉$ for $T / D = 2$ ) and for the lowest impeller speed $N = 210 rpm$ is equal to $〈 η 〉 = 30 μ m$ , while the minimum Kolmogorov scale, $η_{K_{i}} = L (〈 η 〉 / L)^{4 / (α + 3)}$ , for $α = 0.12$ , equals to $6.3 μ m$ . In the case of the highest impeller speed, $N = 350 rpm$ , the respective values are $〈 η 〉 = 20 μ m$ and $η_{Ki} = 3.8 μ m$ .

The population

Conclusions

Breakage of viscous drops in turbulent flow is a very complex process and different mechanisms of breakage occur most probably simultaneously. It has been shown that the proper prediction of the influence of dispersed phase viscosity and impeller speed on the mean drop size and its evolution in time does not guarantee the proper shape of drop size distributions. Different types of breakage were taken into account and the possibility of their dominance at different stages of breakage process was

Notation

$C_{g}, C_{p}, C_{x}$	constants in breakage model
$d$	drop diameter, m
$d_{\max}$	maximum stable drop size, m
$D$	impeller diameter, m
$f (α)$	multifractal spectrum
$g (d)$	breakage rate, $s^{- 1}$
$L$	integral scale of turbulence, m
$n (υ, υ^{'})$	number density of drops, $m^{- 6}$
$P (α)$	probability density function for $α$
$T$	tank diameter, m
$T_{L}$	Langrangian time macroscale in the inertial subrange, s
$u$	velocity, $m s^{- 1}$
$υ$	drop volume, $m^{3}$
Greek letters
$α$	multifractal exponent
$β (υ, υ^{'})$	daughter drop distribution, $m^{- 3}$
$β_{t}, β_{μ}$	constants in viscous drop breakage model
${\dot{γ}}_{D}$	maximum strain

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Modelling of high viscosity oil drop breakage process in intermittent turbulence

Abstract

Introduction

Section snippets

Experimental

Model formulation

Results and discussion

Conclusions

Notation

Journal of Non-Newtonian Fluid Mechanics

Chemical Engineering Science

Chemical Engineering Science

Experimental validation of slow flow theory. Journal of Non-Newtonian Fluid Mechanics

Chemical Engineering Science

Chemical Engineering Science

Chemical Engineering Science

Chemical Engineering Science

Chemical Engineering Science

Chemical Engineering Science

Chemical Engineering Science

Effect of dispersed-phase viscosity on the maximum stable drop size for breakup in turbulent flow

Journal of Chemical Engineering of Japan

Interpretation of turbulent mixing using fractals and multifractals

Chemical Engineering Science

Drop break-up in intermittent turbulencemaximum stable and transient sizes of drops

Canadian Journal of Chemical Engineering

An experimental investigation of drop deformation and break-up in steady, two-dimensional linear flows

Journal of Fluid Mechanics