Break-up of droplets in Karr reciprocating plate extraction column

The breaking rate of individual drops was investigated in a Karr type reciprocating plate extraction column. The binary systems used were: water-1,2-dichloroethane, water-toluene and water-n-butanol. The breakage probability and the conditional probability of breaking-up into a given number of daughter droplets, as well as the drop size distribution of daughter droplets, were the measured characteristics. Relations between the breakage probabilities and the breakage frequency were derived.A mathematical model of the frequency of breaking-up into > and more droplets developed was based on the assumption that collisions with turbulent eddies of the Kolmogoroff region of universal equilibrium are responsible for the process. A probabilistic model of daughter drop size distribution was also derived in the form of a β-distribution. The models were compared with experimental results and a good agreement was obtained.     

On the effect of phase fraction on drop size distribution of liquid–liquid dispersions in agitated vessels

The theory of Kolmogorov–Hinze is the base for many studies that have been done on mean drop size and drop size distribution of liquid–liquid dispersions in agitated vessels. Although this theory has been used extensively in the literature, but it does not always give a satisfactory result in the studies and therefore needs to be modified. This paper addresses the effect of phase fraction on drop size distribution in agitated vessels and on the proportionality coefficient and Weber number exponent in the relation d₃₂/D ∝ We^m. The experimental data that were taken from Pacek et al. (1998) and Desnoyer et al. (2003) have been applied to this relation to investigate the effect of phase ratio. It is shown that even at low phase fractions, the Kolmogorov–Hinze theory necessarily does not give the best result with the −0.6 exponent for the Weber number. Furthermore, for the non-coalescing system, a range of exponent for the Weber number typically from −0.6 to −0.43 can be considered where the system may be approximated as a pseudo-coalescing system at Φ = 0.4 in which the obtained results are in good agreement with the results of Pacek et al. (1998).     

The effect of pH on experimental and simulation results of transient drop size distributions in stirred liquid-liquid dispersions

A novel parameter study with experimental and numerical investigations of transient drop size distributions was carried out in order to study published model approaches for dispersed systems on the basis of the population balance equation. In terms of breakage and coalescence behaviour the dependency of the drop size distributions on power input, phase fraction, and especially pH was studied with the system toluene-water. With higher pH, coalescence is hindered considerably. As a consequence, the transient evolution of drop size distributions after starting the stirrer is changing and the time for reaching the stationary distribution increases. For the simulation applying the breakage and coalescence models a very efficient solver for the population balance equation (PBE), the program PARSIVAL^® is used. The simulation results of transient drop size distributions are in good agreement with the experimental data for various power inputs. The influence of the dispersed phase fraction is not characterized correctly.A proportionality between the Sauter mean diameter and the Weber number d₃₂∼We^-0.5 was measured for pH 13 and different phase fractions. The commonly reported exponent -0.6 for systems with low coalescence seems to be not applicable with higher pH and increased dispersed phase fraction.     

Modelling local bubble size distributions in agitated vessels

Photography and capillary suction probe were used to measure local bubble size distributions (BSDs) from Rushton turbine agitated (14/200 L) air-tap water and CO₂-n-butanol dispersions. A multiblock stirred tank model with population balances (PBs) for bubbles was created to describe local BSDs in agitated vessels. Unknown parameters in breakage and coalescence models were adjusted by comparing the predicted and measured local BSDs. The BSDs from both investigated systems and varying vessel-operating conditions were included simultaneously to the fitting. The adjusted models were incorporated to MUSIG PB model in CFX-5.7 and tested for the laboratory stirred tanks. The multiblock model showed to be an optimal trade-off between the accuracy and CPU time for the investigation of gas-liquid hydrodynamics and validation of closure models. As a result of fitting, the adjusted model seems to describe local BSDs more accurately in agitated vessels than the model of Lehr et al. [2002. Bubble-size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443], which has been successful in bubble column studies. This shows that phenomenological breakage and coalescence closures need experimental validation for various flow environments.     

Experimental study on drop breakup time and breakup rate with drop swarms in a stirred tank

The direct experimental data for breakup parameters of drop breakup time, multiple breakage, and breakup rate are urgently required to understand drop breakup phenomena. In this regard, drop breakup experiments were carried out in a stirred tank using a high-speed online camera. The influences of the rotating speed, interfacial tension, and drop viscosity on the above breakup parameters were then quantitatively investigated. An mechanism correlation for the breakup time is proposed and is further verified by comparing with the results of Solsvik and Jakobsen (Chem Eng Sci, 2015;131:219-234). The percentage of multiple breakage comparing to binary breakup was statistically counted. The results indicated that the dimensionless drop diameter η = d/d_max can be adopted to characterize the proportion of binary breakup. Finally, the breakup rate was experimentally measured and the breakup probability was calculated using the inverse method.     

Three-dimensional numerical simulation of a horizontal rotating fluidized bed

Three-dimensional numerical simulations of a horizontal rotating fluidized bed (RFB) containing glass bead particles (d_s = 82 μm, ρ_s = 2450 kg/m³) and washed alumina (d_s = 89 μm, ρ_s = 1550 kg/m³) were performed. FLUENT 6.1 software was used to carry out our simulation. The numerical results were compared with the experimental data of Qian and Pfeffer et al. [G.H. Qian, I. Bagyi, I.W. Burdick, R. Pfeffer, H. Shaw, Gas-Solid Fluidization in a Centrifugal Field.” AIChE J. 47 (5) (2001) 1022-1034]. The rotating speed of the RFB was set at 325 rpm (34 rad/s), which is equivalent to a centrifugal acceleration of 7 g.The flow behavior of the solid particles was analyzed; the bed thickness and the calculated pressure drop were compared with the experimental results. Our calculated pressure drop agreed very well with the experimental results.     

Experimental confirmation of the influence of drop size distribution on liquid—liquid extraction column performance

The predicted influence of drop size distribution on the performance of liquid—liquid extraction columns has been experimentally verified for non-coalescing dispersions in a rotating disc contactor. Moderate increases in drop size distribution width, at a constant average drop size (d₃₂), caused reductions of up to 56% in the number of transfer units.     

Dynamic simulation of agitated liquid—liquid dispersions—II. Experimental determination of breakage and coalescence rates in a stirred tank

Using the theoretical procedure outlined in the first part of this work, breakage and coalescence rates were determined experimentally in a stirred tank. After reaching steady-state conditions, the intensity of agitation was suddenly changed and the variation in drop size distribution with time was monitored. The coalescence and breakage constants were evaluated by optimising the fit of the experimental results with the theoretical solution of the model equations. No a priori assumptions concerning the dependence of the interaction rates on drop size, system properties and operating conditions were made. Precise techniques for measuring the drop size distribution in turbulent dispersions were developed and tested. Empirical equations for dependence of breakage and coalescence constants on drop volume, holdup and system properties were derived.     

湍流分散体系中液滴破碎频率模型的黏性修正

在分析研究分散相黏度对液滴变形和破碎影响的基础上,提出了一个改进的液滴破碎频率模型并拓展了液滴破碎判据标准.同时通过Monte Carlo模拟的随机方法,得到了湍流搅拌槽中液-液分散体系的液滴直径分布和Sauter平均直径d₃₂.通过与文献中关于d₃₂的实验结果比较发现,该模型预测的Sauter平均直径更接近实验值,对于黏性分散相改进的液滴破碎频率模型要优于Coulaloglou和Tavlarides提出的模型.计算结果表明对于黏性分散相液滴,其黏度限制了液滴变形,使得液滴破碎频率被大大减少, 液滴直径明显增加,液滴直径分布向右偏移.     

Drop-breakage in agitated liquid—liquid dispersions

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.     

Wake shedding and circulatory flow in bubble and droplet-type contactors

A review of published work on continuous phase circulation in spray columns, and on attached wake volumes for single droplets, revealed an apparent paradox in that reported values of the former were an order of magnitude greater than the latter when expressed as a ratio of the dispersed phase flow. These results were confirmed in experiments using a photochromic tracer to reveal the entrainment and circulatory flow.Theoretical considerations show that droplets translate an amount of continuous phase relative to their own volume of 1.5C_D/d per unit distance traversed. Droplets carry with them an attached wake (“cap”) which for Re_d< about 200 is effectively permanent, the translated continuous phase passing around droplet and “cap” leaving a wake trail. At Re_d > 200 a fraction j of the translated continuous phase accumulates in the “cap”, which becomes unstable and sheds a fraction s_av as toroids at regular intervals of height z_s. Estimated values are given for j, s_av, and z_s.This result is extended to the case of a continuous droplet flow, leading to an expression for the rate of increase in circulatory flow of continuous phase in the central core with height above the droplet distributor. This flow is balanced by an increasing momentum loss to the wall until a steady state is reached. The implications of this result on the performance of spray columns is discussed.     

Dispersion-Polar Surface Tension Properties of Organic Solids

A new definition for work of adhesion W_a is applied to computationally define the dispersion γ_s ^d and polar γ_s ^d components of the solid surface tension γ_s = γ_s ^d + γ_s ^d for twenty-five low energy substrates. These calculated surface properties are correlated with surface composition and structure. Surface dipole orientation and electron induction effects are respectively distinguished for chlorinated and partially fluorinated hydrocarbons. Published values for critical surface tension of wetting γ_c are correlated with both γ_s ^d and γ_s.     

Dispersion of water into oil in a rotor–stator mixer. Part 2: Effect of phase fraction

In Part 1 (Rueger and Calabrese, 2013), we monitored dilute water-in-oil dispersions in a batch Silverson L4R rotor–stator mixer to establish breakage mechanisms and develop a mechanistic basis for correlation of equilibrium mean drop size. In this study (Part 2) we consider the effect of water phase fraction under similar processing conditions, thereby requiring consideration of coalescence. Most of the work on the effect of phase fraction in stirred vessels was done with a low-viscosity continuous phase in turbulent flow with inertial subrange scaling (d > η). For that case drop size increases linearly with phase fraction, ?. In this study, viscous oils comprised the continuous phase, with water as the drop phase. The equilibrium DSD was measured in both laminar and turbulent flow conditions. The diameter of the largest drops was always less than the Kolmogorov microscale (d < η). A much greater increase (than the aforementioned linear relationship) in drop size with phase fraction was observed for ? ≤ 0.05; including cases where an oil soluble surfactant was present and where metal mixing head surfaces were rendered hydrophobic by treatment with silane functional groups. It is argued that this significantly greater dependence on ? is due to the flow field being locally laminar near the drops with coalescence rate being strongly affected by the collision efficiency, which depends on the viscosity of both phases. The presence of surfactant decreased drop size. The silane treatment decreased drop size; possibly by altering water drop interactions with mill head surfaces. Additional experiments were performed at higher phase fraction, where surfactant was required to stabilize the emulsion. The equilibrium drop size was found to plateau for 0.10 < ? < 0.50. The high phase fraction behavior is attributed to the competing rates of coalescence and breakage and their dependence on ? and drop size.     

Effects of the excluded volume interactions on the conformational properties of star polymers

The effects of the excluded volume interactions on the conformational properties of star polymers have been studied. First order calculations at the critical dimensionality d = 4 yield the critical exponents of the average quantities up to first order in ε = 4-d. We thus find the partition function, the probability of the end of a branch to reach the central core and the probability of contact of the ends of two branches. The size of the macromolecule, expressed by the mean square radius of gyration 〈s²〉_star is studied in the region where the interactions between the polymeric units repel one another and in the region where the units attract one another. The results are compared with the results of previous works and with experiments.     

Predicting the classification characteristics of coal. Part 3. Gross calorific value of dry,ash-free coal

For 63 samples of Ukrainian, Russian, and imported coal, equations for predicting the gross calorific value Q_s^daf on the basis of the following coal characteristics are developed: W^a, O_d^daf, Q_s^af, and C_ar. The error is within the standard tolerances (σ ≤ 0.3 MJ/kg). With sufficient accuracy, Q_s^daf may be predicted from equations based on petrographic characteristics such as the vitrinite reflectance, the content of liptinitegroup minerals, and the sum of lean macerals (I + 2Sv/3). In these equations, the coefficients correspond to the heat of combustion of the vitrinite components at different metamorphic stages, the liptinite, and the lean macerals.     

Coalescence and break-up in dilute polydispersions

Functional relationships for coalescence rate dependence on drop size and hold-up were derived via the collision rates and coalescence efficiency. Experiments in an agitated vessel indicated the coalescence rate to be controlled by the viscous flow regime and, per unit drop concentrations, to be proportional to the third power of the sum of the diameters of the two coalescing drops. By combining the experimentally known coalescence rate dependence on drop diameter with the independently determined dependence of the latter on the dispersed phase hold up, the breakup rate was found to depend on d^2.0.     

Mass transfer from suspended solids to a liquid in agitated vessels

A new fundamental approach to the formulation of mass transfer from suspended solids to a liquid in agitated vessels is presented. Influence of various dimensionless groups on mass transfer is studied using the water-banzoic acid system for experimental work.Results are compared with previous works in agitated vessels and a correlation is proposed:Sh = 0.046Re^0.283Ga^0.173U^?0.011(T/d)^0.019Sc^O.461     

Local turbulent energy dissipation rate in an agitated vessel: New approach to dimensionless definition

Using theory of turbulence, particularly using turbulence spectrum analysis, the relations ε^* = ε/(u ⁴/ν) = const., v_K/u = const. and Λ/η_K = const. were derived. Assuming that u ∝ (Nd) from this it follows that the widely used dimensionless local turbulent energy dissipation rate defined as ε/((N ³ d ²) is directly proportional to impeller Reynolds number, i.e. ε/((N ³ d ²) ∝ Re, and length scale ratio Λ/d is indirectly proportional to impeller Reynolds number, i.e. Λ/d ∝ Re^–1, in an agitated vessel at high Reynolds number. The relations obtained by turbulence spectrum analysis were used for estimation of local turbulent energy dissipation rates experimentally measured by Ståhl Wernersson and Trägårdh (1998, 1999) covering the range of Re = 87600–910200 and own experimental data covering the range of Re = 50000–189000. The experiments have been performed in tanks of 300 mm and 400 mm in the inner diameter for three different viscosities and for various impeller rotational speeds.