Mixing of newtonian and non-newtonian liquids: Screw agitator and draft coil system

Mixing efficiency and power consumption have been investigated for several Newtonian and non-Newtonian liquids in a novel system consisting of a screw agitator rotating in a draft coil. For Reynolds numbers larger than 50, the inertial forces increase the pumping capacity of the screw impeller and hence its mixing efficiency. Shear-thinning effects can be accounted for by taking the effective rate of deformation to be proportional to the impeller rotational speed. Elasticity effects could be satisfactorily correlated with the Weissenberg number. The ratio of the mixing time to the average circulation time is constant. The power number could not be correlated with the Reynolds number; however, the ratio of the power number to the circulation number is inversely proportional to the Reynolds number for Newtonian as well as for shear-thinning inelastic fluids. The power consumption for elastic fluids is much larger.     

Electrostatic Drop Formation in Liquid/Liquid Systems

Electrostatic drop formation in liquid/liquid systems was studied, using high frequency AC fields (45 kHz). The dispersion of nonconductive into conductive fluids was investigated under various conditions, as are the effect of aqueous phase conductivity, capillary geometry and organic phase viscosity on the resulting drop size. The experimentally determined drop sizes and literature data, were correlated with a model equation, which was derived from a simple force balance, with an empirical term for the electric force. The model parameters were obtained in a toluene/water system and the model allows the prediction of the drop sizes of other organic solvents, if the capillary geometry is kept constant.     

Heat transfer to newtonian and non-newtonian liquids in a screw agitator and draft coil system

Heat transfer has been investigated for several Newtonian and non-Newtonian liquids mixed in a flat bottomed vessel equipped with a screw agitator and a coil acting simultaneously as draft tube and heat exchanger. Heat transfer rates from coil to liquid were determined for different coil designs, rheological properties and operating conditions in the heating and cooling modes. A circulation Reynolds number is defined, the characteristic length being the effective height of the heat exchanger (the coil) and the characteristic velocity being the circulation velocity of the fluid which was determined experimentally. Using this Reynolds number, it was possible to establish a single correlation for the Nusselt number as a function of Reynolds and Prandtl numbers. Geometric ratios do not appear in this correlation which could adequately represent more than 200 experimental data. A similar single correlation could not be obtained when using the conventional mixing Reynolds number. This novel system is shown to be very efficient for handling rheologically complex fluids.     

Bubble formation in viscous liquids under constant flow conditions

Bubble formation from single nozzles has been studied in liquids of different viscosities. The viscosity is varied in the range 50 to 500 c.p., whereas flow rates up to 100 cm³/second have been investigated. A model based on a two step (viz. expansion and detachment) mechanism has been proposed for bubble formation. The model explains the results of the present investigation as well as those reported in the literature for similar systems. As an extreme case, the model is tested on liquids of very low viscosity after dropping the viscosity terms from the equations and is found to explain even these data quite well.     

Bubble drag in contaminated non-newtonian solutions

The motion of a bubble in an infinite fluid is examined in the case where the surrounding fluid is non-Newtonian and contains impurities. An expression is developed for the drag force as a function of the shear-thinning character as well as of the concentration of surfactant of the fluid. The obtained expression for the drag force correlates quite nicely with experimental data for small bubbles.     

Drag on non-spherical particles in non-newtonian fluids

Extensive experimental results on the free fall of a range of non-spherical particles such as square bars, cylinders, spheres and crushed rock chips in Newtonian, inelastic, viscoelastic and Boger fluids are presented. It is demonstrated that the use of a volume equivalent sphere diameter in addition to a shape factor provides an adequate approximation for the non-sphericity of particles used in this study. The applicability of two rheological models, namely, the power-law and the Carreau viscosity model has been examined in representing the drag coefficient results. Appropriate predictive expressions of the drag coefficient as a function of the particle Reynolds number and the Deborah number, encompassing wide ranges of rheological and kinematic conditions, are presented.     

Drop mixing in suspension polymerisation

In suspension polymerisation, monomer is suspended as liquid droplets in a continuous water phase by means of strong agitation and the presence of a suspending agent. As the suspension polymerisation proceeds, the viscosity of a monomer-polymer droplet increases with conversion. Hence, the physical behaviour of the droplet changes during the process. When new dispersible material is added to the existing suspension drops, the new material and existing drops can remain segregated for significant amounts of time. The aim of this project was to study the behaviour of drop mixing when new material is added to the existing suspension polymerisation. This study concentrated on the effect of the dispersed phase viscosity on drop mixing. The results show that viscosity affects drop size and that may then affect the rate of coalescence between drops. A critical drop size exists which determines the coalescence efficiency effect. Above the critical drop size, mixing rate increases as the drop viscosity decreases. While below the critical drop size, drop size of the dispersion determines the coalescence rate; as the drop size increases, coalescence rate also increases. The investigation of the effect of suspending agent shows that Tween 20 is more efficient in stabilising and protecting the drops, based on a weight basis, than PVA as the coalescence rate is lower with Tween 20.     

Drop size distribution and mean drop size in a pulsed packed extraction column

Drop size distribution and mean drop size are used for calculation of interfacial area available for mass transfer. In this study, the drop size distribution and Sauter mean drop diameter (d₃₂) have been investigated using three different liquid systems in the absence of mass transfer in a pilot plant pulsed packed column. The drop size was measured at four different points along the active column height. Three operating variables have been studied including the pulse intensity (af) and flow rates of both liquid phases. The effect of liquid properties and height of the active column were also investigated. A combination of the pulse intensity and interfacial tension had the largest effect on the drop size distribution while none of the flow rates were of significance. The height of the column played an important role at the bottom of the active column, but the associated effect was reduced with increase of the height. Finally, a normal probability function of number density was proposed for prediction of the drop size distribution with an Average Absolute Relative Error (AARE) of 8.8% for their optimized constant. Furthermore, two correlations were presented involving height or flow rates of the two phases along with operating variables and physical properties of the liquids. These correlations had AARE values of about 8.5 and 7.8%, respectively.     

Drainage in thin planar non-newtonian fluid films

Equations for the radial and linear drainage of non-Newtonian fluids in horizontal and inclined films are presented. For a power law fluid with index m, the variation in dimensionless film thickness Δ with dimensionless time T is given by: where Δ and T are appropriately defined for drainage in radial horizontal and linear inclined films. The corresponding approximate expression for a Bingham plastic fluid is: in which A is the minimum film thickness defined appropriately at the asymptotic limits when Δ » A and Δ ? A.     

Drop formation in a co-flowing ambient fluid

Drop formation at a capillary tip in laminar flow is investigated experimentally. The disperse phase is injected via a needle into another co-flowing immiscible fluid. Two different drop formation mechanisms are distinguished: Either the drops are formed close to the capillary tip—dripping—or they break up from an extended liquid jet—jetting. The effect of the process and material parameters on the drop formation depends on the breakup mechanism and has to be investigated for each flow domain separately. In this study, we focus on dripping. The drop breakup is affected by the flow dynamics of both the disperse and the continuous phase. Consequently, we investigate the effect of flow rates, fluid viscosities and interfacial tension on the droplet size and observe the dynamics of satellite drop generation. Whereas the fundamentals of disperse fluid injection via a capillary into an ambient fluid have been investigated extensively, the focus of this article is on providing a comprehensive experimental data set for proving the applicability of this technique as a dispersing tool. It is shown that drop formation at a capillary tip into a co-flowing ambient liquid represents a promising technique for the production of monodisperse droplets where the droplet size is controlled externally by the flow strength of the continuous phase. The breakup dynamics changes significantly at the transition point from dripping to jetting. Consequently, the transition point between the flow domains represents an important operating point. In this article, dripping is demarcated from jetting by studying the influence of the various material and process parameters on the transition point.     

Hindered settling in non-newtonian power law liquids

New experimental results on the hindered settling of model glass bead suspensions in non-Newtonian suspending media are reported. The data presented encompass the following ranges of variables: 7.38 × 10^?4 ≤ Re_1∞ ≤ 2; 0.0083 ≤ d/D ≤ 0.0703; 0.13 ≤ C ≤ 0.43 and 1 ≥ n ≥ 0.8. In these ranges of conditions, the dependence of the hindered settling velocity on concentration is adequately represented by the corresponding Newtonian expressions available in the literature. The influence of the power law flow behaviour index is completely embodied in the modified definition of the Reynolds number used for power law liquids.     

Experimental study on drop formation in liquid-liquid fluidized bed

Drop formation in liquid-liquid fluidized bed was investigated experimentally. The normal water was injected via a fine-capillary spray nozzle into the co-flowing No. 25 transformer oil with jet directed upwards in a vertical fluidized bed. Experiments under a wide variety of conditions were conducted to investigate the instability dynamics of the jet, the size and size distribution of the drops. Details of drop formation, drop flow patterns and jet evolution were monitored in real-time by an ultra-high-speed digital CCD (charge couple device) camera. The Rosin-Rammler model was applied to characterize experimental drop size distributions. Final results demonstrate that drop formation in liquid-liquid system takes place on three absolutely different developing regimes: bubbling, laminar jetting and turbulent jetting, depending on the relative Reynolds number between the two phases. For different flow domains, dynamics of drop formation change significantly, involving mechanism of jet breakup, jet length pulsation, mean size and uniformity of the drops. The jet length fluctuates with time in variable and random amplitudes for a specified set of operated parameters. Good agreement is shown between the drop size and the Rosin-Rammler distribution function with the minimum correlation coefficient 0.9199. The mean drop diameter decreases all along with increasing jet flow rate. Especially after the relative Reynolds number exceeds a certain value about 3.5×10⁴, the jet disrupts intensely into multiple small drops with a diameter mainly ranging from 1.0 to and a more and more uniform size distribution. The turbulent jetting regime of drop formation is the most preferable to the dynamic ice slurry making system.     

Liquid circulation time in concentric-tube airlift columns with non-newtonian fermentation broths

Liquid circulation times were measured in a 40-dm³ concentric-tube airlift fermenter with simulated media over a wide range of rheological properties. Circulation times decreased with increasing shear-thinning, and the influence of draft-tube geometry on circulation time was found to depend on the shear-thinning of the media. A semi-theoretical correlation for both Newtonian and non-Newtonian fermentation media was developed.     

Particle formation and growth in ab initio emulsifier-free emulsion polymerisation under monomer-starved conditions

Particle formation and growth in the monomer-starved emulsifier-free emulsion polymerisation of monomers with different water solubility including methyl acrylate (MA), methyl methacrylate (MMA), and vinyl acetate (VA) were studied. The rate of formation of precursor particles, via homogenous nucleation, is proportional to the monomer concentration in the water phase. One may think that the maximum number of particles will be obtained when the water phase is saturated with the monomer. The number of PMA particles showed a maximum when the water phase was starved with the monomer. The number of PVA particles did not show any sensitivity to the monomer concentration in the water phase. More unexpectedly the final number of PMMA particles showed a minimum when the water phase was just saturated with the monomer. The minimum in the final number of PMMA particles was correlated with the enhanced rate of particle growth due to the gel effect. Under monomer-starved conditions, the number of particles produced was in the order of water solubility of the monomers; MA > VA > MMA. A reverse order was produced under monomer-saturated conditions as particle coagulation became progressively more important for some of the monomers.     

Drag on individual cubic assemblies of spheres in non-newtonian tube flow

An obstacle in modeling aseptic processing of particulate foods is the lack of a reliable estimator for the drag force of the non-Newtonian liquid phase on the suspended particles as they flow through the holding tubes of such systems. The objective was to develop an expression for the drag force on cubic assemblies of spherical particles suspended in a pseudoplastic fluid flowing in a tube. An apparatus was assembled for direct measurement of the drag force exerted by solutions of sodium carboxymethyl cellulose (CMC) on the assemblies inside a tube. An empirical drag correction factor, as a function of particle volume fraction (applicable to Stokes' law), was developed.     

Salt dissolution in drilling muds — a generalized correlation for mass transfer in non-newtonian fluids

The rate of dissolution of rock salt in drilling mud was measured as a function of flow rate and temperature under conditions simulating those in a well. A water based drilling mud, containing about 10% solids and additives was used, as well as a polymer “mud” composed of a Xanthan gum polymer solution and 5% salt, but no solids. The non-Newtonian muds were pumped through a “slit” flow cell, with a slab of rock salt flush with one side of the cell wall. The data (including water over the same range of conditions) were described by a mass transfer coefficient, and were correlated in dimensionless form based on the theoretical solution of the analogous heat transfer problem, adapted to non-Newtonian fluids. The non-Newtonian properties were described by an effective viscosity, which is consistent with either the power law or Bingham plastic viscosity model.     

Coal liquefaction in lignin-derived liquids under low severity conditions

It is found that lignin-derived liquids when reacted with coal under mild reaction conditions (375 °C and 2.17 × 10⁶ − 3.55 × 10⁶ N m⁻¹) enhance the rate of coal depolymerization. Up to 30% enhancement in coal conversion rate is achieved using lignin-derived liquids. The influence of time of reaction and temperature on the degree of reaction was investigated. The lignin liquid-assisted coal depolymerization products (liquid) are observed to contain a significant amount of the desirable pentane-soluble fraction. Influence of the time of storage of lignin-derived liquids on coal conversion was also determined. Also reported are data on elemental analyses of the solid and liquid products. The liquid product analyses using n.m.r. and s.e.c. techniques are also presented. Based upon the experimental data collected, it is hypothesized that enhancement in coal depolymerization rate can be explained by a reaction pathway involving intermediates formed from lignin-derived lignin liquids. A mathematical model describing the reaction chemistry has been developed. Computed rate constants are also reported. The analysis indicates that the lignin-derived intermediates are short-lived as compared to the time needed for complete coal depolymerization.     

Correlations for liquid-phase mass transfer coefficients in bubble column reactors with newtonian and non-newtonian fluids

The earlier work of Calderbank and Moo-Young (1961) dealing with the liquid-phase mass transfer coefficient in gas-liquid dispersions is examined. Their well-known empirical correlations for small and large bubbles which are free to move under gravity are theoretically derived. The analyses are based on the approach for natural convection mass transfer, and include the case where the fluid is non-Newtonian. The predictions of the models are compared with reported experimental data and correlations.     

A general correlation for purely viscous non-newtonian fluids flowing in ducts of arbitrary cross-section

An alternative correlation for the flow of purely viscous non-Newtonian fluids in ducts of arbitrary cross-section is proposed. It involves two dimensionless groups which are Unique relationships exist between ? and Re^*_G for both laminar and turbulent flows which enable direct predictions of pressure drop from flow rate results or vice-versa. Excellent agreement between the new correlations and available experimental data for purely viscous non-Newtonian fluids flowing in circular tubes and square ducts is demonstrated.     

Drop penetration time in heterogeneous powder beds

Wet granulation is a technique in which enlarged particles or ‘granules’ are produced from the coalescence of fine particles, with the intention of improving the powder properties. High shear granulators are often used to carry out the granulation process where the powder mass is agitated in a vessel by mechanical means while liquid is sprayed from above onto the powder bed surface. When the binder droplets impact the powder surface, the drop penetration time of the droplet into the powder is important for uniform binder dispersion and the prediction of the formation of granule nuclei from the nucleation map, which depends on the dimensionless spray flux. Previous studies on the drop penetration time were carried out on predominantly hydrophilic powder beds. Although this gives a good prediction of the nucleation behaviour in granulation, it does not reflect the condition where hydrophobic drugs are used in the formulation without surfactants. This paper aims to look at the effects of powder bed hydrophobicity on the drop penetration time.Single drop nucleation experiments using a syringe and a small powder bed were carried out on varying ratios of salicylic acid and lactose powders to study the kinetic of drop penetration. As expected, the drop penetration time increased as the proportion of hydrophobic component increased in the powder mixture. However, long drop penetration times were observed for low degrees of drug loading, showing that hydrophobicity strongly influences the drop penetration time. The wettability of the powder mixture also has a pronounced affect on the granule properties in which the hydrophobicity of the powder mixture is proportional to the granule strength and inversely proportional to the granule size. These findings have important implications in terms of the design of the granulation process where conditions of minimum spray flux or efficient mechanical forces are recommended to produce a more uniform granulation batch.