Simulations of pendant drop formation of a viscoelastic liquid

A modified Volume-of-Fluid (VOF) numerical method is used to predict the dynamics of a liquid drop of a low viscosity dilute polymer solution, forming in air from a circular nozzle. Viscoelastic effects are represented using an Oldroyd-B model. Predicted drop shapes are compared with experimental observations. The main features, including the timing of the shape evolution and the bead-on-a-string effect, are well reproduced by the simulations. The results confirm published conclusions of the third author, that the deformation is effectively Newtonian until near the time of Newtonian pinch-off and that the elastic stress becomes large in the pinch region due to the higher extensional flow there.

Pendant drop formation of shear-thinning and yield stress fluids

A volume-of-fluid numerical method is used to predict the dynamics of shear-thinning liquid drop formation in air from a circular orifice. The validity of the numerical calculation is confirmed for a Newtonian liquid by comparison with experimental measurements. For particular values of Weber number and Froude number, predictions show a more rapid pinch-off, and a reduced number of secondary droplets, with increasing shear-thinning. Also a minimum in the limiting drop length occurs for the smallest Weber number as the zero-shear viscosity is varied. At the highest viscosity, the drop length is reduced due to shear-thinning, whereas at lower viscosities there is little effect of shear-thinning. The evolution of predicted drop shape, drop thickness and length, and the configuration at pinch-off are discussed for shear-thinning drops. The evolution of a drop of Bingham yield stress liquid is also considered as a limiting case. In contrast to the shear-thinning cases, it exhibits a plug flow prior to necking, an almost step-change approach to pinch-off of a torpedo shaped drop following the onset of necking, and a much smaller neck length; no secondary drops are formed. The results demonstrate the potential of the numerical model as a design tool in tailoring the fluid rheology for controlling drop formation behaviour. (c) 2006 Elsevier Inc. All rights reserved.

Instabilities and drop formation in cylindrical liquid jets in reduced gravity

The effects of convective and absolute instabilities on the formation of drops formed from cylindrical liquid jets of glycerol/water issuing into still air were investigated. Medium-duration reduced gravity tests were conducted aboard NASA's KC-135 and compared to similar tests performed under normal gravity conditions to aid in understanding the drop formation process. In reduced gravity, the Rayleigh-Chandrasekhar Equation was found to accurately predict the transition between a region of absolute and convective instability as defined by a critical Weber number. Observations of the physics of the jet, its breakup, and subsequent drop dynamics under both gravity conditions and the effects of the two instabilities on these processes are presented. All the normal gravity liquid jets investigated, in regions of convective or absolute instability, were subject to significant stretching effects, which affected the subsequent drop and associated geometry and dynamics. These effects were not displayed in reduced gravity and, therefore, the liquid jets would form drops which took longer to form (reduction in drop frequency), larger in size, and more spherical (surface tension effects). Most observed changes, in regions of either absolute or convective instabilities, were due to a reduction in the buoyancy force and an increased importance of the surface tension force acting on the liquid contained in the jet or formed drop. Reduced gravity environments allow better investigations to be performed into the physics of liquid jets, subsequently formed drops, and the effects of instabilities on these systems. In reduced gravity, drops form up to three times more slowly and as a consequence are up to three times larger in volume in the theoretical absolute instability region than in the theoretical convective instability region. This difference was not seen in the corresponding normal gravity tests due to the masking effects of gravity. A drop is shown to be able to form and detach in a region of absolute instability, and spanning the critical Weber number (from a region of convective to absolute instability) resulted in a marked change in dynamics and geometry of the liquid jet and detaching drops. (C) 2002 American Institute of Physics.

Liquid distribution in wet granulation: dimensionless spray flux

This study investigates binder distribution in wet granulation and focuses on the nucleation zone, which is the area where the liquid binder and powder surface come into contact and form the initial nuclei. An equipment independent parameter, dimensionless spray flux Psi (a), is defined to characterise the most important process parameters in the nucleation process: solution flowrate, powder flux, and binder drop size. Ex-granulator experiments are used to study the relationship between dimensionless spray flux, process variables and the coverage of binder fluid on the powder surface. Lactose monohydrate powder on a variable speed riffler passed under a flat spray once only. Water and 7% HPC solution at two spray pressures were used as binders. Experiments with red dye and image analysis demonstrate that changes in dimensionless spray flux correlate with a measurable difference in powder surface coverage. Nucleation experiments show that spray flux controls the size and shape of the nuclei size distribution. At low Psi (a), the system operates in the drop controlled regime, where one drop forms one nucleus and the nuclei size distribution is narrow. At higher Psi (a), the powder surface cakes creating a broader size distribution. For controlled nucleation with the narrowest possible size distribution, it is recommended that the dimensionless spray flux be less than 0.1 to be in the drop-controlled regime. (C) 2001 Elsevier Science S.A. All rights reserved.

Transient mesenteric ischaemic episodes tracked by continuous jejunal PCO2 monitoring during liquid feeding

Objective: To test the effect of liquid feeds on the responses to splanchnic ischaemia of a continuous rapid response PCO2 sensor inserted in the jejunum. Design: Prospective experimental animal study in a university research laboratory. Subjects: Adult male Wistar rats. Interventions: Adult male Wistar rats (285-425 g) were anaethetised with sodium pentobarbitone 60 mg/ kg i.p. and ventilated with 100 % oxygen and isoflurane via tracheostomy to a PaCO2 of 30-40 mmHg. A sensor was inserted into the mid-jejunum to record PCO2 every second. Distal aortic pressure was transduced. Four control rats received no feeds whilst in another four rats liquid feed was infused into the proximal jejunum at 3 ml/h. In each rat five episodes of splanchnic ischaemia were induced by 2-min elevations of an aortic sling to a mean distal aortic pressure of 30 mmHg. Measurements and main results: PCO2 elevations were always detectable, usually less than a minute from the onset of splanchnic ischaemia in both fed and unfed rats, with no difference in mean times to detectable response. In the fed rats there was a small but significant increase in the time to peak sensor response (196 +/- 16 vs. 180 +/- 12 s) and a trend towards an elevated mean baseline luminal PCO2 (67 +/- 9 vs. 55 +/- 4 mmHg). Conclusions: Brief episodes of splanchnic ischaemia were tracked successfully by a rapid response jejunal continuous PCO2 sensor during the infusion of a proprietary liquid feed preparation despite minor changes in PCO2 response characteristics and a possible elevation in baseline luminal PCO2.

Scale-up of mixer granulators for effective liquid distribution

There is considerable anecdotal evidence from industry that poor wetting and liquid distribution can lead to broad granule size distributions in mixer granulators. Current scale-up scenarios lead to poor liquid distribution and a wider product size distribution. There are two issues to consider when scaling up: the size and nature of the spray zone and the powder flow patterns as a function of granulator scale. Short, nucleation-only experiments in a 25L PMA Fielder mixer using lactose powder with water and HPC solutions demonstrated the existence of different nucleation regimes depending on the spray flux Psi(a)-from drop-controlled nucleation to caking. In the drop-controlled regime at low Psi(a) values. each drop forms a single nucleus and the nuclei distribution is controlled by the spray droplet size distribution. As Psi(a) increases, the distribution broadens rapidly as the droplets overlap and coalesce in the spray zone. The results are in excellent agreement with previous experiments and confirm that for drop-controlled nucleation. Psi(a) should be less than 0.1. Granulator flow studies showed that there are two powder flow regimes-bumping and roping. The powder flow goes through a transition from bumping to roping as impeller speed is increased. The roping regime gives good bed turn over and stable flow patterns. This regime is recommended for good liquid distribution and nucleation. Powder surface velocities as a function of impeller speed were measured using high-speed video equipment and MetaMorph image analysis software, Powder surface velocities were 0.2 to 1 ms(-1)-an order of magnitude lower than the impeller tip speed. Assuming geometrically similar granulators, impeller speed should be set to maintain constant Froude number during scale-up rather than constant tip speed to ensure operation in the roping regime. (C) 2002 Published by Elsevier Science B.V.

Drop penetration into porous powder beds

The kinetics of drop penetration were studied by filming single drops of several different fluids (water, PEG200, PEG600, and HPC solutions) as they penetrated into loosely packed beds of glass ballotini, lactose, zinc oxide, and titanium dioxide powders. Measured times ranged from 0.45 to 126 s and depended on the powder particle size,viscosity, surface tensions, and contact angle. The experimental drop penetration times were compared to existing theoretical predictions by M. Denesuk et al. (J. Colloid Interface Sci. 158, 114, 1993) and S. Middleman (Modeling Axisymmetric Flows: Dynamics of Films, Jets, and Drops, Academic Press, San Diego, 1995) but did not agree. Loosely packed powder beds tend to have a heterogeneous bed structure containing large macrovoids which do not participate in liquid flow but are included implicitly in the existing approach to estimating powder pore size. A new two-phase model was proposed where the total volume of the macrovoids was assumed to be the difference between the bed porosity and the tap porosity. A new parameter, the effective porosity (epsilon)eff, was defined as the tap porosity multiplied by the fraction of pores that terminate at a macrovoid and are effectively blocked pores. The improved drop penetration model was much more successful at estimating the drop penetration time on all powders and the predicted times were generally within an order of magnitude of the experimental results. (C) 2002 Elsevier Science (USA).

Experimental study of drop-interface coalescence in the presence of polymer stabilisers

An experimental study has been carried out to characterise the performance of polymer stabilisers, partially hydrolysed polyvinyl acetate (PVAc), used in suspension polymerisation processes. The stabilisers are ranked by their ability to stabilise the dispersion characterised by the median coalescence time of a single drop with its homophase at a planar liquid/liquid interface. Results show that the stability of the dispersion relates closely to the molecular properties of the PVAcs. Other conditions being equal, PVAcs with higher molecular weights or lower degrees of hydrolysis can better stabilise a liquid-liquid dispersion. The stability of the dispersion also depends strongly on where the PVAc resides. The presence of a PVAc in the dispersed phase significantly reduces stability. Consistent with results reported in the literature, considerable scatter has been observed on the coalescence times of identical drops under the same conditions. An explanation for the scatter is also proposed in the paper, based on the classical Reynolds model for film thinning. (C) 2002 Elsevier Science B.V. All rights reserved.

Nucleation regime map for liquid bound granules

Nucleation is the first step in granulation where the powder and liquid first contact. Two types of nucleation in wet granulation processes are proposed. Drop controlled nucleation, where one drop forms one nucleus, occurs when drops hitting the powder surface do not overlap (low spray flux Psi(a)) and the drop must wet quickly into the bed (short drop penetration time t(p)). If either criterion is not met, powder mixing characteristics will dominate (mechanical dispersion regime). Granulation experiments were performed with lactose powder, water, PEG200, and 7% HPC solution in a 6 L and a 25 L mixer granulator. Size distributions were measured as the drop penetration time and spray flux were varied. At short penetration times, decreasing Psi(a) caused the nuclei distribution to become narrower. When drop penetration time was high, the nuclei size distribution was broad independent of changes in dimensionless spray flux. Nucleation regime maps were plotted for each set of experiments in each mixer as a function of the dimensionless distribution width delta. The nucleation regime map demonstrates the interaction between drop penetration time and spray flux in nucleation. The narrowest distribution consistently occurred at low spray flux and low penetration time, proving the existence of the drop controlled regime. The nucleation regime map provides a rational basis for design and scale-up of nucleation and wetting in wet granulation.

Determination of external and internal mass transfer limitation in nitrifying microbial aggregates

In this article we present a study of the effects of external and internal mass transfer limitation of oxygen in a nitrifying system. The oxygen uptake rates (OUR) were measured on both a macro-scale with a respirometric reactor using off-gas analysis (Titrimetric and Off-Gas Analysis (TOGA) sensor) and on a micro-scale with microsensors. These two methods provide independent, accurate measurements of the reaction rates and concentration profiles around and in the granules. The TOGA sensor and micro-sensor measurements showed a significant external mass transfer effect at low dissolved oxygen (DO) concentrations in the bulk liquid while it was insignificant at higher DO concentrations. The oxygen distribution with anaerobic or anoxic conditions in the center clearly shows major mass transfer limitation in the aggregate interior. The large drop in DO concentration of 22 - 80% between the bulk liquid and aggregate surface demonstrates that the external mass transfer resistance is also highly important. The maximum OUR even for floccular biomass was only attained at much higher DO concentrations ( approximate to 8 mg/L) than typically used in such systems. For granules, the DO required for maximal activity was estimated to be > 20mg/L, clearly indicating the effects of the major external and internal mass transfer limitations on the overall biomass activity. Smaller aggregates had a larger volumetric OUR indicating that the granules may have a lower activity in the interior part of the aggregate. (C) 2004 Wiley Periodicals, Inc.

Dynamic interfacial tension of aqueous solutions of PVAAs and its role in liquid-liquid dispersion stabilization

In liquid-liquid dispersion systems, the dynamic change of the interfacial properties between the two immiscible liquids plays an important role in both the emulsification process and emulsion stabilization. In this paper, experimentally measured dynamic interfacial tensions of 1-chlorobutane in the aqueous solutions of various random copolymers of polyvinyl acetate and polyvinyl alcohol (PVAA) are presented. Theoretical analyses on these results suggest that the adsorption of the polymer molecules is controlled neither by the bulk diffusion process nor the activation energy barrier for the adsorption but the conformation of polymer molecules. Based on the concept of critical concentration of condensation for polymer adsorption, as well as the observation that the rate at which the dynamic interfacial tension changes does not correlate to the PVAA's ability to stabilize a single drop, it is postulated that the main stabilization mechanism for the PVAAs is by steric hindrance, not the Gibbs-Marangoni effect offered by the small molecule surfactants.

Local liquid holdups and hysteresis in a 2-D packed bed using X-ray radiography

An X-ray visualization technique has been used for the quantitative determination of local liquid holdups distribution and liquid holdup hysteresis in a nonwetting two-dimensional (2-D) packed bed. A medical diagnostic X-ray unit has been used to image the local holdups in a 2-D cold model having a random packing of expanded polystyrene beads. An aqueous barium chloride solution was used as a fluid to achieve good contrast on X-ray images. To quantify the local liquid holdup, a simple calibration technique has been developed that can be used for most of the radiological methods such as gamma ray and neutron radiography. The global value of total liquid holdup, obtained by X-ray method, has been compared with two conventional methods: drainage and tracer response. The X-ray technique, after validation, has been used to visualize and quantify, the liquid hysteresis phenomena in a packed bed. The liquid flows in preferred paths or channels that carry droplets/rivulets of increasing size and number as the liquid flow rate is increased. When the flow is reduced, these paths are retained and the higher liquid holdup that persists in these regions leads to the holdup hysteresis effect. Holdup in some regions of the packed bed may be an order of magnitude higher than average at a particular flow rate. (c) 2005 American Institute of Chemical Engineers

Experimental and analytical study of the effect of contact angle on liquid convective heat transfer in microchannels

In this paper we examine the effect of contact angle (or surface wettability) on the convective heat transfer coefficient in microchannels. Slip flow, where the fluid velocity at the wall is non-zero, is most likely to occur in microchannels due to its dependence on shear rate or wall shear stress. We show analytically that for a constant pressure drop, the presence of slip increases the Nusselt number. In a microchannel heat exchanger we modified the surface wettability from a contact angle of 20 degrees-120 degrees using thin film coating technology. Apparent slip flow is implied from pressure and flow rate measurements with a departure from classical laminar friction coefficients above a critical shear rate of approximately 10,000 s(-1). The magnitude of this departure is dependant on the contact angle with higher contact angles surfaces exhibiting larger pressure drop decreases. Similarly, the non-dimensional heat flux is found to decrease relative to laminar non-slip theory, and this decrease is also a function of the contact angle. Depending on the contact angle and the wall shear rate, variations in the heat transfer rate exceeding 10% can be expected. Thus the contact angle is an important consideration in the design of micro, and even more so, nano heat exchangers. (c) 2006 Elsevier Ltd. All rights reserved.

The effect of elasticity on drop creation in T-shaped microchannels

Polymeric microdrops of low viscosity, elastic fluids have been generated in T-shaped microfluidic devices using a cross-flow shear-induced drop generation process. Dilute (c/c* similar to 0.5) aqueous solutions of polyethylene oxide (PEO) of various molecular weights (3 x 10(5) -2 x 10(6) g/mol) were used as the drop phase fluids whilst silicone oils (5 mPa s

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

The dynamics of drop formation and pinch-off have been investigated for a series of low viscosity elastic fluids possessing similar shear viscosities, but differing substantially in elastic properties. On initial approach to the pinch region, the viscoelastic fluids all exhibit the same global necking behavior that is observed for a Newtonian fluid of equivalent shear viscosity. For these low viscosity dilute polymer solutions, inertial and capillary forces form the dominant balance in this potential flow regime, with the viscous force being negligible. The approach to the pinch point, which corresponds to the point of rupture for a Newtonian fluid, is extremely rapid in such solutions, with the sudden increase in curvature producing very large extension rates at this location. In this region the polymer molecules are significantly extended, causing a localized increase in the elastic stresses, which grow to balance the capillary pressure. This prevents the necked fluid from breaking off, as would occur in the equivalent Newtonian fluid. Alternatively, a cylindrical filament forms in which elastic stresses and capillary pressure balance, and the radius decreases exponentially with time. A (0+1)-dimensional finitely extensible nonlinear elastic dumbbell theory incorporating inertial, capillary, and elastic stresses is able to capture the basic features of the experimental observations. Before the critical "pinch time" t(p), an inertial-capillary balance leads to the expected 2/3-power scaling of the minimum radius with time: R-min similar to(t(p)-t)(2/3). However, the diverging deformation rate results in large molecular deformations and rapid crossover to an elastocapillary balance for times t>t(p). In this region, the filament radius decreases exponentially with time R-min similar to exp[(t(p)-t)/lambda(1)], where lambda(1) is the characteristic time constant of the polymer molecules. Measurements of the relaxation times of polyethylene oxide solutions of varying concentrations and molecular weights obtained from high speed imaging of the rate of change of filament radius are significantly higher than the relaxation times estimated from Rouse-Zimm theory, even though the solutions are within the dilute concentration region as determined using intrinsic viscosity measurements. The effective relaxation times exhibit the expected scaling with molecular weight but with an additional dependence on the concentration of the polymer in solution. This is consistent with the expectation that the polymer molecules are in fact highly extended during the approach to the pinch region (i.e., prior to the elastocapillary filament thinning regime) and subsequently as the filament is formed they are further extended by filament stretching at a constant rate until full extension of the polymer coil is achieved. In this highly extended state, intermolecular interactions become significant, producing relaxation times far above theoretical predictions for dilute polymer solutions under equilibrium conditions. (C) 2006 American Institute of Physics