Pressure drop and mixing behaviour of non‐Newtonian fluids in a static mixing unit

Static or motionless mixers have received wide application in chemical and allied industries due to their low cost and high efficiency. The pressure drop and mixing behaviour of such mixers have been widely studied. However, the available information for non‐Newtonian fluids is scanty. The results of pressure drop and mixing studies conducted with a locally made motionless mixer (MALAVIYA mixer) and four non‐Newtonian fluids—aq. CMC, PVA, and PEG solutions are reported in this article. The new mixer causes less pressure drop compared to some of the commercial mixers. Mixing behaviour of the unit is more closer to plug flow and a two‐parameter model correlates the dispersion data.     

Characterisation of the mixing of non‐newtonian fluids with a scaba 6SRGT impeller through ert and CFD

An attempt has been made to study the mixing of yield‐pseudoplastic fluids with a Scaba 6SRGT impeller using electrical resistance tomography (ERT) and computational fluid dynamics (CFD). The ERT system with four sensor planes, each containing 16 equispaced stainless steel electrodes, was used to measure the mixing time. The multiple reference frames (MRF) technique and the modified Herschel–Bulkley model were applied to simulate the impeller rotation and the rheological behaviour of the non‐Newtonian fluids, respectively. To validate the model, the CFD results for the power consumption were compared to the experimental data. The validated model was then employed to obtain further information regarding the averaged impeller shear rate, impeller circulation, and pumping capacities. The CFD and ERT data were utilised to investigate the effect of the impeller power, fluid rheology, and impeller size on the mixing time. The mixing time results obtained in this study were in good agreement with those reported in the literature. © 2011 Canadian Society for Chemical Engineering     

Laminar mixing of shear thinning fluids in a SMX static mixer

Flow and mixing of power-law fluids in a standard SMX static mixer were simulated using computational fluid dynamics (CFD). Results showed that shear thinning reduces the ratio of pressure drop in the static mixer to pressure drop in empty tube as compared to Newtonian fluids. The correlations for pressure drop and friction factor were obtained at Re_MR?100. The friction factor is a function of both Reynolds number and power-law index. A proper apparent strain rate, area-weighted average strain rate on the solid surface in mixing section, was proposed to calculate pressure drop for a non-Newtonian fluid. Particle tracking showed that shear thinning fluids exhibit better mixing quality, lower pressure drop and higher mixing efficiency as compared to a Newtonian fluid in the SMX static mixer.     

Pressure drop in a split‐and‐recombine caterpillar micromixer in case of newtonian and non‐newtonian fluids

Microreactors are very promising tools for the design of future chemical processes. For example, emulsions of very narrow size distribution are obtained at much lower energy consumption than the one spent with usual processes. Micromixers play thereby an eminent role. The goal of this study is to better understand the hydrodynamic properties of a split‐and‐recombine Caterpillar micromixer (CPMM) specially with regard to handling viscoelastic fluids, a topic hardly addressed so far in the context of micromixers in general, although industrial fluids like detergent, cosmetic, or food emulsions are non‐Newtonian. Friction factor was measured in a CPMM for both Newtonian and non‐Newtonian fluids. For Newtonian fluids, the friction factor in the laminar regime is f/2 = 24/Re. The laminar regime exists up to Reynolds numbers of 15. For shear‐thinning fluids like Carbopol 940 or viscoelastic fluids like Poly Acryl Amide (PAAm) aqueous solutions, the friction factor scales identically within statistical errors up to a generalized Reynolds number of 10 and 0.01, respectively. Above that limit, there is an excess pressure drop for the viscoelastic PAAm solution. This excess pressure drop multiplies the friction factor by more than a decade over a decade of Reynolds numbers. The origin of this excess pressure drop is the high elongational flow present in the Caterpillar static mixer applied to a highly viscoelastic fluid. This result can be extended to almost all static mixers, because their flows are generally highly elongational. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2679–2685, 2013     

Tomography images to analyze the deformation of the cavern in the continuous‐flow mixing of non‐Newtonian fluids

Tomography, an efficient nonintrusive technique, was employed to visualize the flow in continuous‐flow mixing and to measure the cavern volume (V_c) in batch mixing. This study has demonstrated an efficient method for flow visualization in the continuous‐flow mixing of opaque fluids using two‐dimensional (2‐D) and 3‐D tomograms. The main objective of this study was to explore the effects of four inlet‐outlet configurations, fluid rheology (0.5–1.5% xanthan gum concentration), high‐velocity jet (0.317–1.660 m s^?1), and feed flow rate (5.3 × 10^?5?2.36 × 10^?4 m³ s^?1) on the deformation of the cavern. Dynamic tests were also performed to estimate the fully mixed volume (V_{fully mixed}) for the RT, A310, and 3AM impellers in a continuous‐flow mixing system, and it was found that V_{fully mixed} was greater than V_c. Incorporating the findings of this study into the design criteria will minimize the extent of nonideal flows in the continuous‐flow mixing of complex fluids and eventually improve the quality of end‐products. © 2013 American Institute of Chemical Engineers AIChE J, 60: 315–331, 2014     

Breakup dynamics of slender bubbles in non‐newtonian fluids in microfluidic flow‐focusing devices

This study aims to investigate the breakup of slender bubbles in non‐Newtonian fluids in microfluidic flow‐focusing devices using a high‐speed camera and a microparticle image velocimetry (micro‐PIV) system. Experiments were conducted in 400‐ and 600‐μm square microchannels. The variation of the minimum width of gaseous thread with the remaining time before pinch‐off could be scaled as a power‐law relationship with an exponent less than 1/3, obtained for the pinch‐off of bubbles in Newtonian fluids. The velocity field and spatial viscosity distribution in the liquid phase around the gaseous thread were determined by micro‐PIV to understand the bubble breakup mechanism. A scaling law was proposed to describe the size of bubbles generated in these non‐Newtonian fluids at microscale. The results revealed that the rheological properties of the continuous phase affect significantly the bubble breakup in such microdevices. © 2012 American Institute of Chemical Engineers AIChE J,, 2012     

Natural convection in a vertical porous cavity filled with a non‐newtonian binary fluid

Numerical and analytical study of natural convection in a vertical porous cavity filled with a non‐Newtonian binary fluid is presented. The density variation is taken into account by the Boussinesq approximation. A power‐law model is used to characterize the non‐Newtonian fluid behavior. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure, while the two horizontal ones are assumed impermeable and insulated. Both double‐diffusive convection (a = 0) and Soret‐induced convection (a = 1) are considered. Scale analysis is presented for the two extreme cases of heat‐driven and solute‐driven natural convection. For convection in a thin vertical layer (A ? 1), a semianalytical solution for the stream function, temperature, and solute fields, Nusselt and Sherwood numbers are obtained using a parallel flow approximation in the core region of the cavity and an integral form of the energy and constituent equations. Numerical results of the full governing equations show the effects of the governing parameters, namely the thermal Rayleigh number, R_T, the Lewis number, Le, the buoyancy ratio, φ, the power‐law index, n, and the integer number a. A good agreement between the analytical predictions and the numerical simulations is obtained. © 2012 American Institute of Chemical Engineers AIChE J, 58: 1704–1716, 2012     

Experimental determination of the shear rate in a stirred tank with a non‐newtonian fluid: Carbopol

The local shear rate generated in a cylindrical tank equipped with a Rushton turbine was investigated using particle image velocimetry in a shear‐thinning fluid (Carbopol). This non‐Newtonian fluid was used in an attempt to mimic fermentation broths. Three Reynolds numbers corresponding to the transition regime were investigated. The hydrodynamics is analyzed, and the velocity field is decomposed by proper orthogonal decomposition into mean flow, organized motion, and turbulence. Then, the contributions of each flow structure to the total dissipation of kinetic energy are presented. The spatial heterogeneity of shear rate is discussed and a new expression is proposed for shear rate. This work shows that the local shear rate is highly heterogeneous in a tank. Future works will need to focus on other types of stirrer and investigate the effect of scaling up reactors on the shear rate heterogeneity. © 2012 American Institute of Chemical Engineers AIChE J, 59: 2251–2266, 2013     

The effect of mixer properties and fill level on granular flow in a bladed mixer

The discrete element method was used to study the effect of mixer properties and fill level on the granular flow of monodisperse, cohesionless spheres in a bladed mixer. For fill levels just covering the span of the blades, a three‐dimensional (3‐D) recirculation zone develops in front of the blades, which promotes vertical and radial mixing. Increasing fill level reduces the size of the recirculation zone, decreases bed dilation and hinders particle diffusivities. However, above a critical fill level, the behavior of the particles within the span of the blade is found to be invariant of fill level. At low‐fill levels, the pressure within the particle bed varies linearly with bed height and can be approximated by hydrostatics. At higher fill levels, a constant pressure region develops within the span of the blades due to the angled pitch of the blades. Cylinder wall friction is shown to significantly influence granular behavior in bladed mixers. At low‐wall friction, the 3‐D recirculation zone observed for high‐wall friction conditions does not develop. High‐wall friction leads to an increase in convective and diffusive particle mixing. Shear stresses are shown to be a function of wall friction. Blade position along the vertical axis is shown to influence flow patterns, granular temperature and stress. The effect of increasing the mixer diameter at a constant particle diameter was also studied. When the mixer diameter is larger than a critical size such that wall effects are minimized, the observed granular behavior follows simple scaling relations. Particle velocities and diffusivities scale linearly with mixer size and blade speed. Normal and shear stress profiles are found to scale linearly with the total weight of the particle bed. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Discrete element simulation of free flowing grains in a four‐bladed mixer

Numerical simulations of granular flow in a cylindrical vessel agitated by a four‐blade impeller were performed using the discrete element method. Velocity, density, and stress profiles within the mixer displayed a periodic behavior with a fluctuation frequency equal to that of the blade rotation. Blade orientation was found to affect flow patterns and mixing kinetics. For an obtuse blade pitch orientation, a three‐dimensional recirculation zone develops in‐front of the blade due to formation of heaps where the blades are present. This flow pattern promotes vertical and radial mixing. No recirculation zone was observed when the blade orientation was changed to an acute blade pitch. The system's frictional characteristics are shown to strongly influence the granular behavior within the mixer. At low friction coefficients, the 3‐D recirculation in front of the obtuse blade is not present reducing convective mixing. Higher friction coefficients lead to an increase in granular temperature which is associated with an increase in diffusive mixing. Normal and shear stresses were found to vary with mixer height with maximum values near the bottom plate. Additionally, a strong dependence between the magnitude of the shear stresses and the friction coefficient of the particles was found. The stress tensor characteristics indicate that the granular flow in our simulations occurs in the quasi‐static regime. At the same time, the averaged pressure was found to vary linearly with bed height and could be predicted by a simple hydrostatic approximation. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

The effect of non‐ideal mixing on the number of steady states and dynamic behaviour for autocatalytical reactions in a CSTR

In this paper, we analyze the concentration multiplicity and dynamic behavior for an autocatalytical reaction, A + R → (n + 1)R + products with an overall rate expression given by – γ_a= kc_a^pc_r^r(p > 0 and r > 0) in a imperfectly mixed (Cholette's model) CSTR. We proved that non‐ideal mixing had an effect on the number of steady states and dynamic behavior for the reaction orders r > 1 and r = 1. However, the above‐mentioned effect does not happen for the reaction order r < 1. Furthermore, a simulated example was used to demonstrate our results.     

Enhancement of the liquid feed distribution in gas solid fluidised beds by non‐mechanically induced nozzle pulsations

The effect of non‐mechanically induced nozzle pulsations was investigated in the current work, and it was found that appropriately tailored spray nozzles pulsations resulted in the dramatic improvement of the liquid feed spray distribution on particles of a fluidised bed. Non‐mechanically induced pulsations were imposed on the liquid spray, using liquid and gas circuits that favour the development of beneficial pulsations. The resulting effect on liquid dispersion on the fluidised bed particles was determined with a conductance method. © 2013 Canadian Society for Chemical Engineering     

Measurement of mass transfer coefficient in an airlift reactor with internal loop using coalescent and non‐coalescent liquid media

In this work the sulfite oxidation (SOM), dynamic pressure‐step (DPM) and gassing‐out (GOM) methods were compared for volumetric mass transfer coefficient measurement in an airlift reactor with internal loop. As a liquid phase both, non‐coalescent and coalescent media were used. Among the methods discussed here, the mass transfer coefficient (k_La) values obtained by the DPM appear as the most reliable as they were found to be independent of oxygen concentration in the inlet gas, which confirmed the physical correctness of this method. The difference between data measured using air and oxygen was not higher than 10%, which was comparable to the scatter of experimental data. It has been found that the sulfite oxidation method yielded k_La values only a little higher than those obtained by the DPM and the difference did not exceed 10%. Up to an inlet gas velocity (U_GC) of ?0.03 m s^?1 the GOM using oxygen as a gas medium gave k_La values in fact identical with those obtained by the DPM. At higher flows of the inlet gas, the GOM yielded k_La values as much as 15% lower. The enhancement in oxygen mass transfer rate determined in non‐coalescent media was estimated to be up to +15%, when compared with a coalescent batch. The experimental dependence of k_La vs the overall gas hold‐up was described by an empirical correlation. 1 Copyright © 2004 Society of Chemical Industry