Experimental study on geometric structure of isolated mixing region in impeller agitated vessel

Isolated mixing region in agitated vessel with rotated two-bladed paddle impeller and no baffle was visualized experimentally and its structural property was investigated in detail. A set of thin filaments spirally wrapping around the core of the toroidal isolated mixing region is observed under low Reynolds number conditions, which is smaller than 60. Three-dimensional geometrical structure of filament in isolated mixing region depends on the periodical perturbations caused by the rotating impeller. We have succeeded in the determination of three-dimensional geometrical structure of filament in isolated mixing region based on relation between the movement of fluid particle and filament numbers and/or wire turns. Interestingly, the wire turns of filaments are opposite to movements of fluid particles.     

Low Reynolds number flow in a channel with oscillating wavy-walls: An analytical study

An analytical study using perturbation methods has been investigated on the flow profiles and power requirements in an oscillating flow field with a wavy-walled boundary. The velocity field is found for a fluid in between two wavy-walled plates that oscillate in phase. The wavy-walled boundary causes the flow to produce regions of recirculations within the recesses of the boundary. Once the velocity profiles are identified, the power required to drive the oscillatory fluid motion is then calculated and compared to a flat plate geometry without recesses. As expected, the analytical results show that more power is needed to drive a wavy-walled system than a flat plate configuration.     

Investigation of laminar flow in a stirred vessel at low Reynolds numbers

Many mixing applications involve viscous fluids and laminar flows where the detailed as well as overall flow structures are important. In order to understand the fluid dynamic characteristics of low Re laminar flows in mixing vessels, the flow induced by a Rushton impeller for three Re namely, 1, 10 and 28, was studied both experimentally and computationally. It was found that for the highest Re, the flow exhibited the familiar outward pumping action associated with radial impellers under turbulent flow conditions. However, as the Re decreases, the net radial flow during one impeller revolution was reduced and for the lowest Re a reciprocating motion with negligible net pumping was observed. This behaviour has not been reported in the literature in the past and represents a highly undesirable flow pattern from the standpoint of effective mixing. The CFD results successfully reproduced this behaviour. In order to elucidate the physical mechanism responsible for the observed flow pattern, the forces acting on a fluid element in the radial direction were analysed. The analysis indicated that for the lowest Re, the material derivative of radial velocity near the blade tip is small thus a balance exists between pressure and viscous forces; the defining characteristic of creeping flow. The velocity and pressure forces are in phase because the velocity is driven by the pressure field generated by the rotation of the impeller. Based on these findings, a simplified analytic model of the flow was developed that gives a good qualitative as well as quantitative representation of the flow.     

Investigation of the convective motion through a staggered herringbone micromixer at low Reynolds number flow

A computational study is presented of the complex flow through a staggered herringbone micromixer (SHM), which utilises sequences of asymmetrical herringbone grooves in cycles where a set of topologically similar grooves represent a half cycle. It was analysed using finite-element (method) based software to elucidate the fluid flow within the channel and characterise the effect of the grooves at moving fluid across the channel thus creating non-axial fluid movement. Three separate physical systems were modelled: a channel containing a single groove, a half cycle of infinite grooves and an infinite system with one groove per half cycle. A range of groove heights were investigated for the single groove for the Reynolds number range 0-15 to identify the mechanics through which fluid is transported across the channel by the grooves, the effect that inertial and viscous forces have on the process and to identify a groove height range for optimised cross channel fluid transfer. The flow field within the grooves at various heights was analysed and their relationship with non-axial flow within the bulk channel identified. The culminating effect of increasing grooves per half cycle on their ability to transport fluid across the channel is analysed by comparing the entrainment of fluid into and across the groove for both a single and infinite grooves. The maximum increase in fluid entrainment per groove for the addition of extra grooves to a cycle was found to be 14%. The helicity (or swirl) of the flow within the channel is found to be small for all three systems, while increased helicity within the flow was found to correspond to an increase in energy dissipation.     

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.     

Dimensional analysis for planetary mixer: Mixing time and Reynolds numbers

Mixing time number is a convenient parameter to characterize mixing performance of stirred tanks. This dimensionless number is now well established for agitated vessels equipped with vertically and centrally mounted impeller for Newtonian as well as for non-Newtonian fluids. To our knowledge, there is more ambiguity concerning its definition for planetary mixers especially when they have dual motion (around two perpendicular axes) to achieve homogenization. In this study, dimensional analysis of mixing time and reliability of the modified Reynolds and mixing time numbers are proposed for such a planetary mixer particularly named as TRIAXE^® system. These two numbers are based on the maximum tip speed of mixer as the characteristic velocity. Modified dimensionless numbers are consistent with the definition of conventional Reynolds and mixing numbers (when only one revolving motion around the vertical axis of the mixing device occurs in the vessel).Mixing time experiments with TRIAXE^® mixer for highly viscous Newtonian fluids showed that the proposed modified Reynolds and mixing time numbers succeeded to obtain a unique mixing curve irrespective of the different speed ratio chosens. This agreement proves that the proposed modified dimensionless numbers can be well adapted for engineering purposes and they can be used to compare the mixing performance of planetary mixers.     

Mixing efficiency of a multilamination micromixer with consecutive recirculation zones

Adding recirculation zones to a mixer for a microplant is proposed for enhanced mixing efficiency. A multilamination interdigital micromixer has been widely used in microchemical plants for precision or small scale chemical process. The mixing efficiency of this micromixer is relatively low as the mixing of two fluids is executed by the laminar diffusion process. To assist the mixing by fluid action, a series of recirculation zones were added to the mixing chamber. The effectiveness of the recirculation zones on mixing was estimated through a numerical simulation which indicated the dependence on Reynolds number. Mixing efficiency increased at Reynolds number that is relevant to the condition that is prevalent in a microchemical plant. The proposed micromixer was fabricated by the lithography process on the photosensitive glass wafers. The mixing qualities of the fabricated micromixer were measured by two methods; the flow visualization of dilution type experiments and the reactivity measurement. The measurement of color intensity of the mixed fluid followed the predictions by the simulation. For a Reynolds number greater than 400 that was relevant in mixers for microchemical plant, a mixing efficiency higher than 90% was obtained by adding the recirculation zones.     

Mechanism of mixing enhancement with baffles in impeller-agitated vessel, part I: A case study based on cross-sections of streak sheet

Enhancement mechanism of mixing with baffle in agitated vessel using rotated two-bladed paddle impeller was investigated under a laminar condition. In mixing pattern, the toroidal isolated mixing region in the baffled vessel becomes distortive and much smaller than that of unbaffled vessel. From the visualization of streak cross-sections in the baffled vessel, interestingly, the renewed streak folds (streak lobes) are generated at the vicinity of baffles in both the vertical and horizontal cross-sections. These behaviors of streak are unlike the unbaffled case that the streak stretches straightforwardly. The streak lobe is known as the mixing template that its number and size are key factor for laminar mixing in agitated vessel. The results suggest that baffles can effectively transform the circumferential flow to vertical and/or radial flows. Consequently, in the baffled vessels, not only the vicinity of vessel wall but also the tip of baffles can become the origination of streak lobe formation, and folds of streak in the vertical and circumferential directions are further enhanced with baffles.     

Mixing analysis in a coaxial mixer

The performance of a coaxial mixer in the laminar-transitional flow regime was numerically investigated with Newtonian and non-Newtonian fluids. These mixers comprised two shafts: a central fast speed shaft mounted with an open turbine, and a slow speed shaft fitted with a wall scraping anchor arm. To model the complex hydrodynamics inside the vessel, the virtual finite element method (POLY3D^TM software) coupled with a Lagrange multiplier approach to cope with the non-linearity coming from the rheological model was employed. Co-rotation and counter-rotation mode were compared, based on several numerical criteria, namely, mixing time, power consumption and pumping rate. It was found that co-rotating mode is more efficient than counter-rotating mode in terms of energy, pumping rate and homogenization time.     

Viscous fluid mixing in a tilted tank by periodic shear

A tilted-partially filled rotating tank is studied, both experimentally and theoretically at small Reynolds and capillary numbers, to study mixing viscous fluid by periodic shear. The maximum mixed cross-sectional area, A_max(α)=A(Δt_max(α)), and mixing rate, 1/Δt_max(α), are estimated as a function of the flow parameters, which are the tilt angle, α, and free surface height, H₀. A nonlinear flow model is found by expanding linear solid body rotation about a curved rotation axis that is needed to satisfy the zero shear stress and no normal velocity component for the flow in the vicinity of the free surface. A linear analysis of the nonlinear solution reveals an underlying periodic shear that is responsible for fluid mixing. The analysis suggests that the rate of mixing per unit area is a maximum near α=52π/180. Laser fluorescence experiments are performed to examine the mixing patterns via experimental Poincaré mapping [Fountain, G.O., Khakhar, D.V., Ottino, J.M., 1998. Visualization of three-dimensional chaos. Science 281, 683-686.]. Steady-state images of the mixed cross-sectional area are compared with the theory as a function of the flow parameters.     

CFD analysis of a rotor-stator mixer with viscous fluids

The characterization of the hydrodynamics of a rotor-stator mixing head has been carried out in the laminar regime with viscous Newtonian fluids. The rotor-stator considered is a very common design composed of a flat blade rotating in a fixed slotted cage. A numerical methodology has been used based on the virtual finite element method to model the velocity patterns, estimate the distribution of shear stress and the flow rate through the head. We have found that the numerical prediction of the power consumption and flow profiles compare well with experimental data. The generation of a pseudo-cavern around the mixing head and how it scales with the Reynolds number have also been investigated, showing that there is a minimum speed limit below which the rotor-stator cannot be used.     

Mixing in a fluid jet agitated tank: effects of jet angle and elevation and number of jets

The effects of jet angle and elevation on mixing in a fluid jet agitated tank were investigated using computational fluid dynamics (CFD). Results show that, for a given geometric arrangement, the angle of the jet injection is significantly more important in determining the time required for 95% mixing than the length of the jet. For an aspect ratio of 1 and for a side jet injected at the bottom of a tank, the longest jet length, corresponding to an angle of injection of 45°, does not give the shortest time as suggested by many previous workers but one of the longest mixing times. An angle of injection of 30° gives the shortest mixing time.Results also show that the mixing time does not change monotonically with the angle of injection or with the level at which the jet is injected. This means that when designing a jet mixer, careful consideration should be given to the angle as well as the location of the jet.Results also show that a significant reduction in the mixing time is possible if two side jets are used instead of one. The improvement is between 40% and 68% for jet Reynolds numbers between 3000 and 7000.     

Large Eddy Simulation of Turbulent Reactive Mixing at High Schmidt and Reynolds Numbers

Large eddy simulation is used to investigate the reactive scalar transport in a confined jet reactor at high Reynolds and Schmidt numbers. Numerical simulations are performed for a fast neutralization reaction of acid and base supported by experimental data. Based on detailed planar laser‐induced fluorescence measurements, a simple conditional micromixing model for infinitely fast chemistry is developed and successfully applied to the jet mixer configuration. Results obtained for the reactive scalar transport are in excellent agreement with measurements, whereas established micromixing approaches based on the eddy dissipation model, multi environment model, and presumed probability density function with infinetly fast chemistry models indicate discrepancies in the determination of micromixing rate and product concentration.     

Coiled flow inverter as an inline mixer

Helical coils are widely used in the process industries to improve the mixing efficiency under laminar flow conditions. It was further observed that in the regular helical coils, there exists a confined region in the tube cross-section where fluids are entrapped and can escape only by diffusion. In the present work, an attempt has been made to further enhance the mixing in the coiled tube at low Dean number using the phenomenon of flow inversion. The study is performed in coiled flow inverter (CFI) [Saxena, A.K., Nigam, K.D.P., 1984. Coiled configuration for flow inversion and its effect on residence time distribution. A.I.Ch.E. Journal 30, 363-368] which was developed using the concept of inverting the direction of fluid by 90^°. It comprises coils with equidistant 90^° bends. The scalar mixing of two miscible fluids has been quantified for different process conditions (Dean number, Schmidt number and number of bends) by using scalar transport technique. There was a significant increase in mixing performance of CFI as compared to regular helical coils at low Dean number. The mixing efficiency increased with the increase in Dean number and number of bends. It was also observed that the mixing performance was enhanced with increase in Schmidt number. A new correlation has been proposed for unmixedness coefficient of CFI as a function of Dean number, Schmidt number and number of bends. The proposed correlation has maximum error of ±20% with the numerical predictions.     

Optimization analysis of the staggered herringbone micromixer based on the slip-driven method

In this paper the mixing effect of the staggered herringbone micromixer (SHM) was investigated by using the slip-driven method. This method simplified the 3D flow in the staggered herringbone micromixer into a 2D cavity flow with an axial Poiseuille flow. The solution of the 2D cavity flow was obtained by solving the biharmonic equation. An improved design with a cosine asymmetric factor P(z) was proposed, and its mixing effect was demonstrated by comparing the effect with the original design [Stroock, A.D., Dertinger, S.K.W., Ajdari, A., Mezic, I., Stone, H.A. and Whitesides, G.M., 2002, Chaotic mixer for microchannels, Science, 295: 647–651; Stroock, A.D., Dertinger, S.K.W., Whitesides, G.M. and Ajdari, A., 2002, Patterning flows using grooved surfaces, Anal Chem, 74: 5306–5312]. Four methods evaluating the mixing effect were used: (1) mixing images at different cycles; (2) Poincaré Sections; (3) segregation intensity and (4) stretching computation. Finally, an optimized value of P₀ = 1/6 was obtained, and the mixing effect of the improved design for different P₀ is discussed.     

Low-Reynolds-number motion of a heavy sphere between two parallel plane walls

A novel boundary-integral algorithm [Staben, M.E., Zinchenko, A.Z., Davis, R.H., 2003. Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow. Physics of Fluids 15, 1711-1733; Erratum: Phys. Fluids 16, 4206] is used to obtain O(1)-nonsingular terms that are combined with two-wall lubrication asymptotic terms to give resistance coefficients for near-contact or contact motion of a heavy sphere translating and rotating between two parallel plane walls in a Poiseuille flow. These resistance coefficients are used to describe the sphere's motion for two cases: a heavy sphere driven by a Poiseuille flow in a horizontal channel and a heavy sphere settling due to gravity through a quiescent fluid in an inclined channel. When the heavy sphere contacts a wall in either system, which occurs when the gap between the sphere and the wall becomes equal to the surface roughness of the sphere (or plane), a contact-force model using the two-wall resistance coefficients is employed. For a heavy sphere in a Poiseuille flow, experiments were performed using polystyrene particles with diameters 10%-60% of the channel depth, driven through a glass microchannel using a syringe pump. The measured translational velocities for these particles show good agreement with theoretical results. The predicted translational velocity increases for increasing particle diameter, as the spheres extend further into the Poiseuille flow, except for particles that are so large (diameters of 80%-85% of the channel depth) that the upper wall has a dominant influence on the particle velocity. For a heavy sphere settling in a quiescent fluid in an inclined channel, the transition from the no-slip regime to slipping motion occurs for a larger inclination angle of the channel with respect to the horizontal for an increase in particle diameter, since the larger particles are more slowed by the second wall. Limited experiments were performed for Teflon spheres with diameters 64%-95% of the channel depth settling in a very viscous fluid along the lower wall of an inclined acrylic channel. The measured translational velocities, which are only about 15%-25% of the tangential component of the undisturbed Stokes settling velocity, are in close agreement with theory using physical parameters obtained from similar experiments with a single wall [Galvin, K.P., Zhao, Y., Davis, R.H., 2001. Time-averaged hydrodynamic roughness of a noncolloidal sphere in low Reynolds number motion down an inclined plane. Physics of Fluids 13, 3108-3119].     

Performance of Kenics static mixer over a wide range of Reynolds number

The present study deals with the numerical simulation of flow patterns and mixing behaviour in Kenics static mixer over a wide range of Reynolds number. Three different sets of Kenics mixer (aspect ratio = 1.5) comprised of 3, 9 and 25 elements each have been characterized. The Reynolds number was varied in the range of 1 to 25,000 (i.e., from laminar to turbulent flow regime). The numerical approach takes into account the aspects of the fluid flow at higher Reynolds number values including circumferential velocity profiles at different cross-sections within the Kenics mixer, which were neglected in previous studies. It was observed that cross-sectional mixing in the turbulent flow regime takes place up to 30% of each element length at element-to-element transition; beyond that velocity profiles were uniform. The experiments were also carried out to measure the circumferential and axial velocity profiles and pressure drop in three different Kenics Mixers using air as fluid. The pressure drop per unit element (ΔP/η) was found to be independent of the number of Kenics mixing elements used in the system. The total pressure drop across Kenics mixer obtained by CFD simulations were compared with the experimental pressure drop values and correlations available in the literature. The numerical results were found in good agreement with the experimental as well as the results reported in the literature. A new pressure drop correlation in the Kenics static mixer has been developed.     

Structure of powder flow in a planetary mixer during wet-mass granulation

Wet massing granulation, a widely used industrial process, is difficult to monitor and control and the structure of the flow is poorly understood. Flow patterns in a planetary mixer were investigated using positron emission particle tracking. Both dry and wet powders of a model pharmaceutical formulation were studied to develop understanding of the influence of moisture content on the flow structure during granulation. The flow structure was characterised using the distributions of the velocity components in different cross-sections of the mixer. Fourier analysis showed that the dry system is essentially dissipative and disordered whereas the wet system, being more inertial, shows signs of being more ordered with a periodic recirculation within the bowl. In both systems, radial and axial displacements are strongly correlated. For the dry system, within a central radial core region, the behaviour of the particle was determined by the rapid movement of the agitator, forming a single toroidal recycling cell. The radial and axial velocities of the tracer were up to two orders of magnitude lower than the tangential component. However, in the regions close to the wall, the particle was found to exhibit small movements dictated by the planetary rotation. For wet systems these two main regions were again observed. However, velocity field and velocity distribution showed the presence of two toroidal circulation loops, one above the other. In the wall region, the small movements governed by the planetary motion were again found, but with the amplitude of the displacements reduced by an order of magnitude.     

Dimensionless number for identification of flow patterns inside a T-micromixer

Results are presented from a numerical study examining the flow dynamics of the liquid phase inside T-type micromixers. The main aim of the study was to determine an identification number for the differentiation of the different flow regimes in the liquid phase in T-type micromixers. The critical value for the identification number at which the transition from vortex flow to engulfment flow occurs was obtained. The results were used to optimize the geometrical parameters and the operating conditions to achieve high mixing performance for the liquid phase in T-type micromixers. The model results were found to be consistent with experimental data for different T-mixers available in the literature.