EFFECT OF SUSPENDED FIBRES ON MACRO-MIXING AND MICRO-MIXING IN A STIRRED TANK REACTOR

The effects of suspended fibre on macroscale and microscale mixing in a small stirred tank reactor were studied under batch conditions using the competitive, consecutive azo coupling between 1-naphthol and diazotized sulfanilic acid. The mixing quality was determined from the distribution between the mono and bis substituted reaction products. Nylon (2 and 3 millimeters in length) and fully bleached softwood kraft pulp (FBK) fibre suspensions were examined at volumetric concentrations up to the limit that complete suspension motion could be maintained in the vessel at impellet rotational speeds of 7 and 10s^-1. The adsorption of the product dyes on the fibre was found to be proportional or very nearly proportional to their concentrations in the aqueous phase and did not interfere with the assessment of mixing in the suspension.

Suspended fibres were found to slightly increase the 'critical feed time' of the diazotized sulfanilic acid, corresponding to an increase in the macromixing or bulk blend lime of the vessel. Continued increase in the fibre concentration led to the formation of a well mixed cavern centered on the impeller and the creation of stagnant regions adjacent to the vessel walls. The departure from the Newtonian fibre-free case is due to changes in the flow through and distribution of the energy dissipative regions in the vessel. The most effective location for chemical addition to ensure good microscale mixing remains in the impeller vicinity.     

Full field measurement at the micro-scale using micro-interferometry

This paper presents micro-interferometry as a measurement technique to extract temperature profiles and/or mass transfer gradients rapidly and locally in micro-devices. Interferometry quantifies the phase change between two or more coherent light beams induced by temperature and/or mass concentration. Previous work has shown that temporal noise is a limiting factor in microscale applications. This paper examines phase stepping and heterodyne phase retrieval techniques with both CCD and CMOS cameras. CMOS cameras are examined owing to the high speed at which images can be acquired which is particularly relevant to heterodyne methods. It is found that heterodyne retrieval is five times better than phase stepping being limited to 0.01 rad or λ/628. This is twice the theoretical limit of λ/1,000. The technique is demonstrated for mixing in a T-junction with a 500 μm square channel and compared favourably to a theoretical prediction from the literature. Further issues regarding application to temperature measurements are discussed.     

A new adaptive procedure for using chemical probes to characterize mixing

The iodide–iodate chemical probe method is modified by a novel adaptive procedure to investigate the mixing abilities of two compact curved-duct reactors. Both reactors have a rectangular cross section; the first has smooth curvature (called the wavy duct) and the second has sharper bends (zigzag duct). In the conventional procedure, this method is used to characterize local micro-mixing, and for all experiments (for different Reynolds numbers and injection points) the reagent initial concentrations are kept at the same values. Even with wall injection, the selectivity of the chemical system is generally improved by increasing the flow Reynolds number. Nevertheless, two limitations encountered in using chemical probes (with the conventional protocol) to characterize the mixing abilities of the present reactors that prevent the conventional protocol of the chemical probe from discriminating between the mixing abilities of the two mockups. First, the duct walls are corrugated, so that the wall injection used to measure local micro-mixing is affected by the wall roughness, independently of the Reynolds number. Second, the flow Reynolds numbers are relatively low due to the small size of the duct sides, so that the measurements are inevitably hindered by meso-mixing effects. The challenge is thus to adapt the chemical method for characterizing the global mixing, by enlarging the measurement volume so as to capture and take into account all mixing scales. In the new adaptive procedure, the kinetics of the second reaction are adjusted in such a way as to impose the same reactive volume for different Reynolds numbers, leading to more relevant results for the segregation index X_S. Experimental results reveal that the mixing performance of the zigzag channel as assessed by this method is slightly above that of the wavy one. Finally, the segregation index in both reactors is related to the mixing time t_m by using a physical model in the literature.     

Mixing assessment by chemical probe

Quantification of micro-mixing is a fundamental issue in industrial chemical processes. Local mixing that is not “fast enough” compared with the reaction kinetics reduces the selectivity of the reaction. Micro-mixing can be characterized by chemical probe methods based on observation of a local chemical reaction that results from the competition between turbulent mixing at micro-scales and the reaction kinetics. However, real-world experimental conditions rarely comply with the grounding assumptions of this method. Starting from physical considerations, the present study aims to establish some guidelines for obtaining quantitative information from the chemical probe and for improving the accuracy of the method by an adaptive protocol. For the first aspect, an analytical approach is proposed to define the validity domain based on analysis of the turbulent time scales. For the second purpose, a novel experimental procedure is suggested that entails targeting the concentrations of the chemical species that can provide the optimal conditions for a relevant use of the chemical probe.     

Microfluidic mixing via transverse electrokinetic effects in a planar microchannel

A new micromixer incorporating integrated electrodes deposited on the bottom surface of a glass/PDMS microchannel is used to induce a localized, perpendicular electric field within pressure driven axial flow. The presence of the electric field drives electro-osmotic flow in the transverse direction along the channel walls, creating helical motion that serves to mix the fluid. A numerical model is used to describe the three-dimensional flow field, where characterization is performed via particle tracking of passive tracer particles, and the conditional entropy (S _lc) is utilized to approximate the extent of mixing along cross-sectional planes. The geometrical parameters and operating conditions of the numerical model are used to fabricate an experimental device, and fluorescence microscopy measurements are used to verify mixing of rhodamine B across the width of the microchannel for a wide range of fluid flow rates. The results demonstrate that under certain operating conditions and selective placement of the electrode gaps along the width of the microchannel, efficient mixing can be achieved within 6 mm of the inlet.

Numerical simulation of micro-mixing in gas–liquid and solid–liquid stirred tanks with the coupled CFD-E-model

The coupled CFD-E-model for multiphase micro-mixing was developed, and used to predict the micro-mixing effects on the parallel competing chemical reactions in semi-batch gas–liquid and solid–liquid stirred tanks. Based on the multiphase macro-flow field, the key parameters of the micro-mixing E-model were obtained with solving the Reynolds-averaged transport equations of mixture fraction and its variance at low computational costs. Compared with experimental data, the multiphase numerical method shows the satisfactory predicting ability. For the gas–liquid system, the segregated reaction zone is mainly near the feed point, and shrinks to the exit of feed-pipe when the feed position is closer to the impeller. Besides, surface feed requires more time to completely exhaust the added H⁺ solution than that of impeller region feed at the same operating condition. For the solid–liquid system, when the solid suspension cloud is formed at high solid holdups, the flow velocity in the clear liquid layer above the cloud is notably reduced and the reactions proceed slowly in this almost stagnant zone. Therefore, the segregation index in this case is larger than that in the dilute solid–liquid system.     

Averaging theory and low-dimensional models for chemical reactors and reacting flows

A novel approach based on the Liapunov-Schmidt technique of bifurcation theory is presented for the spatial averaging of a class of convection-diffusion-reaction models. It is used to derive low-dimensional averaged models for different types of homogeneous and catalytic reactors, as well as coupled homogeneous-heterogeneous systems. For the homogeneous isothermal case, the averaged models consist of a pair of balance equations for each species A_j in terms of the mixing-cup (C_j,m) and spatially averaged (〈C_j〉) concentrations. The first (global) equation traces the evolution of C_j,m with residence time while the second (local) equation, which is independent of the reactor type, gives the local concentration gradient as a difference between C_j,m and 〈C_j〉 in terms of the local variables (such as species diffusivities, shear and reaction rates). For the wall-catalyzed reaction case, the averaged models are described by a pair of equations for each species in terms of C_j,m and the surface concentration C_j,s and are similar to the classical two-phase models of catalytic reactors. For the coupled homogeneous-heterogeneous case, the averaged models consist of three balance equations for each species in terms of C_j,m, 〈C_j〉 and C_j,s, and contain four mass transfer or exchange coefficients. The accuracy, convergence and the region of validity of the averaged models are examined for some special cases. Finally, the usefulness of the averaged models in predicting the reactor behavior is illustrated with an example for each of the three cases, homogeneous, heterogeneous and coupled homogeneous-heterogeneous case.     

Investigation of turbulence modulation in solid–liquid suspensions using parallel competing reactions as probes for micro-mixing efficiency

The Bourne and the Villermaux competitive reaction chemistries were applied to study the effects of suspended particles on the yield of an undesired product and hence to infer their effects on local dissipation rates. Two-phase micro-mixing experiments were carried out in a 1 l stirred vessel, agitated by a pitched-blade turbine, using four particle size ranges: 70–100, 250–300, 700–750 and 1000 μm. Experiments were carried out with up to 1.75 vol% particles in the Bourne scheme and 3 vol% in the Villermaux scheme. Both reaction schemes gave qualitatively similar results, although stronger effects of added particles were obtained with the Bourne chemistry. The effect of 700–750 μm particles could not be distinguished from experimental error, but the other size ranges gave increased by-product yields and suppressed the dissipation rates. These results confirmed earlier two-phase PIV observations: smaller particles (70–100 and 250–300 μm) gave maximum suppression at ∼1 vol%. Above this volume fraction, the level of suppression decreased and in some cases turbulence augmentation occurred, indicating that particle concentration, as well as size, is an important factor.     

Cold flow characteristics of a novel high-hydrogen Micromix model burner based on multiple confluent turbulent round jets

As a promising commercial hydrogen-rich gas turbine combustion technology, micro-mixing combustion has been characterized for its excellent performance with low NOx emissions. New flame stabilization mechanism of micro-mixing flames may produce new design criteria. In order to explore that, cold flow characteristics of a novel Micromix model burner based on multiple confluent round jets has been studied experimentally and numerically, which is considered to be the basis for the exploration. A three-dimensional laser Doppler velocimetry system (3D-LDV) was used to measure the flow field of the model burner. It was found that the cold flow characteristics of the burner were different from the twin plane jets, the twin round jets, and the low Reynolds number confluent round jets. Compared to which, the interior of the micro-mixing nozzle is at a very high turbulence intensity level, and the jets merging point of the burner moved upstream; however, the position of the combined point of the burner was close to the confluent round jets. There is no recirculation region between jets near the burner outlet when the nozzle spacing was equal to 3 times the nozzle diameter and the Reynolds number was less than 16,702. The steady computational Reynolds averaged equations (RANS) model results were used to compare with the experimental results. It was found that the RANS results can match the experimental results well, and the three RANS models predict the spatial mixing deficiency less than 1% at the outlet, indicating that the fuel and air were almost completely premixed uniformly.     

Simulation of a toroidal jet-stirred combustor using a partially stirred reactor model with detailed kinetic mechanisms

The detailed chemistry in a jet-stirred laboratory combustor has been computed with a partially stirred reactor (PaSR) model that uses interaction by exchange with the mean as a turbulent moment closure to simulate finite time micro-mixing. Ideal macro-mixing is assumed as characterized by an exponential residence time distribution. Local conditions are relaxed toward the mean at a rate defined by the mixing frequency that is a ratio of the turbulent dissipation to the turbulent mixing energy. The solution technique approximates mean conditions, and solves the deterministic model to refine the approximation, and eventually converge on a solution. The approximation and convergence technique compared favorably with the Monte Carlo modeling calculations presented in the literature, while using, on average, less than 1/100th of the CPU time. The comparison of PaSR model predictions to literature experimental data from a toroidal jet-stirred laboratory combustor operating in both fuel-lean and fuel-rich conditions also showed reasonable agreement with data. Moreover, the PaSR proved valuable as a research tool. It provided an indication of the sensitivity of reactor kinetics to the effects of micro-mixing delay, and predicted temperature and species distributions, while using detailed thermo-kinetic mechanisms. These features, which are beyond the scope of the perfectly stirred reactor (PSR) model, are provided within reasonable computational times.