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.     

Flow and mass transfer in aerated viscous Newtonian liquids in an unbaffled agitated vessel having alternating forward–reverse rotating impellers

Flow and mass transfer characteristics in aerated viscous Newtonian liquids were studied for an unbaffled aerated agitated vessel with alternating rotating impellers (AAVAI), ie with multiple forward–reverse rotating impellers having four delta blades. The effects of operating conditions such as gas sparging rate, agitation rate and the number of impeller stages, and the liquid physical properties (viscosity) on the gas hold‐up, ?_gD, and volumetric oxygen transfer coefficient, k_La_D were evaluated experimentally. The dependences of ?_gD and k_La_D on the specific total power input and superficial gas velocity differed, depending on the ranges of liquid viscosity. Empirical relationships are presented for each viscosity range to predict ?_gD and k_La_D as a function of the specific total power input, superficial gas velocity and viscosity of liquid. Based on a comparative investigation of the volumetric coefficient in terms of the specific total power input between the AAVAI and conventional aerated agitated vessels (CAAVs) having unidirectionally rotating impellers, the usefulness of AAVAI as a gas–liquid agitator treating viscous Newtonian liquids is also discussed. © 2001 Society of Chemical Industry     

Aerosol Capture in Granular Beds in the Sedimentation and Diffusion Dominated Regimes

Single grain capture efficiencies η for low speed gas flow through clean granular beds are reported. The aerosol particles were liquid dioctyl phthalate droplets ranging in diameter D _p from 0.15 to 4.7 μm. The grains were spheres of diameter D _G equal to 2.13, 3.69, or 15.6 mm and crushed oil shale rock with volume equivalent spherical diameter of 2.2 or 17 mm. The superficial gas velocity was downward and varied from 2.5 to 80 mm/s. Sedimentation and Brownian diffusion are the dominant capture mechanisms for these conditions. Consequently, the Gravity number Grv = ρ_pD² _pC_pg/18μU and the Peclet number Pe = D_GU/ D _p=3πμD_pD_GU/KTC_p are important dimensionless groups for correlating data. An approximate solution to the convective diffusion equation for point particles shows that η/Grv is a function of the combination 2^1/3A^1/3Pe^?2/3Grv^?1 only, when Grv « 1 and Pe » 1. A(α_G, Re) is a known function of the fraction solids α_G in the bed and the grain Reynolds number Re = ρD_GU/μ. Our data are successfully correlated by this approach. In the sedimentation dominated regime, theory (η=Grv) is in quantitative agreement with the data. In the diffusion dominated regime, theory (η = 3.97 A^1/3 Pe^?2/3) gives quantitaive agreement with the data, provided the numerical coefficient 3.97 is changed to 2.4. When capture efficiencies for both sedimentation and diffusion are very small (of order 0.001), measured efficiencies are several times larger than the predictions for point particles. If this increase is attributed to interception, then the present theory, extended to include interception, significantly underestimates its influence at small values of the interception number R=D_p/D_G. The discrepancy may be due to deficiencies of present flow models or to some other weak capture mechanism coming into play. Results obtained for beds of spheres can be applied to beds of crushed shale rock, provided a suitable “effective” grain diameter is chosen.     

RIBBING INSTABILITY OF A TWO-ROLL COATER: NEWTONIAN FLUIDS

Data are presented for the critical conditions at which the ribbing instability appears on the surface of a Newtonian liquid film emerging from the nip between two rotating rolls. Data are obtained over two decades in Capillary number (Ca = μU/σ) for values of H₀/R in the range 3 × 10^?3 to 5 × 10^?2. The critical Capillary number is found to be given by the expression

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Data are compared to the predictions that follow from a theory due to Savage, and agreement is found to be poor.     

Effect of scale‐up on wall shear rates in circulating bubble columns

Effective wall shear rates were investigated experimentally in an external loop circulating bubble column made from transparent acrylic resin. The riser (D_R) and downcomer (D_D) diameters were 0.19 m and 0.14 m, respectively. The column working volume (V_R) was 170 dm³, with a scale‐up factor (A_D/A_R) of 0.54, and a dispersion height (H_D) of 2.25 m. Polymer solutions of xanthan gum and carboxymethyl cellulose were used to simulate non‐Newtonian behavior of biological systems. Effective wall shear rates for the non‐Newtonian solutions were found by analogy with Newtonian glycerol solutions, employing downcomer liquid velocity as the measurable and comparable parameter. The experimental shear rate results were found to fit between those of the literature data. A new single correlation taking into account all the relevant data in the literature and the results of this work is proposed. The new correlation is an improvement over the other correlations because it includes two important design constants: scale‐up factor and dispersion height. Copyright © 2005 Society of Chemical Industry     

Design and operation of unbaffled aerated agitated vessels with unsteadily forward–reverse rotating impellers handling viscous Newtonian liquids

Design and operation of unbaffled aerated agitated vessels with multiple unsteadily forward–reverse rotating impellers (AJITERs) for viscous Newtonian liquids were studied. The effects of operating conditions such as gas sparging rate, agitation rate and the number of impeller stages, geometrical conditions such as the diameters of vessel and impeller, and the physical properties of liquids on the drag and added moment of inertia coefficients, necessary to predict the average and maximum power consumptions of the impellers in AJITERs, were evaluated and the empirical relationships which estimate values of each of these coefficients are presented. The effects of operating conditions, geometrical conditions and liquid physical properties on the gas hold‐up, ?_gD, and volumetric oxygen transfer coefficient, k_La_D, were evaluated in relation to the total power input which is the sum of the average power consumption of impellers, ie average agitation power input, and aeration power input. Empirical relationships, useful for design and operation of AJITERs, were obtained for each viscosity range, where the dependences of ?_gD and k_La_D on the specific total power input and superficial gas velocity differed, to predict ?_gD and k_La_D respectively as a function of the specific total power input, superficial gas velocity and liquid physical properties. © 2003 Society of Chemical Industry     

The influence of fluid elasticity on wall effects for creeping sphere motion in cylindrical tubes

Experimental results are presented of wall effect for the slow motion of spheres in elastic, constant-viscosity liquids. The results are correlated in terms of diameter ratio for d/D < 0.3, and Weissenberg number We < 5. Weissenberg number is defined as We = 2θV_m/d, with θ the Maxwellian relaxation time (θ = N₁/2τγ). The wall effect is found to be adequately described by Newtonian expressions for small Weissenberg number, We < 0.01. For larger values of the Weissenberg number, We > 0.2, virtually no wall effect is discernible; the small effect observed is correlated by the wall factor expression The wall effect observed is ascribed to the influence of fluid elasticity alone, since all the fluids used were elastic to a greater or lesser extent, but showed no shear thinning.      

Oxygen transfer into newtonian and non-newtonian fluids in mechanically agitated vessels

Oxygen transfer into Newtonian and non-Newtonian fluids was studied in stirred tank vessels of 0.0018, 0.006 and 0.036 m³ operating volumes. Emphasis was given to the rheological effects of the pseudoplastic medium on the volumetric oxygen transfer coefficient, K_La. Results indicate that K_La is a strong function of gassed power input per unit volume (P_g/V) for the Newtonian fluid, but a weak function of P_g/V for the non-Newtonian fluid, and a strong function of superficial gas velocity (V_s) for both fluids for paddle-type impellers. K_La is found to decrease rapidly with an increase in apparent viscosity for values of μ_a greater than 2.0 Pa · s. In addition to various correlations, a dimen-sionless correlation including the impeller Reynolds number, impeller Weber number, and the aeration number is presented for the prediction of K_La in a gas-liquid non-Newtonian system.     

Settling length for turbulent flow of air in an annulus

The settling length, or distance downstream from the entrance required for the development of the velocity profile, has been determined for four square entrance sectioned annuli, with diameter ratios of 0.2, 0.3, 0.5 and 0.7. Using air, a Reynolds number range of 5,000 to 50,000 was covered, and correlations have been obtained relating the settling length, equivalent diameter, Reynolds number and diameter ratio. The expression L/De = 0.795 R_e³⁷⁴(D₁/D₂)^?0.60 correlated the data for Reynolds numbers lower than 22,000 and for Reynolds numbers greater than this the relation was L/D_e = 15.96 R_e^.077(D₁/D₂)^?624.     

High speed wire coating by withdrawal from a bath of viscoelastic liquid

Data are presented for the thickness H_∞ of liquid coating entrained by continuous withdrawal at speed U of a wire of radius R from the free surface of a large bath. For Newtonian fluids of viscosity μ, density ρ and surface tension σ, the data are carried out to coating speeds beyond the applicability of current theories, to Capillary numbers of nearly one hundred. In the high speed range the data, which cover several orders of magnitude in viscosity, can be well represented by the equation for U_μ/σ = N_ca > 3. All data presented are at an essentially constant Goucher number of 0.08, where N_Go ≡ R(ρg/2σ)^1/2. Data for viscoelastic fluids show phenomena quite distinct, qualitatively and quantitatively, from Newtonian observations. In particular, strongly elastic fluids show a markedly reduced ability to be entrained onto the wire. Further, the coating thickness appears to become independent of Capillary number at high speed.     

Gelation and fusion of vinyl plastisols

The gelation of vinyl plastisols at constant temperature has been found to follow the equation ln [(C ? C_e)/(U ? C_e)] = (? π²/a²)D_τ + ln (8/π²), where C is the resin phase concentration, C_e the equilibrium resin phase concentration, U the critical resin phase concentration, a the average particle size, D the diffusion constant, and τ the time required for the onsent of gelation. A light reflectance apparatus capable of measuring the gelation process is described. The effect that various resin–plasticizer parameters have on the gelation and fusion process is discussed. The light-reflectance apparatus is also useful for estimating various resin and formulating parameters.     

Chromatography and Countercurrent Distribution: Features of the Optimum Phase-Volume Ratio

Abstract

It is commonly believed that the optimum solvent ratio in countercurrent distribution and chromatography may be expressed as V = V_U/V_L = (K_D1 K_Dπ ) ^?½. Here V_U and V_L are the volumes of mobile and stationary phases. This expression, proposed by Bush and Densen and widely accepted, leads to optimum separations only under special conditions. Under most commonly-encountered situations in chromatographic and countercurrent systems, better separations may be achieved by reducing V to the lowest practicable level. Measures of separation effectiveness include resolution, extent of separation, total percent impurity, and quantity factor, the latter two of which are herein developed. Computer simulation is used for testing existing separation parameters and developing new ones on a rational and scientific basis.     

Phospholipid liposomes: Preparation,characterization, and uses

Rhodopsin and cyclic guanosine monophosphat (cGMP)-dependent channel proteins are isolated from the rod outer segment disk membranes of dark-adopted bovine retinae and incorporated in liposomes, prepared by the method of detergent removal dialysis. The ion channel does not lose its transport function (release of Ca²⁺ ions by injection of cGMP) when incorporated in a liposome. Its activity depends on the degree of protein solubilization and the kind of detergent used. The highest activity is obtained by use of the detergent CHAPS. Shape, size, and size distribution of the liposomes are deduced from elastic and quasi-elastic light scattering, the liposome number density by viscometry, and the photopigment or Ca²⁺ content by optical absorbance. The liposomes are heterogeneous with respect to size and shape. Small unilamellar liposomes (R_h = 80 nm) and a narrow size distribution (U_D = 0.16) are obtained by using the detergent CHAPS. With increasing rhodopsin content per liposome, the hydrodynamic radius R_h increases and at the same time the shape of a liposome converts from a sphere to a prolate ellipsoid. The amount of entrapped Ca²⁺ per liposome reaches its maximum value when the Rhodopsin nearest-neighbor distance approaches its minimum value. This suggests an intermembrane protein-lipid-protein lattice, which serves as barriere for Ca²⁺. The influence of temperature or total used Ca²⁺ content is less profound. Increasing temperature yields slightly smaller liposomes.     

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     

Flow through porous media of a shear-thinning liquid with yield stress

Darcy's law for the laminar flow of Newtonian fluids through porous media has been modified to a more general form which will describe the flow through porous media of fluids whose flow behavior can be characterized by the Herschel-Bulkley model. The model covers the flow of homogeneous fluids with a yield value and a power law flow behavior. Experiments in packed beds of sand were carried out with solutions of paraffin wax in two oils and with a crude oil from the Peace River area of Canada. The model fitted the data well. A sensitivity analysis of the fitting parameters showed that the model fit was very sensitive to errors in the flow behavior index, n , of the Herschel-Bulkley model. A comparison of the “n” values calculated from viscometer measurements and from flow measurements agreed well. A more general Reynolds number for flow through porous media, which includes a fluid yield value, was developed. The data were fitted to a Kozeny-Carman type equation using this Reynolds number. The constant in the Kozeny-Carman equation was determined for the two packed beds studied using Newtonian oils. The data could all be represented, within the experimental error, by the relationship f^* = 150/Re^*. Since the mean volume to surface diameter of the packing was determined by the measurement of its permeability to a Newtonian oil, assuming C' = 150, the new definition of the Reynolds number allows the direct use of the Kozeny-Carman equation with Herschel-Bulkley type fluids.     

Electrochemical mass transfer to regular packings in a bubble column

The behaviour of regular packings constructed from corrugated metal sheets was investigated since they constitute an attractive packing material for the electrochemical absorption of gases. Mass transfer coefficients for the regular packing contained in a circular electrolytical cell were determined by the electrochemical method with simulation of the absorption process by bubbling nitrogen through the column. Correlations for the mass transfer rate as a function of fluid dynamic parameters and fluid properties are presented.List of symbols A electrode surface area (m²) - c ₀ bulk concentration (mol m^–3) - D diffusivity (m² s^–1) - E gas hold-up = volume fraction of gas - F Faraday constant (As mo^–1) - Fr Froude number = Vs ²/gL - g gravitational acceleration (m s^–2) - Ga Galileo number = L ³ g/v² - I limiting current (A) - mass transfer coefficient (ms^–1) - L characteristic length (m) - Re Reynolds number = V _s L/ - Sc Schmidt number = /D - Sh Sherwood number = L/D - St Stanton number = /V _S - V _S superficial gas velocity (ms^–1) - z valence change in electrochemical reaction - kinematic viscosity (m² s^–1)     

Axial mixing of liquid in a turbulent-bed contactor

The axial dispersion of liquid in a 12-in. turbulent-bed contactor has been investigated for three packing sizes: ½-in., 1-in. and 1½-in. The gas and liquid flow rates were varied from 500 to 2700 lb./(hr.)(sq. ft.) and from 1500 to 11,000 lb./(hr.)(sq. ft.) respectively. The transient response technique using KCl solution as the tracer was employed for this purpose. The experimentally determined residence-time distribution curves were interpreted by means of a one-dimensional dispersion model. The axial dispersion coefficient, D_L, was found to increase with increasing gas flow rate, liquid flow rate, or packing size. In terms of Peclet number (N_Pe = ū d_p/D_L), the present data showed that N_Pe was dependent on Reynolds number (N, = d_p ū ρ/μ), Gallileo number (N_Ga = d_p³ ρ³ g/μ²), and reduced gas mass velocity (Δ = (G-G_mf)/G_mf), but the ratio of the Peclet number for a turbulent contactor to the Peclet number for a fixed-bed contactor, N_Pe/N_Peo, depended only on Δ, and the diameter ratio d_p/d_t. A correlation of N_Pe/N_Peθo with Δ and d_p/d_t is presented.     

The 1:1 Mixed Stack Complex of Tetrathiafulvalene and 2,5-Dibenzyltetracyanoquinodimethane (TTF:DBTCNQ) at 115 K

Crystallographic constants for the title compound are as follows: M_r = 384.5 + 204.3, triclinic, PĪ, a = 6.878 (2), b = 10.309 (4), c = 11.159 (7) Å, α = 109.94 (4), β = 100.91 (4), γ = 105.64 (3)°, Z = 1, V = 680.8 ų, D_c = 1.46 g cm⁻³, D_m= 1.40 g cm⁻³ (flotation, aqueous KI), λ(MoKα) = 0.71069 Å, μ = 3.27 cm⁻¹, F(000) = 304, R_F = 0.085 for 1948 data with |F₀| > 2.5 σ(F₀). The complex crystallizes in mixed stacks of alternating donors and acceptors with a maximum of intrastack overlap and a minimum of interstack interactions. The degree of charge transfer is shown by a number of criteria to be essentially zero, in stark contrast to the complex of TTF with unsubstituted TCNQ. Comparison is made with the relatively few other complexes of derivatives of TTF and TCNQ which form mixed stack complexes.     

Melt viscosity and flow birefringence of polycarbonate

Melt viscosity and flow birefringence of bisphenol A-type polycarbonate were measured and analyzed by the application of rubber-like photoelastic theory. The melt viscosity in the Newtonian flow region increased with the molecular weight to the power of 3.4. In polycarbonate, the shear stress of the Newtonian flow region was to 10⁶ dyn/cm², whereas in PMMA it was at most 3 = 10⁵ dyn/cm². The flow birefringence δn has a linear relation with shear stress S, that is δn = 5.7 × 10^?10 S. The principal polarization difference of flow unit α₁ – α₂ was 1.62 × 10^?23 cm³, which was obtained by the application of the rubber-like elastic theory. In PMMA, it was 3.9 = 10^?25 cm³; about 1/40 of that was polycarbonate. The anisotropy of polarizability of the flow unit of polycarbonate was also about 40 times larger than that of PMMA. So the anisotropy reflected the large flow birefringence of the polycarbonate.     

A study on the flow characteristics in a pulsed doughnut-disc type plate extraction column

The axial dispersion coefficients in the continuous phase and holdup of dispersed phase have been studied in a 4.2 cm inside diameter and 200 cm height pulsed doughnut-disc type plates extraction column. The axial concentration gradient in a continuous extraction column was expressed mathematically in terms of Peclet number by axial dispersion model. Peclet numbers have been calculated from response curves using KC1 solution as an impulse input fracer. Experimental data have been taken for both continuous and dispersed phase with plate spacing, pulsing amplitudes, frequencies, and superficial velocities as system variables. Modified axial dispersion coefficients have been correlated by regression analysis of experimental data, and following equations were obtained. 1. Axial dispersion coefficient (single phase) E_c = 3.5H^-13 A^1.5.1 f + 30.95 U_c 2. Axial dispsion coefficient (two phase) E_c = 2.36 H^{-0 8} A^1.34 f + 20.89 U_c 3. Fractional holdup of the dispersed phase Φ_d = 4 2xl0^-5H^-0.44 Af^1.28U_d ^0.93