Viscous Newtonian Liquid Research Articles

Mass transfer between a slender bubble and a viscous liquid in axisymmetric extensional flow

Mass transfer between a slender bubble and a viscous Newtonian liquid in axisymmetric extensional and creeping flow has been studied. The exact steady state solution, at large Peclet numbers, has been obtained using the method presented by Levich for uniform flow around a spherical drop and also by the useful equation derived by Lochiel and Calderbank for axisymmetric bodies of revolution.

Gas holdup and liquid velocity in airlift bioreactors containing viscous newtonian liquids

Gas holdup and liquid velocity in airlift bioreactors containing viscous newtonian liquids

Bubble dissolution viscous liquids in simple shear flow

AbstractThe dissolution of a gas bubble in a viscous Newtonian liquid in simple shear and creeping flow was studied experimentally A simple theoretical model for bubble growth or dissolution at high Peclet numbers is also presented. The main result of the model shows that for high capillary numbers (slender bubbles) the dissolution or growth rate is proportional to the shear rate to the 3/8 power The experimental work was carried out in a Couette apparatus. Air and carbon dioxide bubbles were injected into polymer liquids (low‐molecular‐weight polyisobutylenes) and photographed under shear. No “tip‐streaming” was observed, and experimental results compared favorably with predictions of the simple model, based on a mechanism that combines diffusion and convection.

A physically based correlation for the effects of power law rheology and inclination on slug bubble rise velocity

A study has been made of the motion of long bubbles in inclined pipes containing viscous Newtonian and non-Newtonian liquids. A semi-theoretical expression for the rise velocity of air bubbles in water is derived on the hypothesis that the dominant factor is the momentum exchange of the bubble underflow, i.e. the bubble nose shape. The correlation calls on empirical inputs from established literature on bubble rise speeds at high Reynolds number. The effects of increasing Newtonian viscosity are analysed with reference to the momentum exchange and it is shown how viscosity reduces the inclination dependence of the bubble Froude number. Results from an experimental survey in seven different non-Newtonian liquids in three different diameter pipes are presented. These data are correlated so as to decouple the effects of surface tension and viscosity. An empirical relation is proposed for the effective shear rate in the fluid travelling around the bubble nose. Our correlation is compared to literature data from a broad range of Reynolds numbers with excellent agreement except at shallow angles.

Hydrodynamic particle migration in a concentrated suspension undergoing flow between rotating eccentric cylinders

We report on experimental measurements and numerical predictions of shear-induced migration of particles in concentrated suspensions subjected to flow in the wide gap between a rotating inner cylinder placed eccentrically within a fixed outer cylinder (a cylindrical bearing). The suspensions consists of large, noncolloidal spherical particles suspended in a viscous Newtonian liquid. Nuclear magnetic resonance (NMR) imaging is used to measure the time evolution of concentration and velocity profiles as the flow induced particle migration from the initial, well-mixed state. A model originally proposed by Phillips et al. (1992) is generalized to two dimensions. The coupled equations of motion and particle migration are solved numerically using an explicit pseudo-transient finite volume formulation. While not all of the qualitative features observed in the experiments are reproduced by this general numerical implementation, the velocity predictions show moderately good agreement with the experimental data.

Mass transfer to viscous liquids in bubble columns and air-lift reactors: influence of baffles

Gas—liquid mass transfer has been studied in highly viscous Newtonian and non-Newtonian liquids contained in (i) a bubble column of 0.14 m diameter and (ii) an air-lift reactor formed by introducing a draft tube, 0.09 m in diameter, into the bubble column. The mass transfer coefficient, k L a, has been calculated from the rate of mass transfer determined experimentally by noting continuously the weight of pure CO 2 gas absorbed in these liquids. Effects of liquid viscosity, liquid height and gas sparger have been investigated in the bubble column. In addition, the influence of baffles such as baffle caps and sieve plates, introduced into (i) the bubble column and (ii) the draft tube of the air-lift reactor, has also been studied. The effect of sparger (number and diameter of holes) on gas hold-up and k L a was found to be strong at low liquid height: at a given gas velocity, gas hold-up and k L a decreased with increasing liquid height up to 0.8 m; above this height, they remained unaffected. Liquid viscosity strongly influenced k L a but hardly affected the gas hold-up: k L a decreased as viscosity increased; this decrease was marked up to about 0.3 Pa s, above which value, the decrease was gradual. For viscous Newtonian liquids, k L a values in the air-lift reactor were lower than those in the bubble column; this is due to the lower gas hold-up in air-lift reactor caused by the higher liquid circulation velocity and the bubble coalescence in the draft tube. Introduction of baffles in the bubble column and air-lift reactor enhanced the interfacial area and hence k L a. For shear thinning liquids contained in the air-lift reactor, the increased liquid circulation velocity also resulted in a lower value of apparent viscosity, this had a favourable effect on mass transfer. Following a similar argument, the introduction of baffles in the bubble column and air-lift reactor reduced liquid circulation velocity and increased the apparent liquid viscosity. Hence for the shear thinning liquids, the benefit of bubble break-up caused by the baffles is partially offset by the effect of higher liquid apparent viscosity.

Heat‐transfer characteristics in viscous gas‐liquid and gas‐liquid‐solid systems

AbstractLocal heat‐transfer measurements are performed using a special heat‐transfer probe in gas‐liquid and gas‐liquid‐solid systems with viscous Newtonian liquids as the continuous phase. Effects of viscosity on bubble‐liquid and bubble‐liquid‐solid interactions affecting local heat transfer are studied through heat‐transfer experiments with simultaneous flow visualization in a simplified system involving single bubbles or a chain of gas bubbles moving in viscous liquids and liquid‐solid systems. Effects of viscosity on bubble wake and local heat transfer are examined with reference to heat transfer in freely‐bubbling beds (bubble columns and three‐phase fluidized beds). The kinematic viscosity of the fluid greatly influences the nature of flow in the wake which affects local heat transfer in the bed. The local heat transfer decreases with the viscosity due to the rapid decay in the circulation strength of the bubble wake caused by increased viscous dissipation of vorticity. Local heat transfer due to cyclic/periodic injection of bubbles is significantly enhanced due to increased bubble‐wake interactions which rapidly accelerate bubbles and increase average bubble rise velocity. Heat transfer in simplified liquid and liquid‐solid systems with single‐ and chain‐bubble injections characterizes the local heat‐transfer performance of freely‐bubbling beds (bubble columns and three‐phase fluidized beds). A mechanistic model developed accounts for the heat‐transfer behavior in bubble columns and three‐phase fluidized beds with viscous liquids.

液位が異なる場合のへリカルリボン翼撹はん槽内の高粘度ニュートン流体の混合

Highly viscous Newtonian liquids at liquid depths from 1/4 to 1 ratio of vessel diameter were mixed in a helical ribbon agitator. At high and low liquid depths, the mixing time is approximately equal to that at the full liquid depth. But a liquid depth nearly half of the vessel diameter, a poorly mixed zone was created inside the inner edge of the blade at the middle of the liquid depth. The formation mechanism of the poorly mixed zone is explained by considering the effect of liquid depth on the flow pattern

An experimental study of bubble deformation in viscous liquids in simple shear flow

AbstractAn experimental study of the deformation of gas bubbles in viscous Newtonian liquids subjected to simple shear flow has been undertaken as a first step toward understanding bubble dynamics in polymer processing. Measurements of the shape, interfacial area, and volume of air bubbles suspended in the gap between two coaxial, counterrotating cylinders are presented and discussed as function of capillary number. At high capillary numbers (high deformations), the experiments confirm the theoretical model of Hinch and Acrivos.

An accurate numerical solution for mass diffusion-induced bubble growth in viscous liquids containing limited dissolved gas

A mathematical formulation based on potential theory is used to develop an accurate numerical technique to calculate the mass diffusion-induced growth of a spherical gas bubble surrounded by a viscous Newtonian liquid with a limited dissolved gas concentration under isothermal conditions. We solve for the complete concentration profile of the dissolved gas in the liquid enveloping the bubble to predict the bubble growth. These results are contrasted against the dynamics of bubble growth predicted by the widely used approach of employing polynomial profiles to describe the gas concentration. The influence of key dimensionless parameters on the differences in the bubble growth due to the choice of concentration profile is examined. The investigation reveals that the commonly used approximate solutions for the concentration profile not only underpredict the growth rate at the early stages of the growth but also overestimate the steady-state bubble radius due to the implicit assumption of an unlimited supply of dissolved gas in the liquid.

Numerical simulation of Rayleigh-Taylor instability for single and multiple salt diapirs

The diapiric ascent of light rocks through a denser oberburden is simulated using a new numerical method based in part on finite differences. Rocks are modelled as viscous Newtonian liquids and the internal interfaces are located with the help of passive markers. These markers are relocated using a new algorithm equivalent to a cellular automaton rule. This allows the markers to be redistributed very rapidly. This new method appears to be well adapted to quickly resolving geological problems. Simulations of the growth of a single dome are performed under various viscosity ratios for the salt and the overburden. The effect of asymmetrical initial deformations of the salt layer is to produce diapiric structures that slowly return to symmetry as the diapir matures and rises in an isotropic medium. Simulations involving continuous sedimentation of the overburden are also performed. An initial geometry on a basin margin in which multiple diapirs eventually develop is studied. Diapirs grow relatively rapidly near the centre, while on the margins the salt layer flows upward following the basement. Simulations with salt that is more viscous than sediments show the development of previously unnoticed asymmetrical structures.

Airblast Atomization of Viscous Newtonian Liquids Using Twin-Fluid Jet Atomizers of Various Designs

Airblast atomization of viscous Newtonian liquids is carried out using coaxial twin-fluid jet atomizers of different nozzle sizes, slit angles, and slit cross sections for air flow. As the atomizing air swirls downstream along the liquid jet, waves form on the surface of the liquid jet. As a result, the liquid jet sheds ligaments which rapidly collapse into small drops. The atomized drop sizes can be described in terms of three dimensionless groups, namely, liquid-to-air mass ratio (M˙L/M˙A), Weber number (We), and Ohnesorge number (Z) in simple forms whose exponents and coefficients are determined by the best least square fit to the experimental results using the generalized inverse method. In addition, we found that the atomized drop sizes substantially decrease as the atomizing air pressure exceeds a threshold value which varies from less than 170 to 220 kPa depending on the nozzle size and the slit cross section.

ATOMIZATION OF HIGHLY VISCOUS LIQUIDS BY A SPINNING DISK

The drop formation of highly viscous liquids by spinning disks was studied experimentally. Aqueous starch syrup solutions of viscosities ranging from 0.25 to 0.91 Pa s and aqueous carboxymethyl cellulose sodium (CMC) solutions were used. Photographic observation indicated that the drop formation of highly viscous liquids resembles that of low-viscosity liquids, although the range in which ligaments form stably is rather narrow. The drop sizes of highly viscous Newtonian liquids in the ligament formation mode agree with the prediction based on the stability theory of a liquid jet, provided the ligament number is estimated correctly. However, the highly viscous liquids often hinder prediction of the correct number of ligaments. For the non-Newtonian CMC solutions, the drop sizes are larger than that predicted by more than 40%.

A boundary element solution technique for non-isothermal flow of highly viscous liquids

The boundary element method is applied to the solution of problems dealing with the non-isothermal flow of Newtonian viscous liquids. An exponential relationship between the viscosity and temperature is incorporated. The effects of viscous dissipation are also included. The technique is first applied to some simple test problems, and then used to examine the non-trivial problem of computing the non-isothermal swelling of a jet of viscous liquid.

Experimental observations of particle migration in concentrated suspensions: Couette flow

Nuclear magnetic resonance (NMR) imaging was used to observe the evolution of radial concentration and velocity profiles of initially well‐mixed concentrated suspensions of spheres in viscous Newtonian liquids undergoing flow between rotating concentric cylinders (wide‐gap, annular Couette flow). In Couette flow, particles migrate from the high shear‐rate region near the inner rotating cylinder to the low shear‐rate region at the outer wall. The particle concentration near the outer wall approaches maximum packing for randomly distributed spheres at steady state, and velocity profiles reveal that the suspension is almost stagnant in these regions. For unimodal suspensions of spheres, the shear‐induced migration of large particles results in concentric two‐dimensional, circular sheets of particles arranged in hexagonal close‐packed arrangements extending inward from the outer wall. This paper examines the functional dependence of particle migration in concentrated suspensions undergoing shear flow in a wid...

Stratified newtonian flow calculations by the boundary element method

A boundary integral equation formulation is used to model the stratified flow of two Newtonian viscous liquids, in which the geometrical detail of the interface between the layers is not known in advance. The technique is tested by comparing predictions with the results of previous finite element solutions, and found to perform well. Finally, the method is used to examine the two-layer jet theory of Tanner (1980) as a means of simplifying the modelling of complex extrudate swell problems.

Prediction of gas hold up and liquid velocity in airlift loop reactors containing highly viscous Newtonian liquids

Prediction of gas hold up and liquid velocity in airlift loop reactors containing highly viscous Newtonian liquids

Gas hold-up and liquid circulation in internal loop reactors containing highly viscous newtonian and non-newtonian liquids

When highly viscous liquids are used in bubble columns, the bubble population is bimodal; most of the gas passes through as large bubbles, but there is a substantial hold-up of small bubbles whose contribution to the gas flow is small. This paper describes flows of this nature for internal loop reactors (ILRs): an ILR is simply a bubble column containing an internal draught tube to promote liquid circulation. The gas flow enters at the bottom of the draught tube, which contains large and small bubbles: the large bubbles disengage at the top; the small bubbles recirculate with the downflowing liquid outside the draught tube. Two ILRs were used for measurements of gas hold-up, large bubble rise velocity and liquid circulation velocity: (i) a column of diameter 0.15 m containing a draught tube of diameter 0.09 m; (ii) a column of square cross section, 0.6 × 0.6 m, containing a square draught tube, 0.3 × 0.3 m. The rising velocity of single injected bubbles was also measured in clear liquid with no distributor gas flow in a 0.08 m diameter cylindrical column. The results show that the large bubble rising velocity is, to a first approximation, governed by equations appropriate for inviscid motion, notwithstanding the high viscosities of the liquids used: evidently inertial effects are dominant. The small bubbles receive only about 0.3–0.5% of the gas flow. The balance between this input and the rate of coalescence determines the small bubble hold-up. The mean residence time of small bubbles may well be comparable with the “half-life” for oxygen transfer from these bubbles. Hence the common assumption made in mass transfer calculations, that the oxygen concentration in these bubbles is always in equilibrium with the liquid, may not be valid. The liquid circulation velocities in the ILRs were measured by neutrally buoyant flow followers, and calculated from a pressure balance round the circulation loop: the expression used to calculate the pressure loss in the riser had to be modified to take account of liquid carried up by each large bubble; apparently this liquid flow did not contribute to the pressure loss.

Liquid stretching using a falling cylinder

A novel free-fall extensional device was developed and its usefulness in measuring the elongational viscosity of both Newtonian and viscoelastic liquids was demonstrated. A small quantity of liquid is inserted between the ends of two cylinders that are vertically oriented one above the other. The upper cylinder is held fixed while the lower cylinder, initially at rest, is allowed to fall and stretch the adhering sample. Time sequence photos of the stretching process are used to deduce the liquid deformation rate and ligament stress. The elongational viscosity is then determined from the stress/deformation rate ratio. While trial results for Newtonian liquids are consistent with the Trouton expression, viscoelastic testing indicates that the elongational viscosity increases with time and is significantly greater than that of a comparable viscous Newtonian liquid.

Augmentation of highly viscous laminar heat transfer inside tubes with constant wall temperature

An experimental investigation of enhanced tubeside flow and heat transfer under laminar flow conditions is reported. The three test sections in this study included a plain tube, an internally finned tube, and a tube with a twisted-tape insert, all with a nominal diameter of 25.4 mm and a length of 2.44 m. A highly viscous Newtonian liquid, Polybutene 20, was used as the test fluid. The heat transfer results were obtained in a horizontal test section with nearly constant wall temperature. Isothermal pressure drop, nonisothermal pressure drop, and heat transfer data were obtained over a wide range of the parameters: Reynolds number, 15.1–575; Prandtl number, 1260–8130; Graetz number, 868–6570; and bulk-to-wall viscosity ratio, 0.00464–42.8. The effects of free, or natural, convection were negligible in this study. All parameters are evaluated at the arithmetic mean bulk temperature and are based on the inside envelope diameter. Isothermal friction factors for the internally finned tube and the tube with the twisted-tape insert are 1.7 and 3.4 times those of the plain tube for the range of Reynolds numbers tested, with the nonisothermal friction factors showing similar increases. Augmented heat transfer coefficients were above the plain tube values for both heating and cooling. The greatest improvement for heating was for the internally finned tube where Nusselt numbers ranged from 3 to 4 times the plain tube values at corresponding Graetz numbers. For cooling, the twisted-tape Nusselt numbers were 1.5–2.25 times the corresponding plain tube values. Tabulated values and empirical correlations are presented for all of the data obtained.