Viscous Newtonian Liquid Research Articles

A Thermomechanical Model for Energetic Materials with Phase Transformations

A model is developed to describe energetic materials with phase transformations from solid to liquid to gas with an exothermic chemical reaction. The model uses a phase variable and a reaction progress variable as thermodynamically independent state variables. A configurational force balance is used to derive an evolution law for the phase variable. The evolution equation for the reaction progress variable is posed as a basic law. In various limits the material is a classical elastic solid, a Newtonian viscous liquid, and a compressible gas. The model is examined in relation to classical equilibrium thermodynamics in a quasi-static limit. The model formulation is specialized to simple motions which are analyzed in a companion paper.

ULTRASOUND-MODULATED TWO-FLUID ATOMIZATION OF VISCOUS NEWTONIAN LIQUIDS

In this article, ultrasound-modulated two-fluid (UMTF) atomization of viscous Newtonian liquids at a lower ultrasonic frequency (25 kHz) is compared to that at fundamental frequencies of 54 and 110 kHz. The experimental data obtained show a shift to smaller drop sizes at a higher air velocity and a larger ratio of air-to-liquid mass flow rate, consistent with those obtained previously at the higher fundamental frequencies. Also consistent with earlier findings, the drop-size distribution becomes narrower as liquid viscosity increases. The experimental results of drop-size distribution are consistent with the theoretical predictions of greater-amplitude growth rates for the capillary waves generated by higher (third and above) harmonics than by the first and second harmonics based on the modified Taylor’s dispersion relation. However, since the harmonics differ in frequency by 25 kHz only, more than one higher harmonic (up to fifth) make significant contributions in UMTF atomization. Compared to the acoustic-modulated pressure atomization that also operates at 25 kHz, the UMTF atomization requires an ultrasonic drive two orders of magnitude smaller.

Hydrodynamics of power-law fluids in trickle-flow reactors: Mechanistic model, experimental verification and simulations

A fully predictive one-dimensional mechanistic model was developed for describing the hydrodynamics of power-law fluids in trickle-bed reactors. The model is a generalization of the slit approach to the case of non-Newtonian fluids obeying Ostwald–deWaele rheological behavior. Without recourse to adjustable parameters, the proposed model enabled prediction of the experimental values of (i) total two-phase total pressure drop and total liquid holdup in the trickle flow regime, (ii) frictional pressure drop in single-phase flows through packed beds, and (iii) total liquid holdup in gravity driven liquid downflow and stagnant gas through packed beds. Parametric simulations guided by knowledge of the behavior of highly viscous Newtonian liquids in trickle beds highlighted the capability of the model in the simulation and design of trickle flow operation using power-law fluids.

Power Consumption Characteristics of Disc Type Impellers.

This study reports on the unaerated power number (Np) and the ratio of aerated to unaerated power consumption (PG/P) for three disc type impellers in water and highly viscous Newtonian and non-Newtonian liquids. Modified disc type impellers (i.e. CBDT—concave bladed disc turbine and Scaba 6SRGT) were found to give lower Np and higher PG/P values than the flat bladed disc turbine or Rushton turbine (DT), in all liquids. Higher PG/P values are generally assumed to imply superior mass transfer potential of a given impeller. However, an examination of gas hold-up (which is closely linked to mass transfer) generated by DT, CBDT and Scaba 6SRGT, suggests that this is not necessarily true and further investigations may be necessary.

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, ϕgD, and volumetric oxygen transfer coefficient, kLaD were evaluated experimentally. The dependences of ϕgD and kLaD 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 ϕgD and kLaD 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

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

AbstractFlow 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, ϕgD, and volumetric oxygen transfer coefficient, kLaD were evaluated experimentally. The dependences of ϕgD and kLaD 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 ϕgD and kLaD 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

Centrifugal degassing of highly viscous newtonian liquids

AbstractThe movement of gas bubbles in a Newtonian liquid under centrifugal forces was considered. Taking into account wall effects and the increase of bubble diameter during the movement caused by pressure decrease, equations for the bubble movement time in the case of entirely free and immobile bubble surface were derived. Experiments on centrifuging air bubbles showed that in the centrifuge the bubble retained a free surface even at much smaller diameters than under gravity forces. A dimensionless bubble diameter was defined and its critical value above which bubbles behaved as free ones was evaluated.

Power characteristics of unsteadily forward–reverse rotating impellers in an unbaffled aerated agitated vessel

AbstractPower characteristics of an unbaffled aerated agitated vessel with unsteadily forward‐reverse rotating impellers, ie a new type of gas–liquid agitator named ‘AJITER’, treating viscous Newtonian liquids were studied experimentally. Measurements were first made on the agitation torque, ie the torque on the drive shaft on which forward–reverse rotating impellers with four delta‐type blades were attached, and the data obtained were analyzed by fitting them to an equation consisting of two terms with respect to the resistance of the fluid, one due to viscous drag and the other due to added moment of inertia. The effects of operating conditions and physical properties of liquids on the drag and added moment of inertia coefficients were then evaluated, and empirical relationships which estimate values of these coefficients, useful to predict the unsteady behavior and magnitude of agitation torque, were presented. Furthermore, equations were developed for estimating the average and maximum power consumptions as a function of the drag and added moment of inertia coefficients. Prediction of respective power levels in AJITER by these equations was also discussed.© 2001 Society of Chemical Industry

A finite element model of interaction between viscous free surface waves and submerged cylinders

This paper describes the simulation of the flow of a viscous incompressible Newtonian liquid with a free surface. The Navier–Stokes equations are formulated using a streamline upwind Petrov–Galerkin scheme, and solved on a Q-tree-based finite element mesh that adapts to the moving free surface of the liquid. Special attention is given to fitting the mesh correctly to the free surface and solid wall boundaries. Fully non-linear free surface boundary conditions are implemented. Test cases include sloshing free surface motions in a rectangular tank and progressive waves over submerged cylinders.

Particle segregation in monodisperse sheared suspensions in a partially filled rotating horizontal cylinder

Recent experiments in a partially filled horizontal Couette device [Tirumkudulu et al., Phys. Fluids 11, 507 (1999)] have revealed a new instability in the flow of suspensions containing narrow-sized neutrally buoyant particles in a very viscous Newtonian liquid where the suspension under shear segregates into regions of high and low particle concentration along the length of the cylinder. We conducted similar experiments but in a different geometry, viz., a horizontal cylinder, in which the cylinder was partially filled with that same suspension and rotated about its horizontal axis. We found that, within a certain range of parameter space, the initially uniform suspension divided into cylindrical bands of high particle concentration separated by regions of pure liquid. Although it seems likely that this instability is initiated by particle concentration fluctuations, which, in turn, lead to fluctuations in the effective viscosity of the suspension, we have been unable to provide a quantitative explanation for this phenomenon.

Differential criterion of a bubble collapse in viscous liquids.

The present work is devoted to a model of bubble collapse in a Newtonian viscous liquid caused by an initial bubble wall motion. The obtained bubble dynamics described by an analytic solution significantly depends on the liquid and bubble parameters. The theory gives two types of bubble behavior: collapse and viscous damping. This results in a general collapse condition proposed as the sufficient differential criterion. The suggested criterion is discussed and successfully applied to the analysis of the void and gas bubble collapse.

An experimental investigation into the effect of impeller design on gas hold-up in a highly viscous Newtonian liquid

Given the knowledge gap which exists in our understanding of impeller induced gas dispersion in highly viscous liquids, this paper investigates gas hold-up characteristics of six impellers in a highly viscous Newtonian liquid (Castor oil, μ=0.76Pas): four disc-type impellers (conventional Rushton turbine and three other modified designs of disc turbines which are perceived to overcome its drawbacks), and two types of pitched bladed turbines (upflow – PTU and downflow – PTD). Gas hold-up is mainly compared on the basis of specific power dissipation (PG/V), and analysed in the context of: (i) the formation of large and tiny bubbles, and (ii) its time dependency, both being typical features of gas dispersion in high viscosity liquids. The relative performance of these impellers is evaluated by comparing: (a) the final total gas hold-up, (b) the hold-up of tiny bubbles and (c) the parameter describing time dependency of gas hold-up. The key inferences drawn from this study with regard to gas hold-up are as follows:1.Unlike in low viscosity liquids, gas hold-up in high viscosity Newtonian liquid is strongly influenced by impeller type.2.In the case of disc-type impellers, gas hold-up peaks at the threshold specific power required to initiate gas dispersion throughout vessel (PGT/V); it decreases progressively at higher powers. As a consequence, it is suggested that such impellers are operated at a power dissipation level just greater than the threshold value.3.And finally, modified disc-type impellers show a considerable potential for enhanced performance over Rushton turbine, while pitched bladed turbines are, in general, inferior to disc-type impellers.

A shear surface wave at the interface of an elastic body and a micropolar liquid

The propagation of a shear surface wave (SSW) along the interface of an elastic half-space liquid and micropolar half-space is considered. The phase velocity of the wave and its attenuation constant are determined. It is shown that a SSW at the interface of a solid and a micropolar liquid propagates almost without dispersion, unlike a wave at the interface of a solid and a viscous Newtonian liquid in which the dispersion is noticeable at high frequencies. The attenuation of the SSW is considerably weaker in the first case than the second. The attenuation constant decreases as the boundary viscosity increases.

Unsteady mass transfer between a slender bubble and a viscous liquid in a simple extensional flow

AbstractUnsteady mass transfer between a slender bubble and a viscous Newtonian liquid in a simple extensional and creeping flow has been studied. The exact analytical solution, at large Peclet numbers, has been obtained using similarity transformations and by the method of characteristics. It was determined that when a dimensionless time (the strength of the flow multiplied by the time) is greater than 2, then steady state is, in practice, obtained.

On the Choking of the Flow of Piezoviscous Liquids

Experimental evidence for choking of a piezoviscous fluid in a capillary tube is presented. It is shown that under a nearly isothermal condition, it is possible for the flow to experience choking whereby increasing the inlet pressure ceases to affect the flow rate. The occurrence of this phenomenon can be predicted by noting a singularity in the flowrate equation in a capillary tube under typical conditions encountered in injection molding (cf. Denn, 1981). Further examination of the general equations governing the shear flow of laminar, incompressible, linearly viscous (Newtonian) liquids under high pressures reveals a singularity in the solution for the pressure gradient. This apparently unreported phenomenon is shown to occur in liquids whose viscosity, μ, increases exponentially with pressure, p, as μ = μ0eαp, where α denotes the pressure-viscosity coefficient. For a two-dimensional configuration with the shearing action taking place in the x direction and with p = p(x, y), the singularity is shown to take place when: τyx=±(1/α)1+α2τxxτyy, at which case both δp/δx and δp/δy →∞. The occurrence of such a singularity in the pressure gradient may have an important physical implication in lubrication flows particularly in concentrated contacts such as elastohydrodynamic lubrication of rolling element bearings and gears.

The pressure drop created by a ball settling in a quiescent suspension of comparably sized spheres

Measurements are reported of the pressure differences ΔP existing at large distances above and below a ball settling along the axis of a circular cylinder filled with an otherwise quiescent viscous Newtonian liquid in which identical particles, comparable in size to the settling ball, are suspended. The suspensions ranged in solids volume fraction ϕ from 0.30 to 0.50 and consisted of 0.635 cm diameter spheres density-matched to the suspending oil. The settling balls varied in diameter from 0.318 to 1.27 cm, resulting in particle Reynolds numbers always less than about 0.4 based upon ball diameter and the effective viscosity of the suspension. For the moderately concentrated suspension (ϕ=0.30), the product of ΔP with the cross-sectional area A of the containing cylinder was observed to be equal to twice the drag force D on the settling sphere, in accord with theory. In the more concentrated suspension (ϕ=0.50) this product was found to be slightly, but significantly, less than twice the drag on the settling sphere. It is speculated that this lower pressure drop may result from the presence of one or more of the following phenomena: (i) migration of the falling ball off the cylinder axis ; (ii) apparent slip of the suspension at the cylinder wall; (iii) blunting of the otherwise Poiseuillian parabolic velocity profile, the latter phenomenon being known to occur during the creeping flow of concentrated suspensions through circular tubes. Incidental to the suspension experiments, for a homogeneous fluid we verify the classical theoretical formula for the off-axis pressure drop when the sphere settles at a non-concentric position in the cylinder.

Extensional deformation of Newtonian liquid bridges

A numerical investigation is presented of axisymmetric, static and elongating, viscous Newtonian liquid bridges confined between identical circular disks. The time-dependent interface shapes and applied forces on the end plates, which separate at a constant prescribed velocity, are calculated as functions of the capillary number, the viscosity ratio between the inner and outer fluids, and an initial bridge configuration characterized by the aspect ratio. The numerical simulations are in excellent agreement with available experimental data and provide useful insight into the different dynamical responses of extending liquid bridge configurations. In particular, liquid bridges surrounded by fluids of a relatively small viscosity deform in a fore-aft symmetrical manner and undergo breakup sooner than in the case of relatively viscous outer fluids, which also require a greater applied force on the end plates to maintain the desired motion. Decreasing the capillary number (increasing interfacial tension) and the initial aspect ratio result in shorter bridge lengths prior to breakup and an increase in the applied forces on the end plates.

Bubble growth in viscous newtonian and non-newtonian liquids

A model for the dynamics of hydrodynamically controlled spherical bubble growth in quiescent viscous newtonian and non-newtonian liquids is presented. Two constitutive equations were used to describe the behavior of the liquid medium: (1) a simple power law relation and (2) a truncated power law. Application of the truncated power law resulted in four differen cases: (a) at all times the liquid acts as a newtonian liquid; (b) at all times the liquid behaves as a simple power law liquid; (c) at all times the liquid close to the growing bubble obeys a power law relation and the liquid far away from the bubble behaves as a newtonian liquid; (d) all the liquid initially behaves as a newtonian liquid and at some time transforms to a two-region liquid. Analytical expressions were derived for bubble growth as a function of dimensionless system parameters. The relevance of this work to the process of polymer devolatilization is discussed.

Transitional mixing in multiple-turbine agitated tanks

Blending of viscous newtonian liquids was studied in dual- and triple-turbine agitated tanks. The dimensionless power, mixing and interstage flow numbers were all found to be dependent on the Reynolds number as long as the full development of turbulence was inhibited by viscosity (Re < 2 × 10 4) and they were found to be constant above that limit. The complexity of the transitional regime makes it adverse for simple correlation, but, surprisingly, modelling of mixing in the upper transition region (Re > 400) could still be achieved using a compartment model developed elsewhere for turbulent mixing simulation in this geometry. The model corresponds to a simplified physical representation of the hydrodynamics of the tank

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

Gas holdup and liquid circulation velocity meassurements were made for a range of liquid viscosities in a 22 l external loop airlift column and 250 l pilot-scale concentric cylinder airlift bioreactor. The results showed that for a fixed superficial gas velocity, liquid circulation velocity decreased monotonically with increasing liquid viscosity. The gas holdup for a fixed gas flow rate showed an initial increase with liquid viscosity followed by a decrease when liquid viscosity increased beyond a critical value. These observations could not be described satisfactorily using the available models of gas holdup and liquid circulation.