Cake filtration of suspensions in viscoelastic fluids

The fundamental framework for cake filtration of suspensions in viscoelastic media is extended to include the effects of polymer retention, including adsorption in the filter cake, polymer retention and elongational flow in the filter medium, which also undergoes compaction, and evaluation of polymer degradation in the filter cake and medium. Experimental data obtained in constant pressure filtration of starch suspensions in dilute aqueous polyacrylamide solutions confirmed the prediction of an enhanced apparent medium resistance R_ma and a reduced cake resistance α_R. Evaluations are presented of the contributions to the pressure drop due to enhanced normal stresses in elongational flow and to polymer retention (adsorption), and of the ratio of the particle size with and without adsorbed polymer in the cake. The analysis of the data points to high levels of polymer degradation during the flow of the polymer solution through the filter cake and medium.     

Flocculation and viscoelastic behavior of industrial papermaking suspensions

The effects of the surface charge type and density C496, C492 and A130LMW polyacrylamides (PAMs) on the rheological behavior of real industrial papermaking suspensions were quantitatively related to the degree of flocculation for the same industrial papermaking suspensions. The floc sizes were larger but less dense when anionic PAM was used, and this due to the repulsive forces between the anionic PAM and colloidal particles, leading to the development of open structure flocs of less density. On the other hand, rheological measurements showed that the papermaking suspension is thixotropic with a measurable yield stress. The results showed that the magnitude of the critical stress, τ _c , complex viscosity, η*, elastic modulus, G′, and viscous modulus, G″, depend on the number of interactions between the PAM chains and particle surface and the strength of those interactions. Cationic PAM showed higher values of η*, G′, G″ and τ _c compared to anionic PAM. This behavior is in good agreement with Bingham yield stress, τ _B , adsorption and effective floc density results. Similar to oscillatory measurements, creep measurements also showed that the deformation was much lower for the cationic PAM based suspensions than for the anionic PAM based suspensions. Furthermore, the results revealed that increasing the cationic PAM surface charge decreases the floc size but increases the adsorption rate, elasticity and effective floc density proposing differences in the floc structures, which are not revealed clearly in the Bingham yield stress measurements.     

The flow of suspensions

Most rheological and rheo-optical properties of suspensions such as viscosity and light-scattering intensities can be expressed in terms of the average orientation and/or the average concentration distribution of the suspended particles. In general one can distinguish several distinct regimes: (i) infinitely dilute, (ii) dilute, (iii) semi-dilute or moderately concentrated, and (iv) concentrated suspensions. Cases (i) and (ii) are regimes in which particle interactions are either absent or only two-body interactions are important. These cases can, in general, be well described theoretically. Regime (iii) is characterized by n-body (n ≥ 2) interactions and is the least understood. Regime (iv) can often be described in terms of a cell model in which the motion of a reference particle, or the fluid motion around it, is described.     

A new linear viscoelastic model for emulsions and suspensions

A new modified form of the Palierne model is proposed to describe the linear viscoelastic behavior of concentrated emulsions and suspensions. The proposed model takes into consideration the crowding effect and packing limit of particles. The model is verified using two sets of experimental data on the storage and loss moduli of emulsions and suspensions. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Unsteady flow of viscoelastic fluids

Theoretical solutions for unsteady flow of a three constant Oldroyd fluid and a second order fluid under several different flow conditions of practical interest are obtained. The response of these fluids to suddenly applied external force is investigated in each case. Without using the stick-slip boundary condition at the wall, it is possible to show that pressure oscillation occurs with both fluids under a certain case.     

Time-dependent flow of quasi-linear viscoelastic fluids

Transient flow behavior of an incompressible quasi-linear viscoelastic fluid under suddenly applied constant pressure as well as under a periodic pressure gradient was investigated using a three-parameter relaxation function. In the light of these solutions, the roll of viscoelastic relaxation in the overshooting of volumetric flow rate and the effect of viscoelastic parameters on the mean square velocity profile are discussed.     

Turbulent flow properties of viscoelastic fluids

The abnormally high resistance of viscoelastic fluids to sudden deformations and to stretching may be expected to cause the structure of turbulent velocity fields in these systems to differ appreciably from those of Newtonian fluids. An analysis based on these considerations is presented and supported using friction factor data for three concentrations of a water soluble polymer. Pressure losses predicted by use of this correlation are within 15% or less of the experimental values, but as all dimensionless groups which influence the results were not varied independently, the correlation developed may not be universally applicable to all fluids. Suggestions for further and more more specific analyses are made.     

Dimensional analysis of flow of viscoelastic fluids

Dimensional analysis of viscoelastic flow phenomena is analyzed in general terms, and it is shown that the method can only be used for “rheologically homologous” fluids (defined rigorously in the paper). Few generally useful results can be obtained from dimensional analysis when the condition of homologousness is met by making experiments with the same fluid for which predictive equations are sought. Other ways of meeting the condition are discussed, and some results of a general nature are obtained.     

Deformation of drops in extensional viscoelastic flow

The deformation of nylon drops in polyethylene, with and without an interfacial agent, in an extensional flow has been studied. The presence of an interfacial agent reduces the size of the dispersed phase, and the deformation of the drop is reduced. An analysis is given, which accurately predicts the deformation for all values of the capillary number considered. The predicted and observed shapes are, however, only in agreement at low values of capillary number. Possible causes for this discrepancy are discussed. © 1996 John Wiley & Sons, Inc.     

Particle migration in a flow of nanoparticle suspensions

This paper is concerned with particle migration in pressure-driven laminar pipe flows of relatively dilute suspensions of nanoparticles (nanofluids), one of the most frequently used configuration in industries. The motivation behind the work is associated with the thermal behaviour of nanofluids, which can greatly exceed the values predicted by currently available macroscopic theories. A theoretical model is formulated to predict particle concentration, and velocity field of nanofluids in the transverse plane of the pipe. The model takes into account the effects of the shear-induced and viscosity gradient-induced particle migrations, as well as self-diffusion due to the Brownian motion. It is shown that particle concentration in the wall region can be much lower than that in the central core region. This indicates a highly non-uniform thermal conductivity profile across the transverse plane of the pipe, and thus has a significant implication to heat transfer intensification using nanofluids. The results also suggest the existence of an optimal particle size whereby the thermal conductivity is enhanced with little penalty due to the effect of pressure drop.     

Energy dissipation during flow of coagulating concentrated suspensions

The energy dissipation during stationary flow is calculated for suspensions of such concentration that division into separate flocs and surrounding medium can be neglected (absence of sedimentation in the suspension at rest). This restriction removes some uncertainties in the “elastic floc” model [5]. The system is conceived as one giant flox when at rest, and to be divided by shear planes into domains when being sheared.Experiments performed on aqueous suspensions of Ca(OH)₂ (solid volume fractions = 0.25) show that the energy dissipation can be accounted for by that connected with the work required for overcoming the viscous drag experienced by particles moving within the domains. The influence of the nearby presence of other particles on the viscous drag is taken into account, but no separate term for energy dissipation by fluid flow in the flocs is necessary.     

A Tubeless Evaporator

The first author of this paper has invented a process, which incorporates direct contact evaporation, for saline water conversion, and waste concentration, which can include by-products recovery.The process has several potential advantages: Simplicity - major components are four vessels without internals, pumps, and a fan (unneeded in one version of the process); wide application - seawater, waste water, and membrane plant effluents; produces distilled water, co-produces brine, or concentrated brine, or moist solid, or by-products; no pretreatment in the ordinary case (on some applications, trash removal and chlorination is required); no scaling problem in the evaporator; minimum corrosion (no acid addition) ; can be powered by electricity of heat, including waste heat; low energy consumption in the single stage version of the process, extremely low energy consumption in the multistage version of the process.The process uses a working substance (WS), such as a high melting organic compound, at its freezing point, to effect the direct contact evaporation. An acceptable WS must be insoluble in water, inert, and easily separated by specific gravity difference from brine, product water, and any solids produced. It is also desirable that they be non-toxic, non-flammable, cheap, and have a high heat of fusion. Several WSs were identified that had the potential to be used in a commercial plant.At this point, the Office of Water Research and Technology (OWRT) sponsored a research project to investigate the operating characteristics of various WSs in the laboratory and a bench scale plant (BSP). A WS screening program tested melting range, solubility, tendency to entrain or emulsify, and stability, in the laboratory program. The BSP program simulated the operation of major pieces of equipment with WSs that passed the screening program, and seawater and other saline waters.A total of eight WS candidates were subjected to the WS screening program. Of these, two proved to be unsatisfactory. It was believed that these substances could have been made to work, but with other satisfactory materials available, there was little incentive to pursue this effort. The other six were found to be satisfactory for use in the BSP. Three of these were selected for testing in the BSP.Prior to the above effort, there was no data with which to design a pilot plant. Any such attempt would have had to be based on engineering judgement. Now one set of data (feed rates, operating conditions, etcetera) has been taken. These data could be far from optimum. Additional WSs, particularly those with melting points above 100°C are needed for multistage operation. Finally, the direct contact concept should be extended to the preheaters as well as the evaporator in order to make the process completely tubeless. Such a program, sponsored by OWRT, has just commenced.This paper describes the process and its potential advantages in more detail, reports on the results of the laboratory and bench scale programs referred to above, and outlines the program for the future development of the process.     

Velocity measurements in turbulent flow of viscoelastic solutions

An experimental study, based on streak photograph determination of instantaneous velocities, was directed at determining the turbulent flow velocity profiles of polymer solutions in circular pipes. The measurements resolve several discrepancies in interpretation of earlier velocity profile measurements in drag reducing systems. In particular, it is shown for dilute drag reducers that the semilogarithmic profile due to Prandtl with the same slope as for Newtonian fluids is quantitatively correct provided Bogueés empirical correction function is applied to the data. For a relatively concentrated solution, data serve to extent on earlier study which has shown the flow to be transitional at surprisingly high values of Reynolds number.     

Numerical simulation of three-dimensional viscoelastic flow within dies

In recent years, the development of CAE (Computer Aided Engineering) in polymer processing has been remarkable, and it is expected to be more realistic in viscoelastic numerical simulation, particularly in three-dimensional complex geometry. Because of the problems of computational memory capacity, CPU time, and the numerical convergence of viscoelastic flow simulation, three-dimensional viscoelastic simulation applicable to industrial flow behaviors has not yet been attempted. In this paper, we developed the numerical simulation of three-dimensional viscoelastic flow within dies using a decoupled method, streamwise integration, and penalty function methods to decrease memory, and the TME (“Transformation of Equation of Motion to the Elliptic Equation,” S. Tanoue, T. Kajiwara, and K. Funatsu, The Eleventh Annual Meeting, the Polymer Processing Society Seoul, Korea, Extended Abstracts p.439) method, which raises the stability of convergence. We confirmed the reliability of this simulation technique to compare simulation results with experimental data of the stress field at a downstream wall shear rate of 5.41s^?1 within a 60° angle tapered contraction die. We compared the predictions of a viscoelastic model (Phan-Thien and Tanner model) with a pure viscosity model (Carreau model) at a downstream wall shear rate of 120s^?1 and discovered a remarkable effect of viscoelasticity in the shear stress and first normal stress difference in particular in the tapered region.     

A variable-density model of the pipeline flow of suspensions

The turbulent flow of suspensions of fine solid particles in liquids is analyzed by assuming that the suspensions behave essentially as variable-density single phase fluids. Friction factors are found to depend upon the distribution of solid particles within the conduit as well as the Reynolds number of the flow. Comparison of the model with experimental measurements indicates that as long as turbulent suspension of solid particles occurs, the model is a useful alternative to the empirical Durand equation for pipeline design.     

Non-uniformity of gas dispersion in turbine-generated viscoelastic circulation flow

Gas dispersion has been analysed experimentally by measuring local gas hold-up in two lab-scale conventional turbine-agitated vessels loaded with viscoelastic fluids. The gas hold-up radial profiles obtained in various axial positions close and far from the impeller reveal high non-uniformity of gas dispersion. Non-uniformity is quantified and related to elasticity, shear dependent viscosity, shear rate, first normal stress difference coefficient and type of fluid. The low values of gas hold-up obtained for the vessel central area are interpreted as hindered gas dispersion caused by the flow pattern specific for the viscoelastic properties of the circulating fluid. The paper is complementary to the effort for collecting up data for benchmarking numerical CFD simulations (Kumar et al., 1997).     

Steady flow and dynamic viscoelastic properties of branched polyethylene

The presentation of viscoelastic properties of molten high polymers in a complex plane makes three characteristic rheologic parameters appear. These are examined for a series of commercial samples of low density polyethylene. For instance, it enables products to be recognized which are very similar as far as the melt index is concerned but have different molecular weight distribution, different long chain branching index and consequently different processing properties.     

Analysis of nip flow operations involving a viscoelastic roller

The hydrodynamics of a fluid flowing between rotating rollers are considered. In particular, a numerical solution, based on orthogonal collocation, is presented for those cases in which one of the rollers is covered with rubber. Such a roller system is used in the industrial application of thin liquid layers.The effects of the different material and process variables on the kinematics and dynamics of nip flow are analyzed. The results are compared with those for a rigid roller geometry. Conclusions are drawn with respect to efficiency of nip flow and suitability of laboratory equipment. Computational results are compared with available experimental evidence.