EXPANSION AND STRESS RELAXATION OF EXPRESSED CAKE

ABSTRACT

Expansion and stress relaxation of expressed cake are discussed.

The expansion process of expressed cake after release of load is very similar to consolidation of solidndashliquid mixtures, although a liquid flow in the expansion process is opposite in direction to that in consolidalion. This process can be analyzed well by use of the Terzaghi Voigt combined model. It is shown that the rate of primary deformation in expansion is much smaller than that in consolidation under the same change in compressive pressure. It is also found that the ratio of secondary deformation to total deformation in expansion is much larger than that in consolidation.

Stress relaxation of expressed cake, which is observed when expression is stopped before attaining an equilibrium compression state of a material, can be explained by use of a consolidation and expansion theory. In the relaxation process, local expansion appears near the drainage surface while local consolndash idation appears near the center of the cake. The equilibrium cake stress is uniquely determined by the average consolidation ratio when the expression is interrupted.     

Consolidation dewatering and centrifugal sedimentation of flocculated activated sludge

This study investigated experimentally the consolidation dewatering and centrifugal-settling processes for activated sludge subjected to cationic polyelectrolyte flocculation. The results were reported for the dynamic response of sediment cake thickness (an index for cake compaction) under various doses of polyelectrolyte conditioning, compression-permeability cell configuration and mode of operation (batch and continuous) in a centrifugal-settling cell. The reduction in sediment thickness of sludge by consolidation and centrifugation was found to correspond mostly well with the optimal dose of polyelectrolyte based on the capillary suction time. The relaxation/rebound of cake thickness was observed in both consolidation dewatering and centrifugal dewatering with comparable compaction/relaxation time scale ratios. The equilibrium sediment consolidation ratio increases with the effective solid pressure characterized by P_m and P_s, for the consolidation dewatering and centrifugal sedimentation, respectively. The experimentally determined time scales of the cake consolidation dewatering/centrifugal sedimentation processes agree reasonably well with the theory by Landman and Russel (Phys. Fluids A 5 (1993) 550).     

CHANGES OF RHEOLOGICAL PROPERTIES OF APPLE TISSUE UNDERGOING CONVECTIVE DRYING

The aim of this work was to investigate rheological properties of apple cubes undergoing convective drying. Compression-relaxation test was used to follow changes of properties under investigation.

Raw apple appeared to be very heterogeneous material from the rheological point of view. The relationship between stress and strain was concave downwards and the concavity increased until water content of 2·5 g/g d.m. was reached. Then the relationship begun to straighten and for dry material developed stress was linearly dependent on strain. The resistance of deformation decreased with decreasing water content. Analysis of relaxation showed that the rate of relaxation increased with decreasing water content and the unrelaxed stress was smaller the lower was the water content.

Apple cubes undergoing drying are pictured as material composed of three compartments with different rheological properties. The outer layer is dry, inelastic and difficult to deform. Underneath is moist material with no turgor and relatively easy to compress, and the core with properties of raw apples. During drying the second layer grows in expense of the core and porous structure with many voids filled with air is formed. Share of each compartment in the volume of apple cube undergoing drying affects average rheological properties of the material.     

A Stress Singularity Approach for the Prediction of Fatigue Crack Initiation in Adhesive Bonds. Part 1: Theory

Since crack initiation in adhesive bonds tends to occur near the interface corners where the stress fields are singular, we define a fatigue initiation criterion using stress singularity parameter, Q (a generalized stress intensity factor) and the singular eigenvalue, λ.

Hattori et al., successfully used a generalized stress intensity factor to characterize the static strength of bimaterial interfaces. We show that this criterion is only appropriate for situations in which the adhesive contact angle is no larger than 90° and the modulus ratio (adhesive to adherend) is smaller than 0.1. Fortunately, these conditions are often met in real joints, permitting the use of a single eigenvalue approach. We then extend this criterion to the case of fatigue arising from mechanical, thermal, or hygroscopic cycling.

In preparation for Part 2 (experimental), the special case of an epoxy wedge on a flat aluminum substrate is considered. The singularity is analyzed both analytically and numerically. The scale of the region dominated by the singularity is found to be of the order of 100 μm. The size of the plastically yielded zone near the apex is found to decrease extremely rapidly as the stress intensity factor goes down, thereby increasing the applicability of the method at the low stress levels often encountered in fatigue.     

The Effects of Cure Conditions on the Relaxation Behavior of Thermosetting Adhesives

The ability to dissipate mechanical energy by plastic (viscous) deformation is an important strength consideration for structural adhesives. The bulk solid viscosity parameter, μ, used in spring-dashpot mechanical-model characterization of polymeric materials, provides a convenient measure of this capability. The viscosity parameter, in turn, can be related to the relaxation time for the material with the use of the elastic modulus.

This paper presents a study of the effects of cure temperature and time on the stress relaxation behavior of Metlbond 1113 modified-epoxy adhesive with carrier cloth. Short term (t=1/2 minute) relaxation data are successfully fitted with the modified Bingham mechanical model to obtain relaxation time and bulk solid viscosity parameter values corresponding to different cure conditions. Experimental results indicate that both the relaxation time and the bulk viscosity values behave in a bell-shaped increasing-decreasing manner with respect to the cure temperature for all cure time values. This behavior is similar to that of adhesive ultimate strength and elastic modulus as observed by us earlier.     

A QUASI-NEWTON ALGORITHM FOR SOLVING MULTIPHASE EQUILIBRIUM FLASH PROBLEMS

A new algorithm has been developed for solving the multicomponent vapor-liquid-liquid equilibrium Mash problem. The algorithm is an extension of the “inside-out” approach proposed by Boston and Britt for the vapor-liquid equilibrium flash problem.

Conventional flash algorithms use temperature, pressure, composition, and phase fraction as the problem independent variables, In the inside-out approach a new set of independent variables is introduced in place of the conventional variables. The new variables are chosen to be as independent as possible of the conventional variables and as free as possible of mutual interaction. Complex phase equilibrium models are used only to generate parameters for a simple equilibrium ratio model. These parameters become the problem independent variables. The Quasi-Newton method of Broyden is employed to promote convergence of these variables.

The algorithm first obtains a solution for the vapor-liquid equilibrium flash. By examining the liquid phase, a heuristic algorithm is employed which quickly locates a two liquid phase composition region of reduced total system free energy when the original liquid is unstable. The solution of the vapor-liquid-liquid equilibrium flash is initiated only when this occurs.

The performance of the algorithm is demonstrated by a number of problems which exhibit varying degrees of nonideality.     

PARAMETER ESTIMATION IN CAKE WASHING

The uniform-film model for cake washing considers the cake to be composed of channels in which a stagnant film of solute-rich filtrate adheres to the surface of the channel.

Two independent methods are presented for an unbiased evaluation of the uniform-film model parameters. The first is an iterative procedure which requires adjustment of only one model parameter, and the second is a direct analytical procedure based on the method of moments. Both require experimental data to identify the model parameters.

Application of the two methods give wet-base porosities greater than unity which suggests that the experimental data used to determine the model parameters is beyond the domain of applicability of the uniform-film model.     

TERNARY EXTRACTION MODELING USING THE REDLICH-KISTER EXPANSION

Mathematical models for liquid-liquid extraction processes are not widely available. The correlation of liquid-liquid equilibrium for such a model is often difficult. One correlation, based upon the Redlich-Kister expansion for the molar excess Gibb's free energy, has been shown to accurately represent ternary liquid-liquid equilibrium systems used in liquid-liquid extraction operations.

The use of this correlation in an extraction model was investigated and found to be suitable for a ternary liquid-liquid extraction model with only minor limitations. A successful ternary liquid-liquid extraction model was developed using this equilibrium correlation.     

Peel Mechanics

Published treatments of peel mechanics are shown to yield inconsistent relations for the dependence of peel force upon the angle of peel. The paradox is resolved by limiting the stress analyses to small bending deformations of the detaching strip in the still-attached region. This condition holds when the moment arm of the applied peel force is much larger than the length of the high-stress region in the bond, which must therefore be considered a prerequisite for use of the published bond stress distributions.

Failure of some experimental results to conform to the theoretical dependence of peel force upon peel angle are ascribed to inelastic deformation or stretching of the detaching strip.     

DELIQUORING BY EXPRESSION - PART 2 VARIABLE-PRESSURE EXPRESSION

Expression processes under variable-pressure condition are analyzed in view of the flow through compressible porous media. It has been demonstrated that the expression mechanism of slurry consists of two flow phenomena and these types of phenomena can be analyzed first by filtration theory and second by the so-called consolidation theory.

By assuming that the continuous screw expression process con- sists of a succession of batch processes, the basic equations ex- pressing the relationship between the dehydration rate, the feed rate, and the expression pressure distribution are derived.     

DRAG AND MASS TRANSFER IN SLOW NON-NEWTONIAN FLOWS OVER AN ENSEMBLE OF NEWTONIAN SPHERICAL DROPS OR BUBBLES

An approximate solution for the slow motion of an ensemble of spherical drops through a power law fluid is obtained using Happel's free-surface cell model. It is shown that the drag coefficient decreases with decrease of the flow index and that this reduction is more significant at low voidage and large viscosity ratio parameter. The effect of the pseudoplastic anomaly on the mass transfer rate is more pronounced at low voidage for large values of viscosity ratio parameter, unlike the case of a single spherical drop

The present analysis covers the whole range of values of viscosity ratio parameter from infinity (an assemblage of solid spheres) to zero (a swarm of bubbles) and reduces to the solutions for those cases already known

The results for the motion of an ensemble of spherical drops also provide the basis for proposing a tentative expression for the expansion of liquid-liquid fluidized bed at low Reynolds number.     

LIQUID-LIQUID EQUILIBRIA OF ORGANIC COMPOUNDS: MEASUREMENT, CORRELATION AND PREDICTION†

The knowledge of phase equilibria is an important step in the development of extraction processes. This knowledge is usually gained from experiments. However, this procedure is expensive when a suitable solvent has to be found for a specific separation. Therefore methods for predicting phase equilibria are needed. While formerly these methods were largely based on empirical assumptions, the use of the concept of local compositions by Wilson⁶ offers a semi-empirical approach.

There is one disadvantage of this approach: the parameters of models like UNIQUAC or NRTL have to be fitted to different types of data, to liquid-liquid equilibria (LLE) for the immiscible pairs of components and to vapour-liquid equilibria (VLE) or other data for the miscible pairs in a system with mutual solubility.

To demonstrate the problem we performed measurements in the binary systems: n-octane/aniline and methylcylohexane/aniline. of both liquid-liquid equilibrium and vapour-liquid equilibrium: for the second type of measurements ebulliomeiry was used. The prediction of LLE has been improved with two new concepts. One is based on the well-known UNIFAC method. The use of the Lyngby-Dorlmund data bank made it possible to determine a new parameter table merely based on LLE data.

The second method is based on common UNIQUAC parameters which have been determined with the data base.     

Peel Adhesion of Solid Films-The Surface and Bulk Effects

The peel strength of rubber and paint films has been measured over a range of peeling velocities using a dead weight method. At low peel rates the peel force is fairly constant but rises rapidly at higher peeling speeds.

Experiments show that the peel strength is a function both of the energy of interfacial bonds which must be broken as peeling proceeds and of bulk energy losses in a viscoelastic peeling material.

The interfacial effect has two components: an equilibrium surface force which accounts for the peel strength at low velocities, and a viscous peeling force which depends on the peeling rate. This viscous interfacial force explains the increase in peel strength of purely elastic films at higher peeling velocities.

The energy loss in the bulk of the peeling film introduces two additional effects: a magnification of the peel strength in steady peeling over a certain velocity range, and a slowing down or stopping of peeling as transient relaxation occurs shortly after the application of the peel force.     

A WASHING THEORY FOR UNSATURATED FILTER CAKES USING THE CAPILLARY MODEL

A rigorous washing theory is developed using the area averaging technique for unsaturated filter cakes. Limiting cases of the resulting equations are investigated. The assumptions used in the modelling are verified.

The mass transfer parameters, which are evaluated by the application of the moment analysis, are shown to be directly proportional with the volumetric flow rate of the wash liquor. Experimental results also indicate that, for a given wash liquor volumetric flow rate, the increase in the cake thickness causes an increase in the mass transfer parameters.

It should be noted that the proposed model is applicable for large particle sizes. As particle size becomes finer and the size distribution becomes wider, the model should be modified by including dead void spaces containing pockets of the mother liquor in the filter cake     

A COMPARISON OF GAS SEPARATION PERFORMANCE BY DIFFERENT PRESSURE SWING ADSORPTION CYCLES

By simulations using an equilibrium model, a quantative comparison is made for different pressure swing adsorption (PSA) processes for gas separation. The comparison is based on the performance curve, which is defined as the relationship between product purity and product recovery at a fixed feed throughput.

For bed repressurization in the PSA cycle, the use of the light product yields superior separations compared to that using the feed mixture. For the pressure reduction step, it is found that the separation results are better when the heavy-product purge step is used, as compared to that using cocurrent depressurization. For an ultrahigh-purity light product, however, the PSA process using cocurrent depressurization is superior.

A new PSA process is suggested in which the heavy-product purge step is accomplished by using (or pressure-equalizing with) the effluent from another bed which undergoes the countercurrent blowdown step.     

A Stress Singularity Approach for the Prediction of Fatigue Crack Initiation in Adhesive Bonds. Part 2: Experimental

Using the epoxy-aluminum wedge specimens defined and analyzed in Part 1, we measure the number of cycles required to initiate an interfacial fatigue crack near the apex, where the stress field is predicted to be singular. The eigenvalue, λ, and the generalized stress intensity factor, Q, are varied via the wedge angle, and via the beam deflection, respectively. Crack initiation is detected using a strain gage bonded near the tip of the wedge.

Following the methodology developed in Part 1, the fatigue data are then used to construct a fatigue initiation criterion characteristic of the bimaterial interface. This criterion is a 3-D surface, with the ordinate representing the generalized stress intensity factor and the two horizontal axes representing the number of cycles to initiation and the eigenvalue, respectively. Three key assumptions of the model are found to be satisfied in the specimens tested herein: (1) geometric imperfections at the apex are smaller than the singular region, (2) the plastic zones near the apex are also smaller than the singular region, and (3) the locus of initiation is near interfacial.

Finally, a thermomechanical analysis indicates that the residual thermal stresses generated during the fabrication process make a significant contribution to the critical stress intensity factor. With high T_g adhesives and under unfavorable conditions (high modulus, high CTE, poor adhesion), we predict that the residual stresses alone could be sufficient to cause debond initiation.     

Viscoelastic Analysis of an Adhesive Tubular Joint

The investigations so far available with regard to stress analysis of adhesive joints assume that the adhesive is elastic. In the present analysis the time dependent properties of the adhesive are taken into account by assuming that the adhesive is viscoelastic. The viscoelastic analysis of a tubular joint has been attempted using a prony series fitting for the relaxation modulus of two adhesives. The long term redistribution of the stresses in the adhesive is evaluated using the finite element method.

Viscoelastic analysis of an adhesive tubular joint has been performed for the first time, using the finite element method with a prony series fitting for the relaxation modulus of the adhesive. For a typical epoxy it has been found that not only the elastic stresses are different at different levels but also the viscoelastic response shows considerable variation from one level to another. As large a reduction as 57 % is noticed in the normal stress and an even larger reduction of 62% is noticed in the shear stress over three decades of time.

The technique used in this report for the solution of the long term response can be employed for a study of the short-term response also.     

AN EXPLORATORY STUDY OF A COMBINED SONIC AGGLOMERATION AND CROSSFLOW FILTRATION SYSTEM FOR HOT GAS CLEANUP

The Institute or Gas Technology has investigated a combined sonic agglomeration/crossflow filtration system to remove particles smaller than 10 microns from high-temperature, high-pressure gas streams. Sonic energy induces agglomeration so that particles can be removed in a continuously operating cross-flow filler element. Cold-model and preliminary high-temperature, high-pressure results are promising.

The objective of this investigation was to explore the potential effectiveness of sonic agglomeration, crossflow filtration, and a combination of these techniques to remove particles from high-temperature, high-pressure (HTHP) gas streams. The technique of sonic agglomeration has been known since the 1930's, and crossflow filtration has been used successfully in liquid filtration. This investigation is unique in that these two techniques were combined. Sonic energy was used to agglomerate particles to sizes large enough to be separated from the gas stream in a crossflow filter. The crossflow filter has advantages over conventional filters as a paniculate agglomerate removal system because it (1) operates continuously, (2) does not subject the fragile agglomerates to the high stress typical of inertial capture devices, and (3) can control the buildup of a filter cake when properly combined with a sonic agglomerator.

This investigation was supported by the Gas Research Institute and the Institute of Gas Technology Internal Research and Development Fund.

In this preliminary study, we found that—

• A 2-micron porosity filter must be used to achieve 98% paniculate removal from 95% of a dust-laden stream. (In the crossflow operating mode, 5% of the stream bypasses the filter.)

• When sonic agglomeration is combined with crossflow filtration, the same removal efficiency can be achieved with a 10-micron porosity filter.

• Combined sonic agglomeration/crossflow filtration removed particulates smaller than 10 microns in experiments at 265° C and 7000 kPa.

• The pressure drop across a 10-micron filter is about one-half that of a 2-micron filter, which could reduce the energy requirements for filtration.

This method of particulate removal should be applicable to many different coal reactor effluent streams, especially because it can operate at elevated temperatures and avoid gas cooling, liquid condensation, and subsequent liquid-solids separation. Preliminary estimates show that the power requirements of a combined sonic agglomerator/crossflow filter are lower than those of a crossflow filter alone, and that they are lower than or comparable with other particulate removal techniques. Additional tests are needed to establish the degree to which these benefits can be realized.     

EFFECT OF CREEP AND MECHANO-SORPTIVE EFFECT ON STRESS DEVELOPMENT DURING DRYING

Constitutive equations to quantify wood deformation under combined mechanical loading and moisture content change (1] were coupled with the moisture distribution developed during drying to predict stress and strain in 50 by 190-mm Douglas-fir heartwood lumber.

Two combinations of temperature and relative humidity were used to dry the wood. The overall board shrinkage and the immediately released and set strains were measured as a function of time. Those strains were compared with analytic results, which showed good agreement.

The roles that four strain components played in the development of stress-both at board surface and center were compared for different drying conditions. The significance of creep and mechano-sorptive strain in relieving the stress was demonstrated by varying the model parameters.     

FLOW PROPERTIES OF LLOYDMINSTER AND COLD LAKE CRUDES

Data are presented on the viscosities of Cold Lake Crude and Lloydminster crude, over a temperature range of 278-323 K, up to a shear rate of 662 s^-1

The effect of diluents on the flow properties has been measured and discussed. An Arrhenius-type relation between viscosity and temperature was verified and problems associated with the use of a Contraves Rheomat 30 viscometer were discussed, with respect to measurements of time-dependent material functions such as stress growth, stress relaxation and hysteresis behaviour.