Rheology and Permeability of Crosslinked Polyacrylamide Gel

Gels produced by crosslinking polyacrylamide solutions with chromium (III) have been characterized by dynamic rheology studies. To vary the gel strength, different polymer concentrations were used, while keeping the temperature, salinity, and crosslinker concentration constant. Both the loss and storage moduli increased with the polymer concentration for this gel system. The storage modulus at the end of the gelation was used to characterize the gel strength. Steady-state water flow experiments through gel-filled capillary tubes were performed, with the aim of linking the gel strength and flow behavior. The permeability was found to be a function of the water flow rate (velocity) and polymer concentration. Two parameters were used to characterize the flow behavior, intrinsic gel permeability and elasticity index, which are each functions of the polymer concentration. However, only one parameter is needed to fully identify the flow and rheological gel properties, as the elasticity index and storage modulus are linked by a power-law relationship. The loss modulus and intrinsic permeability are correlated with the storage modulus and elasticity index, respectively. A theoretical model for this behavior linking both gel properties based on the dual domain structure was used to demonstrate that the flow and rheological behavior of the gel are indeed related and that the gel strength controls the water permeability. Implications for prediction of flow of water through gels emplaced in a porous medium are discussed.     

Transport of Water and Ions Through a Clay Membrane

A model for hindered transport of water and ions is used to predict transient flow through a clay membrane caused by an initial difference in the concentration of salt solutions in reservoirs on the two sides of the membrane. Transport is assumed to be controlled by three coefficients, which are analogous to the permeability, salt diffusivity, and salt reflection coefficient of the membrane. Initial fluid motion is caused by osmosis, leading to a buildup of pressure on one side of the membrane. However, the clay forms an imperfect ion exclusion membrane and the final steady state is one of equal concentrations and pressures on the two sides of the membrane. The time-dependent differences in pressure and salt concentration across the membrane are predicted to vary as the sum of two decaying exponentials. When the salt reflection coefficient is small, one time scale governs Darcy flow through the membrane and another the diffusion of salt. Experimental results confirm the analysis. Although the salt concentration in the reservoirs was monitored in the experiments, estimates of the transport coefficients can be obtained by measuring only the pressure change across the membrane.     

Investigation of Calcium Carbonate Scaling Inhibition and Scale Morphology by AFM

The calcium carbonate scale inhibition by two inhibitors, polyacrylic acid (PAA) and 2-phosphonobutane-1,2,4-tricarboxylic acid (PBTCA), has been studied in two heat transfer systems: recirculating cooling water and pool boiling systems. It is found that PBTCA has a better inhibition effect than PAA under identical conditions. The inhibition effect increases with increasing fluid velocity for the cooling water system, whereas in the presence of inhibitors, the fluid velocity has less effect on the scaling behavior. When the initial surface temperature increases, the inhibition efficiency decreases. In the presence of inhibitors, the scaling behavior is insensitive to the change of surface temperature. The relationship between the inhibition effect and the fractal dimension has also been investigated. The results show that the fractal dimension is higher in the presence of inhibitors. The better the inhibition effect, the higher the fractal dimension. XRD and FTIR analyses demonstrate that for the CaCO₃ formed in the pool boiling system, the content of vaterite increases with the increase of inhibition effects. The metastable crystal forms of vaterite and aragonite are stabilized kinetically in the presence of inhibitors. The step morphology has been observed by atomic force microscopy. It is shown that the step space on the CaCO₃ surface increases in the presence of inhibitors. Moreover, with the increase in inhibition effect, both the step space and the fractal dimension increase. Step bunching is also found and discussed in this paper.     

Electroosmosis through a Cation-Exchange Membrane: Effect of an ac Perturbation on the Electroosmotic Flow

Electroosmosis experiments through a cation-exchange membrane have been performed using NaCl solutions in different experimental situations. The influence of an alternating (ac) sinusoidal perturbation, of known angular frequency and small amplitude, superimposed to the usual applied continuous (dc) signal on the electroosmotic flow has been studied. The experimental results show that the presence of the ac perturbation affects the electroosmotic flow value, depending on the frequency of the ac signal and on the solution stirring conditions. In the frequency range studied, two regions have been observed where the electroosmotic flow reaches a maximum value: one at low frequencies (Hz); and another at frequencies of the order of kHz. These regions could be related to membrane relaxation phenomena.     

Advective flow and floc permeability

This work monitored advection flow through a floc by bubble tracking. Close examination of the motion of a swarm of hydrogen bubbles that passed over a free-falling floc allowed the extent of advection flow to be estimated at 53% for the original activated sludge floc, and 12% for the flocculated floc. The interior permeability of the sludge flocs was estimated from this information. The fluid force exerted on the falling floc was also considered.     

Contribution to the Determination of Kinetic Parameters of the Sol-Gel Transformation by Rheological Measurements

The system tetraethoxysilane(TEOS)–water–ethanol has been studied by rheological measurements. Different molar ratios of TEOS : water (1 : 4, 1 : 10, and 1 : 20) are studied at different temperatures (30, 40, and 50°C). The dynamic viscosity (rotating mode) at a constant shear rate (100 s⁻¹) and the elastic and viscous moduli (oscillating mode) at a constant frequency (1 Hz) are determined. The viscosity–time curves are evaluated by application of a nucleation and particle growth model. Good agreement between experiments and theory is observed. The model allows the determination of the complex rate constant of silica precipitation. The temperature-dependent measurements gave the possibility to determine the apparent energy of activation by common methods. The results are in agreement with data from the literature. The gel time defined as intersection point of elastic and plastic moduli and its dependence on temperature are evaluated by the Smoluchowski model. The energy of activation for the coagulation was determined and found to be in the correct order of magnitude.     

Light Scattering Study of Turbid Heat-Set Globular Protein Gels Using Cross-Correlation Dynamic Light Scattering

The structure factor of aqueous solutions of the globular protein β-lactoglobulin was determined as a function of heating time at 76°C. We show how the effect of multiple scattering on the scattered light intensity can be effectively corrected using cross-correlation dynamic light scattering even if the transmission is only 1%. The structure factor of aggregated and gelled proteins can be described by the Ornstein–Zernike equation. The system is characterized by a correlation length that increases with heating time and stabilizes some time after the gel is formed. The correlation length of the protein gels decreases with decreasing concentration. Measurements after progressive dilution of a sample close to the gel point showed that the protein aggregates are initially interpenetrated and disinterpenetrate upon dilution.     

Poly(N-vinyl-2-pyrrolidone) and 1-Octyl-2-pyrrolidinone Modified Ionic Microemulsions

The influence of the nonionic polymer poly(N-vinyl-2-pyrrolidone) (PVP) in comparison to the surfactant 1-octyl-2-pyrrolidinone (OP) on the phase behavior of the system SDS/pentanol/xylene/water was studied. In both modified systems a strong increase in the water solubilization capacity was found, accompanied by a change in the spontaneous curvature toward zero. In the polymer-modified system an isotropic phase channel is formed with increasing polymer content that connects the L1 and the L2 phase. The lamellar liquid crystalline phase is destabilized in both cases. In the L1 phase the adsorption of PVP at the surface of the microemulsion droplets and the formation of a cluster-like structure is proven by several methods like ¹³C NMR T₁ relaxation time measurments, zeta potential measurements, and rheology. In the L2 phase a modification of the interface of the inverse droplets is detected by a shift in the percolation boundary (conductivity) and ¹³C NMR T₁ relaxation measurements. The formation of a cluster-like structure can be assumed on the basis of our rheological measurements.     

An empirical kinetic model for the gelation of a concentrated latex suspension in the presence of nonadsorbing polymer chains

An empirical model has been proposed to describe the kinetic aspect of the gelation process of a concentrated latex mixture in the presence of nonadsorbing polymer chains. It was found to allow the identification of two predominant effects, a viscosity effect and an excluded volume one effect that balance during gelation, and to predict the polymer volume fraction for which the transition between these two predominant effects occurs in the dilute polymer concentration range.     

Flow of Multicomponent Electrolyte Solutions through Narrow Pores of Nanofiltration Membranes

The slow flow of a multicomponent electrolyte solution in a narrow pore of a nanofiltration membrane is considered. The well-known semiempirical method of subdivision of electrical potential into quasi-equilibrium and streaming parts and the definition of streaming concentrations and pressure are discussed. The usefulness of this tool for solving the electrohydrodynamic equations is shown and justified: the use of a small parameter enables a system of electrohydrodynamic partial differential equations to be reduced to a system of ordinary differential equations for streaming functions. Boundary conditions for streaming functions at both the capillary inlet and outlet are derived. The proposed model is developed for the flow of a multicomponent electrolyte solution with an arbitrary number of ions. This is coupled with (i) the introduction of specific interactions between all ions and the pore wall and (ii) the inclusion of the dissociation of water in both conservation and transport equations. Effective distribution coefficients of ions are introduced that are functions of both the specific interaction potentials and the surface potential of the nanofiltration membrane material. The axial dependency of surface potential is expressed by the use of a charge regulation model from which the discontinuity in electric potential and ion pore concentrations at the pore inlet and outlet can be described.A relation between the frequently used capillary and homogeneous models of nanofiltration membranes is developed. An example of application of the homogeneous model for interpretation of experimental data on nanofiltration separation of electrolyte solutions is presented, which shows a reasonable predictive ability for the homogeneous model.     

Zeta potential of stearic acid monolayer at the air-aqueous solution interface

The zeta (zeta) potential of an insoluble monolayer of stearic acid at the air-water interface was measured as a function of pH in the presence of 0.0001, 0.001, and 0.01 M NH4NO3. The zeta potential was measured by means of the plane interface technique which involved the determination of the electrophoretic velocity profile of reference (polystyrene latex) particles along the solution depth in a rectangular open quartz cell. The zeta vs pH relationship at 0.001 and 0.01 M NH4NO3 was analyzed in terms of the Gouy-Chapman-Stern-Grahame model for electrical double-layer incorporating a simple site-binding model used previously for many oxide and latex colloid studies. The dissociation constant (pKa) of stearic acid monolayer and double-layer parameters such as integral capacitances of inner and outer Helmholtz layers and the complexation constant of counterion complexes were also estimated.     

Hydrodynamic interaction between spheres coated with deformable thin liquid films

In this article, we considered the hydrodynamic interaction between two unequal spheres coated with thin deformable liquids in the asymptotic lubrication regime. This problem is a prototype model for drop coalescence through the so-called "film drainage" mechanism, in which the hydrodynamic contribution comes dominantly from the lubrication region apart from the van der Waals interaction force. First, a general formulation was derived for two unequal coated spheres that experienced a head-to-head collision at a very close proximity. The resulting set of the evolution equations for the deforming film shapes and stress distributions was solved numerically. The film shapes and hydrodynamic interaction forces were determined as functions of the separation distance, film thickness, viscosity ratios, and capillary numbers. The results show that as the two spheres approach each other, the films begin to flatten and eventually to form negative curvature (or a broad dimple) at their forehead areas in which high lubrication pressure is formed. The dimple formation occurs earlier as the capillary number increases. For large capillary numbers, the film liquids are drained out from their forehead areas and the coated liquid films rupture before the two films "touch" each other. Meanwhile, for small capillary numbers, the gap liquid is drained out first and the two liquid films eventually coalesce.     

Adsorption of polyacrylic acid and its copolymers with acrylonitrile on zinc oxide particles

Adsorption of polyacrylic acid and its copolymers with acrylonitrile, containing different quantities of carboxyl groups, on the dispersion of zinc oxide was investigated. The kinetics of polymer desorption was investigated based on data concerning the change in concentration of free carboxylic groups of polymer and zinc ions in solution. The concentration of free carboxyl groups decreases and the concentration of zinc ions in the liquid phase above the residue after separation of zinc oxide particles increases with time, reaching a constant value. The dependence of the concentration of free carboxyl groups and zinc ions in the liquid phase on the initial concentration of polymer in the plateau section of the kinetic curve was investigated. Adsorption isotherms of copolymers depend on their solubility in water and can be described by different mathematical models.     

Site percolation model for latex film formation in soft polymer matrix

The UV-visible (UVV) technique was used to monitor latex film formation in a soft polymer matrix. Various film samples were prepared by increasing the amount of poly(methyl methacrylate) (PMMA) particles in a poly(isobutylene) (PIB) matrix. These samples were then annealed above the glass transition temperature to promote latex film formation. Transmitted photon intensities, Itr, were measured for each film. It is observed that Itr decrease as the latex content is increased, which was explained by the increase in scattered light intensity, Isc. The drastic increase in Isc above a certain latex content is attributed to the site percolation of latex particles in the PIB matrix. The percolation threshold and the critical exponent were measured and found to be 0.3 and 0.4, respectively. The increase in Itr by annealing of film samples above Tg was explained with the void closure process below 0.8 occupation probability. When the film is occupied completely with the latex particles, interdiffusion of polymer chains was observed. Viscous flow and chain diffusion activation energies were determined and found to be 8 and 51 kcal/mol, respectively.     

Transport Properties of Compact Clays: I. Conductivity and Permeability

Conductivity and permeability of model and natural clays have been studied experimentally. Local properties such as porosity and zeta potentials were measured as functions of the electrolyte solutions. Whenever possible, experimental data were compared to numerical data obtained for random packings of grains of arbitrary shape, and a good agreement was found between them.     

Effect of Insoluble Surfactants on Drainage and Rupture of a Film between Drops Interacting under a Constant Force

The deformation, drainage, and rupture of an axisymmetrical film between colliding drops in the presence of insoluble surfactants under the influence of van der Waals forces is studied numerically at small capillary and Reynolds numbers and small surfactant concentrations. Constant-force collisions of Newtonian drops in another Newtonian fluid are considered. The mathematical model is based on the lubrication equations in the gap between drops and the creeping flow approximation of Navier–Stokes equations in the drops, coupled with velocity and stress boundary conditions at the interfaces. A nonuniform surfactant concentration on the interfaces, governed by a convection–diffusion equation, leads to a gradient of the interfacial tension which in turn leads to additional tangential stress on the interfaces (Marangoni effects). The mathematical problem is solved by a finite-difference method on a nonuniform mesh at the interfaces and a boundary-integral method in the drops. The whole range of the dispersed to continuous-phase viscosity ratios is investigated for a range of values of the dimensionless surfactant concentration, Peclét number, and dimensionless Hamaker constant (covering both “nose” and “rim” rupture). In the limit of the large Peclét number and the small dimensionless Hamaker constant (characteristic of drops in the millimeter size range) a fair approximation to the results is provided by a simple expression for the critical surfactant concentration, drainage being virtually uninfluenced by the surfactant for concentrations below the critical surfactant concentration and corresponding to that for immobile interfaces for concentrations above it.     

Numerical simulations of capillary-driven flows in nonuniform cross-sectional capillaries

In this study the wetting behavior of converging-diverging and diverging-converging capillaries is investigated numerically using an in-house written, finite-element code. An interface tracking procedure based on the predicted change in the total liquid volume, to update the interface location, and Cox's formulation, to determine the dynamic contact angle and the interface shape, is proposed and used. Flow simulations revealed that both converging-diverging and diverging-converging capillaries exhibit significantly slower wetting behavior than straight capillaries and that any deviation in the capillary diameter necessarily tends to slow the overall wetting speed. This behavior was attributed to local regions of very low capillary pressure and high viscous retardation force when the capillary diameter at the interface was significantly larger than the capillary diameter over the upstream fluid. Though the local wetting velocities were different, when equivalent capillaries were compared it was found that both converging-diverging and diverging-converging capillaries had the same total fill time independent of the number of irregular regions, suggesting that the simple model is sufficient for predicting the overall effect. The influence of surface tension and contact angle on the total wetting time was found to be similar for both straight and irregularly shaped capillaries.     

Polydispersity and Functional Group Distribution of Dispersant Polymer: Adsorption Properties and Magnetic Paint Dispersion

The quantitative analysis examining the functional group distribution of a dispersant polymer for magnetic paints is conducted by statistical estimation and adsorption experiments. The dispersant polymer contains averagely one or two functional groups on the chain, and has generally large polydispersity. By the calculation based on the random distribution of the functional group and the molecular weight, a typical design of the dispersant polymer is found to contain a significant amount of nonfunctionalized chains and highly functionalized ones. In adsorption experiments, the adsorbed amount of the polymer mass and the functional group are separately measured to determine the functional group distribution. The distribution is also evaluated by a sequential adsorption experiment, in which the chains are fractionated by the adsorption strength. Obtained experimental results agree with the calculated results. A practical method for increasing the effective chains in the paint is to make use of a preferential adsorption of the functionalized chain.     

Instability for shearing of an electrified Kelvin fluid sheet with or without supporting surface charges

The present study demonstrates the instability of streaming in a fluid layer sandwiched between two other bounded fluids under the influence of a vertical periodic electric field. The fluids are of a viscoelastic nature where the constitutive equation is Kelvin type. Due to the inclusion of streaming flow and the influence of a periodic force, a mathematical simplification is urged. Equation of motion is solved in light of the weakness effect for the viscoelastic properties. The instabilization of the problem is examined in view of the linearization of the perturbation approach. The boundary value problem is discussed for a charged or uncharged fluid sheet. Both cases are lead to derive linear coupled Mathieu equations with complex coefficients and damping terms. Stability analysis is discussed through a simplified configuration for the system of Mathieu equations. It is found that the elasticity parameters as well as the viscosity parameters have a stabilizing influence. The field frequency plays a destabilizing role in the presence of surface charges and a dual role in the absence of surface charges. The presence of surface charges retards the stabilizing influence of the viscoelastic effects. This calculation shows that the fluid velocity retards the destabilizing influence for the electric field. The increase of the thickness of the fluid sheet plays two different roles. A stabilizing role in the presence of surface charges and a destabilizing influence in their absence.     

Electroosmotic Flow of a General Electrolyte Solution through a Fibrous Medium

Although hydrotropy is extensively used in industry, the molecular mechanism of hydrotropic solubilization has not been completely elucidated yet. In this paper the interaction between a nonionic surfactant (ethoxylated fatty alcohol containing between five and six oxyethylenic units) and sodium p-toluene sulfonate is examined. Surface tension measurements confirm that the hydrotropic effect occurs at a concentration in which the hydrotropes self-associate. Photon correlation spectroscopy studies show that for this concentration of hydrotropes a drastic reduction in the surfactant micellar radius occurs. Furthermore the luminescence of the hydrotrope used as a fluorescence probe indicates that at low concentrations p-toluene sulfonate dissolves in the surfactant micelles but beyond the minimum concentration for hydrotropic solubilization the hydrotrope is present in the aqueous phase. These results suggest that the hydrotropic effect is related to alterations in the water structure induced by the hydrotrope molecules and to the presence of hydrotrope aggregates that furnish an appropriate niche for the surfactant amphiphile.