Double-layer Forces Research Articles

Pore constriction in ultrafiltration: A discrete multilayer deposition model with steric exclusion of solutes at the pore inlet

A discrete multilayer model for the deposition of solutes inside membrane pores during ultrafiltration is proposed. The model takes into account the time-dependent steric exclusion of solutes at the pore inlet and the difference between the deposition coefficients for the first and higher layers caused by the action of the double-layer electrostatic repulsion forces between suspended and deposited solutes. The governing differential equations are solved numerically for 2- and 3-layer deposition on the pore wall. Also, a much simpler approximate solution with an error less than 10% is obtained for the main practical scenario by the generalized variable-parameter averaging method. Permeability, rejection, and selectivity-permeability tradeoff curves are calculated and compared for the monolayer coverage (Langmuir adsorption), 2-layer, and 3- layer cases at different values of higher-to-first layer deposition coefficient and initial pore radius. It is shown that the value of the deposition coefficient for the higher deposited layers of solutes can dramatically affect the performance of the membrane. For the monolayer coverage case, simple algebraic equations for finding the rejection coefficient and its minimum are derived. They imply that the rejection coefficient can follow three scenarios: monotonically decreasing, monotonically increasing, or having a minimum. A set of derived equations for determining the initial, minimum, and steady-state values of the rejection coefficient and permeate flux is suggested to use along with an experimental selectivity-permeability tradeoff curve to find the unknown physicochemical and geometrical parameters needed to describe the ultrafiltration process of interest, optimize its process parameters, and change the process of membrane manufacturing in order to obtain a more efficient membrane.

Electrostatic Interaction between Dissimilarly Charged Membranes in Salt-Free Solution

A theoretical study on the electrostatic interaction between the dissimilarly charged membranes in a salt-free solution has been presented in this paper. The results show that the electric double-layer force is always repulsive for positively charged planar surfaces regardless of surface charge density (or potential) and separation; however, a long-range attraction is observed between surfaces with unequally opposite charge densities. Such attractive force also exists and is independent of the separation when both surfaces carry unequally opposite potential.

Deposition of colloidal particles in a microchannel at elevated temperatures

This work reports an experimental study of the thermal effect on the deposition of microparticles onto a solid surface in a microfluidic system, which allows a precise control of the solution temperature and enables the real-time monitoring of the deposition kinetics at the increased temperature. The static particle deposition rate (Sherwood number) has been measured over a range of temperatures between 20 and 70 °C. It is found that the Sherwood number is monotonically increased up to 265 %, with the solution temperature within the test range. A model including the Derjaguin–Landau–Verwey–Overbeek theory-based colloidal surface forces and gravity force is employed, taking into account temperature effects, to qualitatively interpret the experimental findings. The model shows that, by increasing the solution temperature, the attraction energy (van der Waals force) between the particles and the solid surface is increased while the repulsive energy (electric double layer force) is decreased. These findings demonstrate the importance of thermal effects in various thermally driven deposition processes, such as the fouling of bacteria and milk proteins in microscale milk pasteurization units.

The Role of Electrostatics in Protein–Protein Interactions of a Monoclonal Antibody

Understanding how protein-protein interactions depend on the choice of buffer, salt, ionic strength, and pH is needed to have better control over protein solution behavior. Here, we have characterized the pH and ionic strength dependence of protein-protein interactions in terms of an interaction parameter kD obtained from dynamic light scattering and the osmotic second virial coefficient B22 measured by static light scattering. A simplified protein-protein interaction model based on a Baxter adhesive potential and an electric double layer force is used to separate out the contributions of longer-ranged electrostatic interactions from short-ranged attractive forces. The ionic strength dependence of protein-protein interactions for solutions at pH 6.5 and below can be accurately captured using a Deryaguin-Landau-Verwey-Overbeek (DLVO) potential to describe the double layer forces. In solutions at pH 9, attractive electrostatics occur over the ionic strength range of 5-275 mM. At intermediate pH values (7.25 to 8.5), there is a crossover effect characterized by a nonmonotonic ionic strength dependence of protein-protein interactions, which can be rationalized by the competing effects of long-ranged repulsive double layer forces at low ionic strength and a shorter ranged electrostatic attraction, which dominates above a critical ionic strength. The change of interactions from repulsive to attractive indicates a concomitant change in the angular dependence of protein-protein interaction from isotropic to anisotropic. In the second part of the paper, we show how the Baxter adhesive potential can be used to predict values of kD from fitting to B22 measurements, thus providing a molecular basis for the linear correlation between the two protein-protein interaction parameters.

Simulation of particulate fouling at a microchannel entrance region

A computational study is reported on the dynamics of particles near the entrance of a microchannel, as used in microfluidic flow systems. The collision of particles with fins separating the microchannels in these entrance regions makes them particularly susceptible to particle fouling. The study employs a soft-sphere discrete-element method with van der Waals and electric double-layer forces between the particles and the wall. A multi-block-structured grid fit to the flow domain boundaries is used to compute the fluid velocity field using a finite-volume method. The fluid flow is interpolated onto a Cartesian grid for efficient flow field interpolation at the particle locations, and a level-set method is used to represent the flow field boundaries in the particle computation. Particles adhering to the upstream face of the fin separating two microchannels are found to form clusters, which are pulled laterally by the stagnation-point flow near the fin. Even under conditions where the adhesion is sufficiently strong that there is little or no particle rolling on the fin face, the particles are still removed from the fin due to collisions with other particles. Individual particles are removed quickly from the fin face due to collision with upstream particles, whereas particle clusters have sufficient adhesion force with the fin surface that they can withstand collision with other particles for longer periods of time before they are removed in a cascade-like process.

The interrelationship between surface chemistry and rheology in alkali activated slag paste

Ground granulated blast furnace slag can react with an alkaline activating solution to form a cement-like binder based on a calcium–sodium aluminosilicate gel, which is a potential alternative to Portland cement in many applications. This study provides new information regarding the effect of activator type and dosage on rheology by monitoring changes in pH, particle surface charge (zeta potential), and heat evolution in the early stages of the reaction process. Sodium and potassium hydroxide silicate solutions, at two different M2O (M: Na, K) dosages, are used here as activators. Alkali hydroxide activators cause a significant increase in the yield stress of an activated slag paste, especially at higher dosages as reactions take place rapidly, while within the same timeframe, the yield stress of the silicate activated slag remains unchanged. The results imply a direct relationship between a higher reaction rate with the formation of solid products (causing both spatial blockage effects and consumption of free water), and a rapid yield stress increase. However, the dependence of reaction rate on pH for different alkali-activated pastes is, at most, indirect. All activators induce a highly alkaline pH and a concentrated electrolyte solution environment in the fluid paste. As a result of complexation of poorly-hydrated ions on the surfaces of the particles, the magnitude of the zeta potential increases. A direct relationship is observed between the dosage of the activators and zeta potential. A zeta potential further from neutrality generally reduces yield stress by increasing the magnitude of double layer repulsive forces, with the exception of a higher dosage of silicate activator, which shows an indication of some attractive double layer forces.

Dynamic analysis of AFM by applying Timoshenko beam theory in tapping mode and considering the impact of interaction forces in a liquid environment

In an atomic force microscope (AFM), the cantilever vibrates by excitation at a frequency near the fundamental frequency, and the changes in vibration parameters, which result from the nonlinear forces of interaction between sample and cantilever tip, can be used as a tool to reveal the properties of the sample. To properly describe the images acquired by the AFM and to approximate the properties of the investigated sample, it is essential to use analytical and numerical models that can accurately simulate the dynamics of the cantilever and sample. For short beams, the Timoshenko model seems to be very accurate. Considering the fact that short beams (cantilevers) have many applications including the imaging of biological samples in liquid environments, the use of this theory seems to be necessary. In this paper, by employing the Timoshenko beam model, the effect of rotational inertia and shear deformation has been taken into consideration. The interaction forces between sample and cantilever in liquid, ambient air, and vacuum environments are quite different in terms of magnitude and formulation, and they play a significant role in the system’s dynamic response. These forces include hydrodynamic forces, electrostatic double layer force, etc. Using an accurate model for the interaction forces will improve the simulation results significantly. In this paper, the frequency response of the atomic force microscope has been investigated by applying the Timoshenko beam model and considering the forces of interaction between sample and tip in the air and liquid environments. The results indicate that the resonant frequency changes and cantilever vibration amplitude diminishes in a liquid environment compared to the air environment. The simulation results have good agreement with the experimental ones. The frequency responses for the attractive and repulsive regions in the two environments are compared and it is demonstrated that the dynamic response is highly dependent on the hydrodynamic and interaction forces in the liquid medium.

Novel Amphiphilic Comb-Like Polymers: Synthesis, Characterization, and Their Properties as Viscosifying and Filtration Additives for Drilling Fluids

Novel amphiphilic comb-like polymers (CPASA), used as viscosifying and filtration loss additives for low-solid water-based drilling fluids under high temperature and salinity conditions, were prepared from acrylamide, sodium 4-styrenesulfonate, and allyl polyethylene glycol ether with toluylene-end groups via inverse microemulsion polymerization. The chemical structure was characterized by Fourier transform infrared spectroscopy (FTIR) and hydrogen nuclear magnetic resonance (1H-NMR). The thermal stability, aqueous solution properties, and drilling fluid properties were evaluated. Results showed that the comb-like polymers exhibited dramatic enhancement in their thermal- and salt-resistant properties because of the steric hindrance and intermolecular associations of the side-chains. The rheological properties, filtration properties, and negative Zeta potentials of both fresh-water drilling fluid and saturated salt-water drilling fluid were greatly improved by the addition of CPASA before and after thermal aging tests, which were ascribed to the steric hindrance of its comb-like conformation, the strong electrical double layer force of clay particles, and the stable mud network formed by CPASA and clay particles in drilling fluid.

Enamel proteins mitigate mechanical and structural degradations in mature human enamel during acid attack

A hydrazine deproteination process was used to investigate the role of enamel proteins in the acid erosion of mature human dental enamel. Bright field high resolution transmission electron micrographs and x-ray diffraction analysis show no crystallographic changes after the hydrazine treatment with similar nanoscale hydroxyapatite crystallite size and orientation for sound and de-proteinated enamel. However, the presence of enamel proteins reduces the erosion depth, the loss of hardness and the loss of structural order in enamel, following exposure to citric acid. Nanoindentation creep is larger for sound enamel than for deproteinated enamel but it reduces in sound enamel after acid attack. These novel results are consistent with calcium ion-mediated visco-elasticty in enamel matrix proteins as described previously for nacre, bone and dental proteins. They are also in good agreement with a previous double layer force spectroscopy study by the authors which found that the proteins electrochemically buffer enamel against acid attack. Finally, this suggests that acid attack, and more specifically dental erosion, is influenced by ionic permeation through the enamel layer and that it is mitigated by the enamel protein matrix.

Analysis of amplitude modulation atomic force microscopy in aqueous salt solutions

We present a numerical analysis of amplitude modulation atomic force microscopy in aqueous salt solutions, by considering the interaction of the microscope tip with a model sample surface consisting of a hard substrate and soft biological material through Hertz and electrostatic double layer forces. Despite the significant improvements reported in the literature concerning contact-mode atomic force microscopy measurements of biological material due to electrostatic interactions in aqueous solutions, our results reveal that only modest gains of ∼15% in imaging contrast at high amplitude setpoints are expected under typical experimental conditions for amplitude modulation atomic force microscopy, together with relatively unaffected sample indentation and maximum tip–sample interaction values.

Stochastic collision and aggregation analysis of kaolinite in water through experiments and the spheropolygon theory

An approach based on spheropolygons (i.e., the Minkowski sum of a polygon with N vertices and a disk with spheroradius r) is presented to describe the shape of kaolinite aggregates in water and to investigate interparticle collision dynamics. Spheropolygons generated against images of kaolinite aggregates achieved an error between 0.5% and 20% as compared to at least 32% of equivalent spheres. These spheropolygons were used to investigate the probability of collision (Pr[C]) and aggregation (Pr[A]) under the action of gravitational, viscous, contact (visco-elastic), electrostatic and van der Waals forces. In ortho-axial (i.e., frontal) collision, Pr[A] of equivalent spheres was always 1, however, stochastic analysis of collision among spheropolygons showed that Pr[A] decreased asymptotically with N increasing, and decreased further in peri-axial (i.e., tangential) collision. Trajectory analysis showed that not all collisions occurring within the attraction zone of the double layer resulted in aggregation, neither all those occurring outside it led to relative departure. Rather, the relative motion on surface asperities affected the intensity of contact and attractive forces to an extent to substantially control a collision outcome in either instances. Spheropolygons revealed therefore how external shape can influence particle aggregation, and suggested that this is equally important to contact and double layer forces in determining the probability of particle aggregation.

Importance of Double Layer Force between a Plat and a Nano-Particle in Restricting Fines Migration in Porous Media

Fines migration is defined as separation of a Nano-sized particle by fluid flow in porous media and its migration along some distances and its entrapment in a narrow pore throat or its settlement on pore wall. Although this phenomenon happens in scales of Nano-meters, it can lead to sever irretrievable damages. This damage includes permeability reduction that causes drastic oil recovery reduction. There are several forces impacting a fine that is placed on a pore wall. Some of most important forces affecting settlement of a fine in porous media in presence of a fluid are electrical forces. Electrical forces consist of several long and short range forces. This study focuses on a long range force called Double Layer Force (DLF) that beside Van der Waals is one of most powerful electrical forces. DLF is a repulsive force that can repel a particle from pore wall and result separation of a Nano-sized solid which subsequently moves along with flowing fluid and clogs a throat. The DLF depends on the solid material (reservoir rock and fine) and fluid properties (i.e. ionic strength, pH). This study investigates how each of these parameters affects DLF and introduces proper conditions for reservoir water flooding for controlling fines migration.

Particle aggregation mechanisms in ionic liquids.

Aggregation of sub-micron and nano-sized polystyrene latex particles was studied in room temperature ionic liquids (ILs) and in their water mixtures by time-resolved light scattering. The aggregation rates were found to vary with the IL-to-water molar ratio in a systematic way. At the water side, the aggregation rate is initially small, but increases rapidly with increasing IL content, and reaches a plateau value. This behaviour resembles simple salts, and can be rationalized by the competition of double-layer and van der Waals forces as surmised by the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). At the IL side, aggregation slows down again. Two generic mechanisms could be identified to be responsible for the stabilization in ILs, namely viscous stabilization and solvation stabilization. Viscous stabilization is important in highly viscous ILs, as it originates from the slowdown of the diffusion controlled aggregation due to the hindrance of the diffusion in a viscous liquid. The solvation stabilization mechanism is system specific, but can lead to a dramatic slowdown of the aggregation rate in ILs. This mechanism is related to repulsive solvation forces that are operational in ILs due to the layering of the ILs close to the surfaces. These two stabilization mechanisms are suspected to be generic, as they both occur in different ILs, and for particles differing in surface functionalities and size.

Effect of Fluid Flow Characteristics on Migration of Nano-Particles in Porous Media

Inter-particle and molecular forces are of most important forces affecting fines migration. Investigating the impact of these types of forces requires information about electrical properties of constitutive component and Nano-sized solids. Surface potential is a well-known parameter, which can be used to measure aforementioned forces. The force balance among electrical, gravity, drag and buoyance forces tracing on a particle can be estimated using fluid properties and physical properties of reservoir such as surface potential, pore size distribution and fine size distribution. The task is to set these forces at conditions that fine migration does not take place. This paper investigates the impact of several parameters that could influence pertinent forces. Effect of ionic strength of flowing fluid is taken into account to evaluate Debye length that determines double layer forces. The impact of injection rate on a parameter named erosion number is also studied. The results of this study show that how introducing salts and injection rate can affect stability of fines on their locations.

Polyelectrolyte adsorption, interparticle forces, and colloidal aggregation

This review summarizes the current understanding of adsorption of polyelectrolytes to oppositely charged solid substrates, the resulting interaction forces between such substrates, and consequences for colloidal particle aggregation. The following conclusions can be reached based on experimental findings. Polyelectrolytes adsorb to oppositely charged solid substrates irreversibly up to saturation, whereby loose and thin monolayers are formed. The adsorbed polyelectrolytes normally carry a substantial amount of charge, which leads to a charge reversal. Frequently, the adsorbed films are laterally heterogeneous. With increasing salt levels, the adsorbed mass increases leading to thicker and more homogeneous films. Interaction forces between surfaces coated with saturated polyelectrolyte layers are governed at low salt levels by repulsive electric double layer interactions, and particle suspensions are stable under these conditions. At appropriately high salt levels, the forces become attractive, principally due to van der Waals interactions, but eventually also through other forces, and suspensions become unstable. This situation can be rationalized with the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). Due to the irreversible nature of the adsorption process, stable unsaturated layers form in colloidal particle suspensions at lower polyelectrolyte doses. An unsaturated polyelectrolyte layer can neutralize the overall particle surface charge. Away from the charge reversal point, electric double layer forces are dominant and particle suspensions are stable. As the charge reversal point is approached, attractive van der Waals forces become important, and particle suspensions become unstable. This behaviour is again in line with the DLVO theory, which may even apply quantitatively, provided the polyelectrolyte films are sufficiently laterally homogeneous. For heterogeneous films, additional attractive patch-charge interactions may become important. Depletion interactions may also lead to attractive forces and suspension destabilization, but such interactions become important only at high polyelectrolyte concentrations.

The Effect of Surface Charge on the Deposition Rate of Particles with Metals

The influence of ζ-potential on the electrodeposition of particles with metals was investigated by the codeposition of three different types of particles (BaSO4, CaF2 and K1.33Mn8O16) with three different metals (nickel, copper and zinc) from seven different, unsupported (binary) and well-supported plating solutions across the whole pH range. The surface charge of the particles in the plating solutions was modified by adding potential determining ions that are electrochemically silent. The surface charging behavior of the different particles was determined in indifferent electrolytes and in diluted plating baths. In all cases, making the surface potential more positive increased the deposition rate of particles, while if the surface charge is reduced or made negative, the deposition rate of particles decreased. By comparing the magnitudes of the different forces acting on particles and how they are affected by changes in the surface charge of the particles, we conclude that the change in the codeposition are due to either a change in the mass transport of particles by the electrophoretic force or a change in the particle-electrode adhesion due to the double layer force.

A New Approach for Evaluating Migration of Nano Particles in Porous Media

Inter-particle and molecular forces are of most important forces affecting fines migration. Investigating the impact of these types of forces requires information about electrical properties of constitutive component and Nano-sized solids. Surface potential is a well-known parameter, which can be used to measure aforementioned forces. The force balance among electrical, gravity, drag and buoyance forces tracing on a particle can be estimated using fluid properties and physical properties of reservoir such as surface potential, pore size distribution and fine size distribution. The task is to set these forces at conditions that fine migration does not take place. This paper investigates the impact of several parameters that could influence pertinent forces. Effect of ionic strength of flowing fluid is taken into account to evaluate Debye length that determines double layer forces. The impact of injection rate on a parameter named erosion number also studied. The results of this study show that how introducing salts and injection rate can affect stability of fines on their locations.

Electric Double-layer Forces between Dissimilarly Charged Planar Surfaces in Salt-free Solution

A theoretical study on the electric double-layer force between planar surfaces that may carry dissimilar constant charges or potential in a salt-free solution has been presented in this paper. The results show that the electric double-layer force is always repulsive for positively charged planar surfaces regardless of surface charge density (or potential) and separation; however, a long-range attraction is always existed between oppositely charged surfaces.

The quantitative description between zeta potential and fluorescent particle adsorption on Cu surface

The influence factor for polystyrene based fluorescent particles' adsorption on Cu surface in liquid environment was investigated. The fluorescent particles with a size of 100 nm were used as the adsorbing particle for avoiding the disturbance to the adsorption result. The contrast between the fluorescent image and SEM image showed that there was a one‐to‐one correspondence between the fluorescent spot and the particle. This revealed the method of counting the fluorescent spot to obtain the adsorbing particle result is accurate. Zeta potential and ionic strength would affect the value of electrical double layer force. And the electrical double layer force and Van der Waals force between particles and surface determined the behavior of particles when particles got close to Cu surface. Results showed that particle adsorption on Cu surface was linear to the multiply of zeta potential for particles and Cu surface. Also, the influence of ionic strength on fluorescent particle adsorption was investigated. Finally, the quantitative description between zeta potential, ionic strength and particle adsorption was given. Copyright © 2013 John Wiley & Sons, Ltd.

Stern potential and Debye length measurements in dilute ionic solutions with electrostatic force microscopy

We demonstrate the ability to measure Stern potential and Debye length in dilute ionic solution with atomic force microscopy. We develop an analytic expression for the second harmonic force component of the capacitive force in an ionic solution from the linearized Poisson–Boltzmann equation. This allows us to calibrate the AFM tip potential and, further, obtain the Stern potential of sample surfaces. In addition, the measured capacitive force is independent of van der Waals and double layer forces, thus providing a more accurate measure of Debye length.