Hydrodynamically-driven drug release during interstitial flow through hollow fibers implanted near lymphatics

Current drug delivery devices (DDD) are mainly based on the use of diffusion as the main transport process. Diffusion-driven processes can only achieve low release rate because diffusion is a slow process. This represents a serious obstacle in the realization of recent successes in the suppression of lymphatic metastasis and in the prevention of limb and organ transplant rejection. Surprisingly, it was overlooked that there is a more favorable drug release mode which can be achieved when a special DDD is implanted near lymphatics. This opportunity can be realized when the interstitial fluid flow penetrates a drug delivery device of proper design and allows such fluid to flow out of it. This design is based on hollow fibers loaded with drug and whose hydrodynamic permeability is much higher than that of the surrounding tissue. The latter is referred to as hollow fiber of high hydrodynamic permeability (HFHP). The interstitial flow easily penetrates the hollow fiber membrane as well as its lumen with a higher velocity than that in the adjacent tissue. The interstitial liquid stream entering the lumen becomes almost saturated with drug as it flows out of the HFHP. This is due to the drug powder dissolution in the lumens of HFHP which forms a strip of drug solution that crosses the interstitium and finally enters the lymphatics. This hydrodynamically-driven release (HDR) may exceed the concomitant diffusion-driven release (DDR) by one or even two orders of magnitude. The hydrodynamics of the two-compartment media is sufficient for developing the HDR theory which is detailed in this paper. Convective diffusion theory for two compartments (membrane of hollow fiber and adjacent tissue) is required for exact quantification when a small contribution of DDR to predominating HDR is present. Hence, modeling is important for HDR which would lead to establishing a new branch in physico-chemical hydrodynamics. The release rate achieved with the use of HFHP increases proportional to the number of hollow fibers in the fabric employed in drug delivery. Based on this contribution, it is now possible to simultaneously provide high release rates and long release durations, thus overcoming a fundamental limitation in drug delivery. Perhaps this breakthrough in long-term drug delivery has potential applications in targeting lymphatics and in treating cancer and cancer metastasis without causing the serious side effects of systemic drugs.

Outside-In Hemofiltration for Prolonged Operation without Clogging

Hemofiltration (HF) is used extensively for continuous renal replacement therapy, but long-term treatment is limited by thrombosis leading to fiber clogging. Maximum filter life is typically less than 20 hours. We have achieved for the first time continuous and consistent hemofiltration for more than 100 hours using outside-in hemofiltration with the blood flow into the inter-fiber space (IFS). Although thrombi do deposit in the IFS, they have minimal affect on the blood flow and filtrate flux due to the three-dimensional system of interconnected hydrodynamic flow channels in the IFS. Microscopic examination of sections of the fiber bundle showed that deposited thrombi have dimensions about the size of the gaps between the hollow fibers and remain isolated from each other. A simple mathematical model is developed to describe the effect of thrombus deposition on the fluid flow that accounts for the enhanced performance arising from the interconnected flow. The hydrodynamic advantage of outside-in HF decreases at low anticoagulant concentration due to the instability in the blood and the very high volume fraction of thrombi that deposit in the entrance zone of the filter. These results clearly demonstrate the significant potential advantages of using outside-in hemofiltration for long-term renal replacement therapy.

Convective diffusion of nanoparticles from the epithelial barrier toward regional lymph nodes

Drug delivery using nanoparticles as drug carriers has recently attracted the attention of many investigators. Targeted delivery of nanoparticles to the lymph nodes is especially important to prevent cancer metastasis or infection, and to diagnose disease stage. However, systemic injection of nanoparticles often results in organ toxicity because they reach and accumulate in all the lymph nodes in the body. An attractive strategy would be to deliver the drug-loaded nanoparticles to a subset of draining lymph nodes corresponding to a specific site or organ to minimize systemic toxicity. In this respect, mucosal delivery of nanoparticles to regional draining lymph nodes of a selected site creates a new opportunity to accomplish this task with minimal toxicity. One example is the delivery of nanoparticles from the vaginal lumen to draining lymph nodes to prevent the transmission of HIV in women. Other known examples include mucosal delivery of vaccines to induce immunity. In all cases, molecular and particle transport by means of diffusion and convective diffusion play a major role. The corresponding transport processes have common inherent regularities and are addressed in this review. Here we use nanoparticle delivery from the vaginal lumen to the lymph nodes as an example to address the many aspects of associated transport processes. In this case, nanoparticles penetrate the epithelial barrier and move through the interstitium (tissue) to the initial lymphatics until they finally reach the lymph nodes. Since the movement of interstitial liquid near the epithelial barrier is retarded, nanoparticle transport was found to take place through special foci present in the epithelium. Immediately after nanoparticles emerge from the foci, they move through the interstitium due to diffusion affected by convection (convective diffusion). Specifically, the convective transport of nanoparticles occurs due to their convection together with interstitial fluid through the interstitium toward the initial lymph capillaries. Afterwards, nanoparticles move together with the lymph flow along the initial lymph capillaries and then enter the afferent lymphatics and ultimately reach the lymph node. As the liquid moves through the interstitium toward the initial lymph capillaries due to the axial movement of lymph along the lymphatics, the theory for coupling between lymph flow and concomitant flow through the interstitium is developed to describe this general case. The developed theory is applied to interpret the large uptake of Qdots by lymph nodes during inflammation, which is induced by pre-treating mouse vagina with the surfactant Nonoxynol-9 prior to instilling the Qdots. Inflammation is viewed here to cause broadening of the pores within the interstitium with the concomitant formation of transport channels which function as conduits to transport the nanoparticles to the initial lymph capillaries. We introduced the term "effective channels" to denote those channels which interconnect with foci present in the epithelial barrier and which function to transport nanoparticles to initial lymph capillaries. The time of transport toward the lymph node, predicated by the theory, increases rapidly with increasing the distance y0 between the epithelial barrier and the initial lymph capillaries. Transport time is only a few hours, when y0 is small, about some R (where R is the initial lymph capillary radius), due to the predomination of a rather rapid convection in this case. This transport time to the lymph nodes may be tens of hours (or longer) when y0 is essentially larger and the slow diffusion controls the transport rate in a zone not far from the epithelial barrier, where convection is weak at large y0. Accounting for transport by diffusion only, which is mainly considered in many relevant publications, is not sufficient to explain our nanoparticle uptake kinetics because the possibility of fast transport due to convection is overlooked. Our systematic investigations have revealed that the information about the main transport conditions, namely, y0 and the pore broadening up to the dimension of the interstitial transport channels, is necessary to create the quantitative model of enhanced transport during inflammation with the use of the proposed model as a prerequisite. The modeling for convective diffusion of nanoparticles from the epithelial barrier to the lymph node has been mainly accomplished here, while the diffusion only scenario is accounted for in other studies. This first modeling is a semi-quantitative one. A more rigorous mathematical approach is almost impossible at this stage because the transport properties of the model are introduced here for the first time. These properties include: discovery of foci in the epithelium, formation of transport channels, definition of channels interconnecting with foci (effective foci and channels), generation of flow in the interstitium toward the initial lymph capillaries due to axial flow within afferent lymphatics, deformation of this flow due to hydrodynamic impermeability of the squamous layer with the formation of the hydrodynamic stagnation zone near the epithelial barrier, predomination of slow diffusion transport within the above zone, and predomination of fast convection of nanoparticles near the initial lymph capillaries.

Theory of effective drug release from medical implants based on the Higuchi model and physico-chemical hydrodynamics

Combining the approach of colloid transport with the generalized Higuchi theory of drug release and with the concept of minimum inhibitory concentration (MIC) known in microbiology, the theory of effective drug release from implants has been developed. Effective release of an antibiotic at a concentration above MIC is a necessary condition to achieve protection against infection from implants such as central catheters. The Higuchi theory in its present form is not predictive of the therapeutic effect from medical implants. The theory of effective release presented in this paper specifies two release modes, namely: one with therapeutic usefulness (effective release) and another without therapeutic effect. Therapeutic usefulness may be achieved when the antibiotic concentration, C_ti , on the implant surface kills the organisms of interest and prevents the formation and propagation of biofilm when C_ti exceeds the corresponding MIC of the released antibiotic compound. Currently, neither the Higuchi theory nor any other theory can provide such prediction. The present approach requires quantification of the antibiotic transport from the drug-polymer blend implant surface into the tissue and accounts for its coupling with drug diffusion inside the blend, a task that has not been developed in existing theories. Our solution to this task resulted in the derivation of an equation for the time of duration of effective release, T_e , which depends on MIC, the Higuchi invariant and the characteristics of convective diffusion within the tissue. The latter characteristics include: diffusivity D_ti and diffusion layer thickness δ which is controlled by the velocity of the interstitial fluid in tissue. A smaller D_ti is favorable because transport from the catheter surface is weaker, while a thinner diffusion layer is harmful because this transport is stronger. The influence of the tangential component of interstitial velocity in the tissue is especially harmful because the diffusion within the incision exit site (IES) will be extremely enhanced such that it may decrease C_ti to zero. The incorporation of convective diffusion into the theory of antibacterial protection by means of antibiotic release has revealed that physicochemical mechanisms predict the effectiveness of antibiotic-loaded catheters and defines the conditions necessary to achieve better protection by means of combining the level of catheter loading with antibiotics and the use of wound (IES) dressing.

The Long-term Release of Antibiotics From Monolithic Nonporous Polymer Implants for Use as Tympanostomy Tubes

A technology is elaborated for the fabrication of a novel tympanostomy tube (TT) from solidified polymer melts (Elvax and Polyurethane) and antibiotics (Ciprofloxacin and Usnic acid) for insertion into tympanic membrane (ear drum) according to the established surgical procedure. The long-term in vitro release kinetics of the antibiotics into liquid water has been assessed using standard methods. The measured kinetic curves revealed two stages of antibiotic release into the finite space. During the first stage (fast), the fast release rate is almost invariant and is determined by the diffusion through the steady diffusion layer formed due to solution agitation. In this first stage, the influence of the initial internal transport is weak because it takes place at negligibly small distance from interface and accordingly, at negligibly concentration drop. After the antibiotic concentration decreases within the much broader layer of matrix near interface, the internal transport becomes important. This manifests itself as the second stage in measured kinetics of release curves which is characterized by a gradual decrease in rate. The minimum inhibition concentrations of three antibiotics/antimicrobial compounds for four bacterial species were measured. The first stage of fast release from the polymer implant lasts 6 days at a polymer loading by Ciprofloxacin (0.03 g/cm(3)) and this was sufficient for preventing biofilm formation on the surface of the implant material. The measured kinetic curves of drug release showed more rapid decrease in the release rate compared to the Higuchi approximation. Comparison with existing theories, which account for the finite rate of drug dissolution, showed that this may explain the observed deviation from the diffusion-controlled Higuchi model. Large dimensions of drug particles and their aggregation retard the dissolution stage and consequently the release rate. Melt blending was found to cause the drug particle aggregation within polymer matrixes which was confirmed by microscopic reexamination of the polymer implant materials.

Surfactant accumulation within the top foam layer due to rupture of external foam films

The analysis of processes taking place in a steady pneumatic (dynamic) foam shows the possibility of different modes of surfactant accumulation within the top layers of bubbles due to rupture of external foam films. An increasing surfactant concentration within the top layers promotes the stabilisation of bubbles and the foam as a whole. Considering the balance of surfactant and water during the bursting of films it is possible to estimate the accumulated surfactant loss caused by a downwards flow through the Plateau borders of the subsurface bubble layer. This effect depends on the particular conditions, especially on the surfactant activity and concentration of the surfactant, water volume fraction in the foam and size of foam bubbles. The process of surfactant accumulation in the top foam bubble layer can be complicated due to the removal of part of the accumulated surfactant through transport with droplets spread out during bubble bursting.

Development in modeling submicron particle formation in two phases flow of solvent-supercritical antisolvent emulsion

The use of a supercritical Solvent (S)-Antisolvent (AS) process (SAS) for fine particle production is finding widespread industrial applications. The perfection of this technology requires insight into many basic laws of interface and colloid science. In SAS the solute is dissolved in an organic solvent and the solution is sprayed into a near critical AS stream. SAS is a complex process involving the interaction of jet hydrodynamics, droplet formation, mass transfer, phase equilibrium, intra-droplet nucleation, and microcrystal growth. A complete description would have to take into account all of these processes; however, such a model is not currently available. In the two-phase flow of an S/AS emulsion, S diffuses from droplets into AS, while AS dissolves inside the S droplets. S replacement by AS (Supercritical CO2) causes solute supersaturation in the droplets. When it occurs near the critical point of the S/AS emulsion (80 bar, 32 degrees C), intra-droplet nucleation and precipitation of the solute occurs. The possibility of solute particle production and the particle size is controlled by the droplet size and by the interrelationship between three time scales. These are the droplet mass transfer time tau N, the nucleation time tau N, i.e., the time necessary for one particle nucleus to form in one droplet, and the droplet residence in the supersaturated stream tau res. An approximate analytical theory for intra-droplet nucleation is developed and the conditions necessary for nanoparticle production are established. The smaller the droplet dimension and the lower the solute concentration, the smaller the particle dimension that is obtained. The recent success in membrane emulsifying may be used for the production of micron-sized droplets. After the AS stream is saturated with S due to partial dissolution of the droplets, a quasi-equilibrium between the droplets and AS stream occurs and a steady and uniform zone with intra-droplet supersaturation is formed downstream. But tau res>tau N is necessary for one nucleus formation per droplet, i.e., tau res has to be much longer than that reported in the literature (10(-3) s), because tau N increases with decreasing droplet dimension. Accordingly, a long residence time version of the SAS process (tau res approximately 1 s) is necessary. However, a long tau res is problematic because of micro-droplet turbulent coagulation. Since an increase in tau res is difficult, a decrease in tau N by means of an increase in S becomes significant. This is achieved by using a phenomenon which we call supersaturation of the second kind S2 In the literature attention is paid only to a decrease in the equilibrium solute concentration, when solvent and antisolvent are mixed. However, S2 occurs due to an actual increase in concentration of solute within the droplets as they shrink due to S dissolution. The smaller the ratio of solvent to antisolvent flow rate, the larger the droplet shrinkage and the higher the S2 achieved. Due to large S2, nanoparticle production becomes possible even for solutes with high surface tension sigma and large molecular volume V o, while earlier it was impossible because of the exponential increase of tau N with increasing V o and sigma. Combining a long tau res and variable and precisely controllable supersaturation, which is uniform in space and enhanced due to S2, creates an opportunity for standardization of characterizing different solutes through their tau N, which is the key solute property affecting nanoparticle production by SAS.

Gravity as a factor of aggregative stability and coagulation

Gravity is a potential factor of aggregative stability and/or coagulation for any heterogeneous system having a density contrast between the dispersed phase and its dispersion medium. However, gravity becomes comparable to other stability factors only when the particle size becomes large enough. Since the particle size may grow in time due to various other instabilities, even nano-systems may eventually become susceptible to gravity. There have been many attempts in the last century to incorporate gravity in the overall theory of aggregative stability, but the relevant papers are scattered over a wide variety of journals, some of which are very obscure. Reviews on this subject in modern handbooks are scarce and inadequate. No review describes the role of gravity at all three levels introduced by DLVO theory for characterizing aggregative stability, namely: particle pair interaction, collision frequency and population balance equation. Furthermore, the modern tendency towards numerical solutions overshadows existing analytical solutions. We present a consistent review at each DLVO level. First we describe the role of gravity in particle pair interactions, including both available analytical solutions as well as numerical stability diagrams. Next we discuss a number of works on collision frequency, including works for both charged and non-charged particles. Finally, we present analytical solutions of the population balance equation that takes gravity into account and then compare these analytical solutions with numerical solutions. In addition to the traditional aggregate model we also discuss work on a fractal model and its relevance to gravity controlled stability. Finally, we discuss many experimental works and their relationship to particular theoretical predictions.

Electrophoresis of soft particles at high electrolyte concentrations: An interpretation by the Henry theory

The existence of electrophoretic mobility at high electrolyte concentrations defines a remarkable peculiarity in the electrosurface characteristics of soft particles. According to Ohshima [H. Ohshima, Colloids Surf. 103 (1995) 249], this effect is caused by the electroosmotic flow within the soft particle shell. An explanation supporting Ohshima's conclusion can be derived from classic electrokinetic theories. Based on the Henry theory [D.C. Henry, Proc. R. Soc. London Ser. A 133 (1931) 106], we demonstrate that the electrophoretic mobility of soft particles does not disappear at decinormal concentration.

Characterization of fractal particles using acoustics, electroacoustics, light scattering, image analysis, and conductivity

Fractals are aggregates of primary particles organized with a certain symmetry defined essentially by one parameter-a fractal dimension. We have developed a model for the interpretation of acoustic data with respect to particle structure in aggregated fractal particles. We apply this model to the characterization of various properties of a fumed silica, being but one example of a fractal structure. Importantly, our model assumes that there is no liquid flow within the aggregates (no advection). For fractal dimensions of less than 2.5, we find that the size and density of aggregates, computed from the measured acoustic attenuation spectra, are quite independent of the assumed fractal dimension. This aggregate size agrees well with light-scattering measurements. We applied this model to the interpretation of electroacoustic data as well. A combination of electroacoustic and conductivity measurements yields sufficient data for comparing the fractal model of the particle organization with a simple model of the separate primary particles. Conductivity measurements provide information on particle surface conductivity reflected in terms of the Dukhin number (Du). Supporting information for the zeta potential and Du can also be provided by electroacoustic measurements assuming thin double-layer theory. In comparing values of Du from these two measurements, we find that the model of separate solid particles provides much more consistent results than a fractal model with zero advection. To explain this, we first need to explain an apparent contradiction in the acoustic and electroacoustic data for porous particles. Although not important for interpreting acoustic data, advection within the aggregate does turn out to be essential for interpreting electrokinetic and electroacoustic phenomena in dispersions of porous particles.

Surface Conductivity Reveals Counterion Condensation within Grafted Polyelectrolyte Layers

Surface conductivity (SC) has been demonstrated to be a valuable parameter for the characterization of surface-bound polyelectrolyte layers (PLs). The measurement of the SC in dependence of the pH and solution concentration yields information about the Donnan potential, PsiD, the intrinsic charge, the potential of the PL electrolyte interface, Psi0, the pK of the ionizable groups within the PLs, and the concentration of segments, n. We discuss herein that SC measurements may additionally provide information about counterion condensation. The mobility of the counterions within grafted poly(acrylic acid) (PAA) layers was estimated from the density of COOH groups and SC data to be only 14% of that of free ions (Zimmermann, et al. Langmuir 2005, 21, 5108). In view of this large deviation and the limited sterical constraints within the brushes, we conclude that the number of freely moving counterions is decreased due to counterion condensation. This interpretation agrees well with the measurement of the osmotic pressure for PAA solution (Boisvert, et al. Polymer 2002, 43, 141), which can be exclusively attributed to the remaining mobile counterions of the polyelectrolyte.

Electrokinetic fingerprinting of grafted polyelectrolyte layers--a theoretical approach

Electrokinetic fingerprinting (EF) was introduced by Marlow and Rowell [Marlow BJ, Rowel RL. Langmuir 1990;6:1088] for the comprehensive characterization of charged particle surfaces. Afterwards, EF was applied by many groups for the characterization of "hard" (i.e. non-swelling) surfaces. However, the advantages of EF could not yet utilized for the characterization of grafted polyelectrolyte layers (PL) since the theoretical background was not yet elaborated. A theory for the characterization of PL at complete dissociation of the functional groups was developed by Ohshima [Adv Colloid Interface Sci 1995;62:189] and later extended by Dukhin et al. [Dukhin S, Zimmermann R, Werner C. J Colloid Interface Sci 2005;286:761] for any degree of dissociation. Further progress in the characterization of soft surfaces may be achieved by combining EF and surface conductivity (SC) measurements. Both theory and experiment demonstrate that integrated measurements of SC and apparent zeta potential zeta(a) in broad ranges of pH and ionic strength provide information about Donnan potential Psi(D), surface charge, pK and surface potential Psi(0), while the interpretation is more uncertain, when only zeta(a) is measured. This advanced method of PL characterization is established for PL grafted on flat surfaces. When PL are formed on spherical particles, the SC may be measured by means of conductometry and/or dielectric spectroscopy. However, the current theories can only be applied within a rather narrow range of the practically relevant conditions. To overcome this limitation, an unified approach to the theory of electrophoresis for spherical particles with grafted PL was elaborated taking into account the existence of two different electrokinetic models for soft surfaces. While one model is focused on hydrodynamic permeability of soft surface and disregards surface current, another model considers the surface current and disregards electrokinetic water transport within the soft surface layer. Unification became possible through generalization of the capillary osmosis theory over soft surfaces.

Electrostatic Switching of Biopolymer Layers. Insights from Combined Electrokinetics and Reflectometric Interference

Structural integrity and functional characteristics of biomacromolecules are largely defined by electrostatic forces between ionized moieties, which are often altered at interfaces. Unraveling these changes requires access to charge state and structure of surface-confined biopolymers in aqueous environments. We therefore combined electrokinetic measurements of interfacial electrical potentials with the simultaneous determination of the optical layer thickness by reflectometric interference spectroscopy. Two examples are summarized to demonstrate the resulting options: The pH-switching of grafted poly(l-glutamic acid) layers caused by dissociation-dependent helix-coil transitions was studied; potential distribution and ion mobility within the grafted polyelectrolyte were unraveled using an new theoretical model for the charging of polyelectrolyte layers. The charge-driven modulation of biopolymers at interfaces was furthermore analyzed in the adsorption of fibronectin onto polymer substrates with varied charge density; the results permit us to reach a conclusion about the relevance of electrostatic matching for orientation and anchorage of the protein. Altogether, the introduced methodology was found suitable to follow the electrosurface characteristics of biomacromolecules in situ.

Electrokinetic phenomena at grafted polyelectrolyte layers

During the last decades the electrokinetic theory of Smoluchowski (Z. Phys. Chem. 92 (1918) 129) was extended to be applicable for soft surfaces (grafted polyelectrolyte layers (PL), biological and artificial membranes, etc.) by either using the Debye approximation or numerical solutions. In the theory of Ohshima (Colloids Surf. A 103 (1995) 249) the nonlinearized Poisson-Boltzmann (PB) equation for thick and uniform PL is solved analytically and a general hydrodynamic equation is derived in an integral form. These advantages in the theory of Ohshima provided a base for the further development of a generalized electrokinetic theory for soft surfaces. In his theory the final equation for the electroosmotic (electrophoretic) velocity is specified for the case of the complete dissociation of ionic sites within PL. Accordingly, the equation may be used only if the difference between pK and pH is very large. However, it turned out that an analytical solution of the nonlinearized PB equation for thick PL is possible for any degree of dissociation. This was achieved using the approximation of excluded coions if the absolute value of the reduced Donnan potential is larger than 2 and due to the simplification in the case of weak dissociation, when the absolute value of the reduced Donnan potential is less than 2. Combining this generalized double layer (DL) theory for PL and the theory of Ohshima enables to obtain an analytical equation for electroosmosis for the general case of any degree of dissociation. This equation creates for the first time a theoretical base for the interpretation of electrokinetic fingerprinting (EF) for the characterization of soft surfaces.

Aperiodic capillary electrophoresis method using an alternating current electric field for separation of macromolecules

Switching from direct current (DC) to alternating current (AC) electric fields has provided substantial improvements in various instrument techniques that use electric fields for manipulating with various liquid-based systems. For example, AC fields are now used in both light scattering and electroacoustic instruments for measuring xi-potential, largely replacing more traditional microelectrophoresis techniques that use DC fields. In this paper, we suggest a novel way to make a similar transition in the area of separation techniques, capillary electrophoresis (CE) in particular. Dielectrophoresis is one well-known separation effect in which a drifting motion of particles is produced in a "spatially nonhomogeneous" AC electric field. However, there is another field effect that also causes a similar drift of particles. Instead of a "spatially nonhomogeneous" field, this method relies on a "temporally nonhomogeneous" field, normally referred to as "aperiodic electrophoresis". Despite a number of recently published experimental and theoretical papers describing this effect, it is less well-known than dielectrophoresis. We present a short overview of some of the relevant papers. We point out for the first time the idea that "aperiodic electrophoresis" might be useful for separation of macromolecules. We suggest several new mechanisms that could induce this effect in a sufficiently strong AC electric field. This effect can be used as a basis for a new separation method having several important advantages over traditional CE. We present a simple scheme as an example illustrating this new method.

Intrinsic charge and Donnan potentials of grafted polyelectrolyte layers determined by surface conductivity data

In order to characterize grafted polyelectrolyte layers based on electrokinetic measurements a theory of the surface conductivity Ksigma was developed, starting from the model of thick polyelectrolyte layers with uniform segment distribution and dissociable groups with an unknown pK value. According to this model the inner part of the polyelectrolyte layer adjacent to the substrate is considered to be isopotential while the potential decay occurs in a zone near the solution side of the layer. A simple equation for the Donnan potential psiD as a function of pH, pK, electrolyte concentration C0, and volume charge density rho was obtained. In the derived equation Ksigma is directly related to psiD while the other terms have less influence on the magnitude of Ksigma and can be accounted for in a second approximation using psiD as determined from the measured Ksigma. Evaluation of the suggested model indicates that Ksigma measurements provide an effective method to characterize polyelectrolyte layers by analyzing the dependence of psiD on pH and C0: The magnitude of Ksigma yields information about the surface charge at complete dissociation of the ionizable groups. The dependence of Ksigma on pH and C0 can be used for the determination of the pK value of the dissociating functions and the segment volume fraction of the polyelectrolyte can be estimated using the measured value of rho.

Electrophoresis of solid particles at large Peclet numbers

A theory of concentration polarization of a thin electrical double layer (DL) on a spherical particle is developed for the regime of large Peclet numbers which is realized in strong electric fields. In this regime, the concentration field arising outside DL is estimated under influence of diffusion and convection. According to the theory developed, polarization of DL at large Peclet numbers causes a change in the Stern potential, the formation of a dipole moment and the long-range potential. The diffuse layer deviates strongly from spherical symmetry and electroneutrality, and the screen of the surface charge is provided not only by the diffuse atmosphere but also by the charge induced in the convective-diffusion layer. The effect of electric field on the induced charge gives rise to the additional electroosmotic slip, that was called "secondary electroosmosis". Thus, a nonlinear additional term for the Smoluchowski formula of electrophoretic velocity is based on the changes of zeta-potential and on the secondary electroosmotic slip. The comparison of theory with experimental results revealed considerable fitting.

Wetting film stability and flotation kinetics

Single bubble experiments performed with different size fractions of quartz particles and different, but known, contact angles revealed two modes of flotation dynamics in superclean water. (1.) A monotonic increase of collection efficiency Ecoll with increasing particle size was observed at high particle hydrophobicity and, correspondingly, a low wetting film stability (WFS). (2.) At low particle hydrophobicity and, correspondingly, high WFS, an extreme dependence of Ecoll on particle size was observed. The use of superclean water in our experiments prevented the retardation of bubble surface movement caused by surfactants or other impurities that is usual for other investigations and where particle-bubble inertial hydrodynamic interactions are suppressed. In the present study the free movement of the bubble surface enhances particle-bubble inertial interaction, creating conditions for different flotation modes, dependent on WFS. At the instant of inertial impact, a particle deforms the bubble surface, which may cause its rebound. Where the stability of the thin water film, formed between opposing surfaces of a bubble and a particle, is low, its rupture is accompanied with three phase contact line extension and contact angle formation before rebound. This prevents rebound, i.e. the first collision is accompanied by attachment. A high WFS prevents rupture during an impact. As a result, a contact angle does not arise and rebound is not prevented. However, rebound is accompanied by a second collision, the kinetic energy of which is smaller and can cause attachment at repetitive collision. These qualitative considerations are confirmed by the model quantification and comparison with measured Ecoll. For the first time the Sutherland equation (SE) for Ecoll is confirmed by experiment for smaller particle sizes and, correspondingly, very small Stokes numbers. The larger the particle size, the larger is the measured deviation from the SE. The SE is generalized, accounting for the centrifugal force, pressing hydrodynamic force and drainage in the low WFS case and, correspondingly, attachment occurs at first collision or during sliding. The derived generalized Sutherland equation (GSE) describes experimental data at low WFS. However, its application without account for possible rebound does not explain the measured extreme dependence in the case of high WFS. The theory for drainage during particle impact and the beginning of rebound enables conditions for either attachment or rebound in terms of the normal component of the impact velocity and the critical film thickness to be derived. Combining this condition with the GSE allowed the equation for Ecoll to be derived, accounting for attachment area shrinkage and attachment during a repetitive collision. This equation predicts the extreme dependence. Thus the WFS determines the modes of flotation dynamics and, in turn, probably affects the mechanisms, which control the flotation domain. At low WFS its upper boundary is controlled by the stability of the particle-bubble aggregate. At high WFS the upper boundary can be controlled by rebound because the latter reduces the attachment efficiency by a factor of 30 or more even with repetitive collision.

Effect of the Nonstationary Viscous Flow in the Capillary on Oscillating Bubble and Oscillating Drop Measurements

The dynamic behavior of a bubble or drop oscillating at the tip of a capillary immersed in a surfactant solution is considered. The pressure variation in the cell and the nonstationary flow in the capillary are taken into account. The amplitude- and phase-frequency characteristics of the system are obtained, which contain information about the relaxation processes at the interface and in the bulk phases. Their dependency on the system geometry, the bulk properties of contacting media, and the viscoelastic properties of the interface is analyzed. Copyright 2000 Academic Press.

Bubble Oscillations in a Closed Cell

A theoretical analysis is given to describe the behavior of an oscillating bubble in a closed measuring cell taking into account the finite liquid compressibility and the cell deformation. The results show that the behavior of a closed liquid cell can differ significantly from that of open cells. For example, under the same conditions two stable meniscus positions can be obtained in a closed cell. In a closed cell a meniscus larger than a hemisphere can be stable even when the gas compartment is open, while in an open cell such a meniscus is always unstable. For closed cells the meniscus can jump between the two equilibrium positions either randomly or under the influence of regular factors, such as external pressure, temperature, and surface tension changes. Relationships are obtained for the description of the pressure response on external harmonic perturbations which make it possible to determine the complex dilatational elasticity as a function of frequency. It is shown that the measured signal can depend on the cell properties, which should be taken into account in the interpretation of experimental data. Copyright 2000 Academic Press.

Lifetime Calculations Relative to Maximum Bubble Pressure Measurements

The theoretical description of maximum bubble pressure experiments needs to consider inertial properties of the gas and liquid. On the basis of an analysis of the time-dependent pressure gradient inside the capillary, bubble lifetime and bubble deadtime are estimated. Numerical calculations of the derived model equations yield different importent dependencies which allow us to better understand bubble pressure experiments at high bubble frequencies: gas flow velocity as function of time, bubble radius as function of time, pressure drop within the capillary as function of time, and bubble lifetime as function of the initial gas velocity. Copyright 1998 Academic Press. Copyright 1998Academic Press