Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

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.     

Electrokinetic effects of adsorbed neutral polymers

On the basis of a previously developed hydrodynamic model for adsorbed polymers the charge flow along a charged interface with adsorbed (uncharged) polymer is calculated. An effective electrokinetic layer thickness is defined and its dependence on the characteristics of the adsorbed polymer and the ionic strength is studied. It is found that tails are very important for the hydrodynamic effects considered because they effectively screen the solvent flow from inner parts of the absorbed layer. The electrokinetic layer thickness increases with decreasing ionic strength, and tends to a limit equal to the hydrodynamic thickness at very low ionic strength.     

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.     

Heterocoagulation of Hydrophobic Particle and Bubble during Microflotation

The laws of the interaction between a gas bubble and a hydrophobic solid particle were studied. The range of the system parameters that can ensure the heterocoagulation of the particle and the bubble was determined.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

On the theory of adsorption kinetics of ionic surfactants at fluid interfaces

The kinetic equation to describe the adsorption process of ionic surfactants (derived in part 1) will be solved numerically. The results show the effect of parameters such as ion valencyz, thickness of theDL x ^–1, and surfactant parameters_eq,K, andK _ads on the adsorption process. The results can be used to decide whether the model can explain experimental data on charged surfactant molecules or not.Nomenclature c concentration - c_e bulk concentration in equilibrium - C =c/c _e dimensionless concentration - D diffusion coefficient - e proton charge - F Faraday's constant - f ₀ =e/kTdimensionless potential - k Bolzmann's constant - K _ads rate constant of adsorption - K _des rate constant of desorption - K(f ₀) coefficient of electrostatic deceleration - K = _eq /c _e Henry's constant - R gas law constant - t time - T absolute temperature - z electrovalence - ₀ adsorption of ions - _eq equilibrium value of _o - = ₀/ _eq dimensionless adsorption - , constants - dielectric constants - x Debye-Hückel reciprocal distance - =Dt/K ² dimensionless time - electric potential     

Interaction of the mu-opioid receptor with GPR177 (Wntless) inhibits Wnt secretion: potential implications for opioid dependence

Background  

Opioid agonist drugs produce analgesia. However, long-term exposure to opioid agonists may lead to opioid dependence. The analgesic and addictive properties of opioid agonist drugs are mediated primarily via the mu-opioid receptor (MOR). Opioid agonists appear to alter neuronal morphology in key brain regions implicated in the development of opioid dependence. However, the precise role of the MOR in the development of these neuronal alterations remains elusive. We hypothesize that identifying and characterizing novel MOR interacting proteins (MORIPs) may help to elucidate the underlying mechanisms involved in the development of opioid dependence.     

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.