Dependence of Colloidal Forces Between Bitumen and Silica on the Chain Lengths of Ammonium Surfactants

Effects of ammonium surfactants with different hydrocarbon chain lengths (C8, C12, C16, and C18) on the colloidal forces between bitumen and silica were studied by atomic force microscopy. The results showed that the chain length of the ammonium surfactants had a significant impact on both the long-range interaction and adhesion forces. With the addition of surfactants with relative short chains of C8 and C12 in the solutions, the long-range repulsive force decreased or even became strong attractive force, while it became repulsive again in solutions of surfactants with long chains of C16 and C18. It was further observed that addition of Ca²⁺ in various surfactants solutions would either depress or enhance the colloidal interactions based on the surfactant chain lengths. It was believed that variation of the interaction behaviors resulted from the mono-layer or bilayer adsorption of various surfactant molecules on the negatively charged surfaces of bitumen and silica, which affected the surface wettability and the surface charge characteristics and then greatly changed the colloidal interactions. The findings indicated that, to have a high bitumen recovery and good froth quality, the surfactant type and concentration of the di-valent metal ions in the oil sand processing slurry must be well considered.     

Dispersion of Colloidal Alumina using a Rhamnolipid Biosurfactant

Dispersability of colloidal alumina in water has been studied using a rhamnolipid containing biosurfactant. Zeta potential measurements revealed that the surface charge of alumina was altered due to adsorption of the biosurfactant and the iso‐electric‐point of alumina shifted from pH 9 to 6.3. Sedimentation tests indicated that the alumina suspension was completely dispersed for 3–5 hours in the presence of biosurfactant after which some settling was observed. Stability of the suspension in the time period studied was found to be independent of pH. Capillary suction time measurements showed that the alumina suspension was dispersed in the presence of the biosurfactant and varied with pH. Maximum dispersion is obtained in the pH range of 3.5–5 and 7–11 while a minimum is obtained around pH 6. This behavior is consistent with the changes in zeta potential in the presence of the biosurfactant and thus capillary suction time measurements appeared to be more reliable than the sedimentation tests. Optimization studies showed that about 60 mg/g of biosurfactant was necessary for best dispersion and dispersion could be done up to 40% solids. The application of a natural biosurfactant for dispersing colloidal alumina has been demonstrated.     

The existence and stability of bulk nanobubbles:a long-standing dispute on the experimentally observed mesoscopic inhomogeneities in aqueous solutions

In theory,nanobubbles can stably exist with a lifetime of microseconds at most,but numerous experimental observations demonstrate that nanobubbles in bulk solution can be stable from hours to weeks.Although various conjectures on the stability mechanism of bulk nanobubbles,such as the contaminant mechanism,skin mechanism,surface zeta potential mechanism,are proposed,there has not yet been a unified conclusion.Since bulk nanobubbles show great potential in a wide spectrum of applications and are relevant to a number of unsolved questions on cavitation and nucleation,the debate over their stability mechanisms has been active.In the past,extensive studies have been carried out to understand the mechanism of nanobubble stability,and important insights have already been provided.This paper will provide a brief overview of our current understanding of the unexpected stability of bulk nanobubbles.     

Distributions and analytic continuation of Dirichlet series

This is the second in a series of three papers; the other two are “Summation Formulas, from Poisson and Voronoi to the Present” [Progr. Math. 220 (2004) 419-440] and “Automorphic Distributions, L-functions, and Voronoi Summation for GL(3)” (preprint). The first paper is primarily expository, while the third proves a Voronoi-style summation formula for the coefficients of a cusp form on . The present paper contains the distributional machinery used in the third paper for rigorously deriving the summation formula, and also for the proof of the GL(3)×GL(1) converse theorem given in the third paper. The primary concept studied is a notion of the order of vanishing of a distribution along a closed submanifold. Applications are given to the analytic continuation of Riemann's zeta function, degree 1 and degree 2 L-functions, the converse theorem for GL(2), and a characterization of the classical Mellin transform/inversion relations on functions with specified singularities.     

Trace formula on the p-adic upper half-plane

This article aims at showing a p-adic analogue of Selberg's trace formula, which describes a duality between the spectrum of a Hilbert-Schmidt operator and the length of prime geodesics appearing in the p-adic upper half-plane associated with a hyperbolic discontinuous subgroup of . Then we construct Markov processes on the fundamental domain relative to such subgroups, to whose transition operators the trace formula applied and a p-adic analogue of prime geodesic theorem is proved.     

The Distribution of the Summatory Function of the Mobius Function

The summatory function of the Möbius function is denotedM(x). In this article we deduce conditional results concerningM(x) assuming the Riemann hypothesis and a conjecture of Gonekand Hejhal on the negative moments of the Riemann zeta function.Assuming these conjectures, we show that M(x), when appropriatelynormalized, possesses a limiting distribution, and also thata strong form of the weak Mertens conjecture is true. Finally,we speculate on the lower order of M(x) by studying the constructeddistribution function. 2000 Mathematics Subject Classification11M26, 11N56.     

Newton polyhedra, unstable faces and the poles of Igusa's local zeta function

In this paper we examine when the order of a pole of Igusa's local zeta function associated to a polynomial is smaller than ``expected'. We carry out this study in the case that is sufficiently non-degenerate with respect to its Newton polyhedron , and the main result of this paper is a proof of one of the conjectures of Denef and Sargos. Our technique consists in reducing our question about the polynomial to the same question about polynomials , where are faces of depending on the examined pole and is obtained from by throwing away all monomials of whose exponents do not belong to . Secondly, we obtain a formula for Igusa's local zeta function associated to a polynomial , with unstable, which shows that, in this case, the upperbound for the order of the examined pole is obviously smaller than ``expected'.

     

Explicit Lower bounds for residues at of Dedekind zeta functions and relative class numbers of CM-fields

Let be a given set of positive rational primes. Assume that the value of the Dedekind zeta function of a number field is less than or equal to zero at some real point in the range . We give explicit lower bounds on the residue at of this Dedekind zeta function which depend on , the absolute value of the discriminant of and the behavior in of the rational primes . Now, let be a real abelian number field and let be any real zero of the zeta function of . We give an upper bound on the residue at of which depends on , and the behavior in of the rational primes . By combining these two results, we obtain lower bounds for the relative class numbers of some normal CM-fields which depend on the behavior in of the rational primes . We will then show that these new lower bounds for relative class numbers are of paramount importance for solving, for example, the exponent-two class group problem for the non-normal quartic CM-fields. Finally, we will prove Brauer-Siegel-like results about the asymptotic behavior of relative class numbers of CM-fields.

     

Fast Computation of ζ(3) and of Some Special Integrals Using the Ramanujan Formula and Polylogarithms

The application of the Fast E-function Evaluation (FEE) method to fast calculation of the value of (3) and of some special integrals on the basis of the Ramanujan formula and its generalization is considered.This revised version was published online in October 2005 with corrections to the Cover Date.