An experimental study of liquid bridges between spheres in a gravitational field

The approximate theory proposed in reference [1] for viscoelastic layered composites is appraised by applying it to a transient wave propagation problem. The problem involves a viscoelastic slab subjected at one end to a dynamic pressure which has either step or trapezoidal variation in time while its other end is kept fixed. The faces of the slab are parallel to the layering. For the case in which the composite material is elastic, which can be obtained from viscoelastic case when viscous terms vanish, the wave profiles for normal stress and particle velocity are determined by using exact and approximate theories, and they are compared. It is found that even the lowest order approximate theory is capable of predicting the essential dynamic characteristics of the layered composite correctly. Further, the influence of the viscosity on wave profiles is studied by using the approximate theory. For the time integration of the approximate equations a numerical algorithm based on FFT is employed.Publisher's Versio

Liquid bridges between spheres in a gravitational field

A theoretical study has been made of the properties of a liquid bridge between spheres of equal and unequal radii taking into account the effect of gravity on the meniscus shape and capillary attractions. The interfacial shape of the bridge is obtained by a numerical solution of the Young-Laplace equation employing the Runge-Kutta method for a given sphere pair, liquid bridge volume, and contact angle. The capillary force, sphere separation, minimum neck diameter, and filling angle of the liquid on both spheres are calculated numerically for interfacial shapes which exhibit the minimum neck diameter. The equal bridge volume problem at different sphere separations for a given set of spheres is solved with the two point boundary-value condition which must be satisfied on the sphere surfaces. This new solution, which takes into consideration gravitational disortion, enables large spheres to be used in experimental studies, and permits accurate measurements of the bridge volumes and the maximum amount of liquid that can be deposited between the spheres in a given system. It is found that the capillary attraction and maximum liquid bridge volume increases as the contact angle decreases and, also, as the radius of the bottom sphere increases. The effects that changing the bridge volume, sphere radii, and contact angle have on the capillary force, the maximum sphere separation, and other factors affecting the system are investigated.Publisher's Versio

Monitoring Of Poly(ethylene Oxide) Entanglement

Polyethylene Oxide (PEO) is an effective flocculant in highly contaminated papermaking furnishes and therefore it is commonly used as a retention aid in newsprint manufacture. However, a decrease in PEO fines retention efficiency with shear and time has been reported which can be ascribed to the disentanglement of not well-dispersed PEO. In this work, a sensor for monitoring PEO entanglement has been used, the principle of which is based on the measurement of the pressure drop created when passing a PEO solution through a narrow capillary. It has been found that, for the capillary geometries used, for freshly-dissolved PEO the main contribution to the overall pressure drop is due to the contraction and expansion of PEO entanglements at the entrance and exit of the capillary, and that the friction in the capillary plays a minor role. On the other hand, for well-dissolved PEO, because of the absence of PEO entanglements, loss of pressure is mainly due to friction.A9196Lawrence, A., Polverari, M., Levesque, B., Francis, W., Effects of system closure on retention-and drainage-aid performance in TMP newsprint manufacture (1999) TAPPI Journal, 82 (4), pp. 188-195Polverari, M., Allen, L., Sitholé, B., Effects of system closure on retention and drainage aid performance in TMP newsprint manufacture - Part II (2001) TAPPI Journal, 84 (3), p. 56Van de Ven, T.G.M., Mechanism of fines and filler retention with PEO/cofactor dual retention aid system (1997) JPPS, 23 (9), pp. J447-J451Carignan, A., Gamier, G., Van de Ven, T.G.M., The flocculation of fines by PEO/cofactor retention aid system (1998) JPPS, 24 (3), pp. 94-99Guner, A., Guven, O., Molecular association in aqueous solutions of high molecular weight poly(ethylene oxide) (1978) Makromol. Chem., 179, pp. 2789-2791Polvelari, M., Van de Ven, T.G.M., Dilute aqueous poly(ethylene oxide) solutions: Clusters and single molecules in thermodynamic equilibrium (1996) J. Phys. Chem., 100, pp. 13687-13695Derek, L.H., Boualem, H., Steven, R.K., Clustering of poly(ethylene oxide) in water revisited (2003) Journal of Polymer Science: Part B: Polymer Physics, 41, pp. 135-138Kratochvil, D., Alince, B., Van de Ven, T.G.M., Flocculation of clay particles with poorly and well-dissolved polyethylene oxide (1999) JPPS, 25 (9), pp. 331-335Abdallah, M., (2002) The Role of Polymer Entanglements in Polyethylene Oxide (PEO) Induced Fines Flocculation, , PhD Thesis, Department of Chemical Engineering, McGill UniversityBednar, F., Périn-Levasseur, Z., Van de Ven, T.G.M., Paris, J., Polyethylene oxide disentanglement (2003) Proceed, of 89th Ann. Meet., pp. 376-380. , Pulp and Paper Technical Association of Canada, Montreal, QC, Canada, Jan. 27-30, 2003McCabe, W.L., Smith, J.C., Harriott, P., (1993) Unit Operations in Chemical Engineering, Fifth Edition, , McGraw-HillBednar, F., Abdallah, M., Périn-Levasseur, Z., Van de Ven, T.G.M., Paris, J., Experimental determination of polyethylene oxide disentanglement (2002) Proceed of Congrès Francophone du Papier, pp. 85-88. , in French, Quebec, QC, Canada, May 29-31, 200

Exploration of driving mechanisms of equilibrium boron isotope fractionation in tourmaline group minerals and fluid: A density functional theory study

The equilibrium boron isotope fractionations (α3–4, Δ11B(Tur-fluid)) between tourmaline mineral groups and fluids at 0.5 GPa, 600–1000 K are investigated using density functional theory calculations. The first solvent shell controls boron isotope fractionation in solution, where the β values of both H3BO3 and B(OH)4− decrease with increasing numbers of hydrogen bonds. In supercritical fluids, the weakening of hydrogen bonds and the diversity in configurations of hydrated boron species both contribute to variations in the vibrational frequencies. The 1000lnαTur-fluid value increases with increasing Mg/(Fe+Mg) ratios in the dravite-schorl solid solution series. This effect, together with the crystallization sequence predicted from the Gibbs free energies of tourmaline formation, accounts well for the association of boron isotope and chemical zonation observed in zoned tourmaline grains. The dependence of boron isotope fractionation on the BO bond length in tourmaline group minerals reflects the changes in relevant molar volumes caused by differences in the mass and charge of the atoms occupying the X, Y, and Z sites of tourmalines. This study suggests that the chemical composition of the tourmaline plays an important role in controlling the boron isotope composition in tourmalines crystallized from hydrothermal systems

EFFECT OF MIXING CONDITIONS ON FLOCCULATION KINETICS OF WASTEWATERS CONTAINING PROTEINS AND OTHER BIOLOGICAL COMPOUNDS USING FIBROUS MATERIALS AND POLYELECTROLYTES

The application of a combined system of a polyelectrolyte, carboxymethyl cellulose (CMC), and highly fibrillated fibrous materials, cellulose triacetate fibrets (CTF), for the recovery of proteins and other biological compounds from model and actual biological systems has been demonstrated . In the present work, reaction batches were scaled-up to a one-liter agitated vessel, with a standard configuration. The effect of mixing conditions on the adsorption and flocculation process was studied. It was observed that flocculation time was very fast, occurring within the period of polymer addition. Long term shearing did not result in floc breakage and the values of percentage light transmission and protein concentration of the final filtrate remained the same during the incubation period. Increasing the shear rate resulted in improved process efficiency, up to an optimum value, above which performance was poorer. Perikinetic and orthokinetic rate parameters were calculated and results analyzed in view of these parameters