Fractal Characterization of Silica Sol Prepared by the Sol-Gel Method: From the Sol Formation to the Flocculation Process

The fractal characterization of silica particles prepared by the sol-gel method was obtained; from the beginning of the sol-gel synthesis to the aggregation process of these particles by adding metal ions in solution, the fractal dimension was determined. At the beginning of the sol-gel process, unstable structures were formed due, essentially, to the auto-catalytic nature of the sol-gel condensation reactions; these particles are fractal structures with a fractal exponent corresponding to a reaction limited aggregation regime. As the time proceeds, the reactants are consumed approaching the system to equilibrium, stabilizing the size of the silica particles. The silica sol can be flocculated by adding metal ions in solution. The fractal exponent for the aggregation process was determined, obtaining a value corresponding to a diffusion limited aggregation regime.     

Engineering a Small HOMO–LUMO Gap and Intramolecular C−H Borylation by Diborene/Anthracene Orbital Intercalation

The diborene 1 was synthesized by reduction of a mixture of 1,2-di-9-anthryl-1,2-dibromodiborane(4) ( 6 ) and trimethylphosphine with potassium graphite. The X-ray structure of 1 shows the two anthryl rings to be parallel and their π(C₁₄) systems perpendicular to the diborene π(B=B) system. This twisted conformation allows for intercalation of the relatively high-lying π(B=B) orbital and the low-lying π* orbital of the anthryl moiety with no significant conjugation, resulting in a small HOMO–LUMO gap (HLG) and ultimately a C−H borylation of the anthryl unit. The HLG of 1 was estimated to be 1.57 eV from the onset of the long wavelength band in its UV/Vis absorption spectrum (THF, λ_onset=788 nm). The oxidation of 1 with elemental selenium afforded diboraselenirane 8 in quantitative yield. By oxidative abstraction of one phosphine ligand by another equivalent of elemental selenium, the B−B and C¹−H bonds of 8 were cleaved to give the cyclic 1,9-diborylanthracene 9 .     

Shear rheometry and visualization of glass fiber suspensions

The nonlinear rheological behavior of short glass fiber suspensions has been investigated in this work by rotational rheometry and flow visualization. A Newtonian and a Boger fluid (BF) were used as suspending media. The suspensions exhibited shear thinning in the semidilute regime and weaker shear thinning in the transition to the concentrated one. Normal stresses and relative viscosity were higher for the BF suspensions than for the Newtonian ones presumably due to enhanced hydrodynamic interactions resulting from BF elasticity. In addition, relative viscosity of the suspensions increased rapidly with fiber content, suggesting that the rheological behavior in the concentrated regime is dominated by mechanical contacts between fibers. Visualization of individual fibers and their interactions under flow allowed the detection of aggregates, which arise from adhesive contacts. The orientation states of the fibers were quantified by a second order tensor and fast Fourier transforms of the flow field images. Fully oriented states occurred for shear rates around 20 s^− 1. Finally, the energy required to orient the fibers was higher in step forward than in reversal flow experiments due to a change in the spatial distribution of fibers, from isotropic to planar oriented, during the forward experiments.     

Rheo-PIV analysis of the slip flow of a metallocene linear low-density polyethylene melt

The continuous extrusion of a metallocene linear low-density polyethylene through a transparent capillary die with and without slip was analyzed in this work by rheometrical measurements and particle image velocimetry (PIV). For this reason, a comparison was made between the rheological behaviors of the pure polymer and blended with a small amount of fluoropolymer polymer processing additive. Very good agreement was found between rheometrical and PIV measurements. The pure polymer exhibited stick-slip instabilities with nonhomogeneous slip at the die wall, whereas the blend showed stable flow. The slip velocity was measured directly from the velocity profiles and was negligible for the pure polymer before the stick-slip but increased monotonously as a function of the shear stress for the blend. The flow curves and the slip velocity as a function of the shear stress deviated from a power law and were well fitted by continuous “kink” functions. Comparison of PIV data with rheometrical ones permitted a direct proof of the basic assumption of the Mooney theory. Finally, the analysis of the velocity profiles showed that there is a maximum in the contribution of slip to the average fluid velocity, which is interpreted as the impossibility for the velocity profile to become plug like in the presence of shear thinning.     

Aggregation of a Distributed Source in Morphogen Gradient Formation

In the development of a biological entity, ligands (such as Decapentaplegic (Dpp) along the anterior–posterior axis of the Drosophila wing imaginal disc) are synthesized at a localized source and transported away from the source for binding with cell surface receptors to form concentration gradients of ligand–receptor complexes for cell signaling. Generally speaking, activities such as diffusion and reversible binding with degradable receptors also take place in the region of ligand production. The effects of such morphogen activities in the region of localized distributed ligand source on the ligand–receptor concentration gradient in the entire biological entity have been modeled and analyzed as System F in [ 1 ]. In this paper, we deduce from System F, a related end source model (System A) in which the effects of the distributed ligand source is replaced by an idealized point stimulus at the border between the (posterior) chamber and the ligand production region that simulates the average effects of the ligand activities in the production zone. This aggregated end source model is shown to adequately reproduce the significant implications of System F and to contain the corresponding ad hoc point source model, System R of [ 2 ], as a special case. Because of its simpler mathematical structure and the absence of any limitation on the ligand synthesis rate for the existence of steady-state gradients, System A type models are expected to be used widely. An example of such application is the recent study of the inhibiting effects of the formation of nonsignaling ligand–nonreceptor complexes [ 3 ].     

On the origin of the hole pressure

Summary One wall of a slit die apparatus contains a slot filled with the test liquid. Photographs of marked streamlines near the slot mouth show a pronounced curvature. A 0.5% aqueous solution of Separan AP 30 and molten polystyrene and polyethylene were investigated at low values of Reynolds number (Re < 1.0). In each case, streamlines are convex towards the slot mouth. This supports the hypothesis ofTanner andPipkin which attributes hole pressures in flowing viscoelastic liquids to the combined effect of holegenerated streamline curvature and shear-generated normal stress differences.

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Zusammenfassung In einer der Wände einer Schlitzdüsenvorrichtung ist eine mit Testflüssigkeit gefüllte Quernut angebracht. Es wurde die Strömung einer 0,5%-igen wässerigen Separan AP 30-Lösung, sowie einer Polystyrol- und einer Polyäthylenschmelze bei kleinen Reynoldszahlen (Re < 1.0) untersucht. In allen Fällen waren die Stromlinien konvex, also zur Schlitzmündung hin gekrümmt. Dadurch wird die Hypothese vonTanner andPipkin unterstützt, wonach die Lochdrücke in strömenden viskoelastischen Flüssigkeiten als Wirkung der durch die Scherung erzeugten Normalspannungsdifferenzen auf die gekrümmten Stromlinien erklärt werden.

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Department of Engineering Mechanics.

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Material Science Program.

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With 4 figures     

Flow development of xanthan solutions in capillary rheometers

Flow experiments through capillaries with 0.2% xanthan in aqueous solution and 0.1 N NaCl brine were carried out to study the influence of the molecular conformation on the flow development at relatively low shear rates, from 20s^–1 to 400s^–1. Capillaries with a wide range of length-to-diameter ratios, L/D = 4.5 to 1015 were used.The apparent viscosity as a function of L/D at a constant shear rate shows a continuous decrement of the viscosity as L/D increases, until an asymptotic value is reached. The decrement in the apparent viscosity is partially explained in terms of slip. It was found that slip is a function of L/D as well as shear stress, i.e., slip develops during flow, thus inducing spatial anisotropy in the fluid until a stable state is reached. However, the substantial difference in apparent viscosity between short capillaries and capillaries longer than 300 D may be attributed to dominant elongational flow due to the contraction in the small capillaries and slip in long capillaries.The flow in a sufficiently long capillary can be divided in four regions rather than three, as is usually assumed. In the first region, which corresponds to the entry, elongational and shear flow coexist and elongational flow dominant. In the second region, end effects and slip development are coupled. In the third region the flow is fully developed and end effects are negligible. However, the fluid shows physical characteristics different from those of the fluid at rest, as a consequence of prior slip development. The fourth zone is the exit region in which the velocity rearranges due to the change of boundary conditions. The length of each region depends on the conformation of the macromolecules and shear rate. In addition, it was found that the stiffness of xanthan increases with the increase of the ionic strength.Finally, a performance of Bagley's analysis in the whole range of L/D studied showed that the use of the Bagley correction is not a reliable way to correct for end effects when the flow is not fully developed and/or in the presence of slip.Dedicated to Arthur S. Lodge at the occasion of his 70th birthday and his retirement from the University of Wisconsin.