When one solution of reactant A is displacing another miscible solution of reactant B, a miscible product C can be generated in the contact zone if a simple A + B → C chemical reaction takes place. Depending on the relative effect of A, B and C on the viscosity, different viscous fingering (VF) instabilities can be observed. In this context, a linear stability analysis of this reaction-diffusion-convection problem under the quasi-steady-state approximation is performed to classify the various possible instability scenarios. To do so, we determine the criteria for an instability, obtain dispersion curves both at initial contact time using an analytical implicit solution and at later times via numerical stability analysis. Along with recovering known results for non-reactive systems where the displacement of a more viscous fluid by a less viscous one leads to a VF instability, it is found that in the presence of a chemical reaction, injecting a more viscous fluid into a less viscous fluid can also lead to instabilities. This occurs when the chemical reaction leads to the build up of non-monotonic viscosity profiles. Various instability scenarios are classified in a parameter plane spanned by R b and R c representing the log-mobility ratios of the viscosities of the B and C solution respectively with respect to that of the injected solution of A. A parametric study of the influence on stability of the Damköhler number and of the time elapsed after contact of the two reactive solutions is also conducted.

The effects of viscoelasticity on the hydrodynamic stability of plane free shear flow are investigated through a linear stability analysis. Three different rheological models have been examined : the Oldroyd-B, corotational Jeffreys, and Giesekus models. We are especially interested in possible effects of viscoelasticity on the inviscid modes associated with inflexional velocity profiles. In the inviscid limit, it is found that for viscoelasticity to affect the instability of a flow described by the Oldroyd-B model, the Weissenberg number, We, has to go to infinity in such a way that its ratio to the Reynolds number, G K We/Re, is finite. In this special limit we derive a modified Rayleigh equation, the solution of which shows that viscoelasticity reduces the instability of the flow but does not suppress it. The classical Orr-Sommerfeld analysis has been extended to both the Giesekus and corotational Jeffreys models. The latter model showed little variation from the Newtonian case over a wide range of Re, while the former one may have a stabilizing effect depending on the product sWe where s is the mobility factor appearing in the Giesekus model. We discuss the mechanisms responsible for reducing the instability of the flow and present some qualitative comparisons with experimental results reported by Hibberd et al. (1982), Scharf (1985a, b) and Riediger (1989). Problem definitionThe mixing-layer flow configuration is standard, as shown in figure 1. U, (respectively U,) is the free-stream velocity of the upper (lower) flow. We denote by uo = i(U, -U,)the free-stream velocity in a reference frame moving with the average velocity of the flow +(q + &), and by S the momentum thickness of the mixing layer. In all the

SUMMARYA ÿnite di erence-pseudo-spectral (FD-PS) algorithm is developed to simulate the viscous ÿngering instability in high mobility-ratio (MR) miscible displacements. This novel algorithm uses the fully implicit alternating-direction implicit (ADI) method combined with a Hartley based pseudo-spectral method to solve the Poisson equation involving the streamfunction and the vorticity. In addition, underrelaxation in the iterative evaluation of the streamfunction is adopted. The new code allowed to model successfully the viscous ÿngering instability for mobility-ratios as high as 1800, and new non-linear viscous ÿngering mechanisms are discovered. A systematic analysis of the e ects of the MR, the Peclet number and the aspect ratio on the ÿnger growth is conducted. It is found that the growth of the interfacial instability accelerates with increase in the MR and Peclet number. At larger values of these parameters the increased sti ness of the corresponding numerical problem caused signiÿcant increase in the computational time as it required ÿner grids and smaller time steps to capture the ÿne structures of the viscous ÿngers.

In this research note, we revisit the pseudo-second-order model for adsorption kinetics, its assumptions, and its application to simulated, random, and published data. In particular, a widely used linear form of the pseudo-second-order modelplotting t/q t against tis shown to result in spurious correlations for typical adsorption experimental data. Depending on the range of data used, data from pseudo-first-order and pseudo-third-order models can also appear to be well-fit by the pseudo-second-order model. Inspection of the residual errors, however, indicates that the errors are not randomly distributed, as they should be. Based on this study, it is recommended to always verify the assumptions of a model, fit the data with the nonlinear form of the model equation, and inspect the residual plot to determine the goodness of fit.

An experimental study and a numerical modeling analysis are carried out to examine the effects of fiber‐fiber interactions and coupling between fiber orientation and polymer chains conformation on the rheological properties of fiber suspensions. The experimental study allowed examination of large fiber volume fractions up to 35% over a range of shear rates that spans eight decades. This study confirmed already known results and led to new ones. In particular, a peak in the steady shear viscosity at the low shear rate region is observed at large volume fractions. Furthermore, new results regarding the applicability of the Cox‐Merz rule, the behavior of the damping factor, and the end pressure drops are reported, and physical interpretations are proposed. The results of the numerical modeling showed that it is necessary to account for the polymer‐fiber coupling factor to obtain a good fit between the model predictions and the experimental measurements. Comparisons between the model predictions and the experimental measurements allowed study of the variation of the parameters that govern the fiber‐fiber interactions and the polymer‐fiber coupling with the properties of the suspension and the flow. POLYM. ENG. SCI., 45:385–399, 2005. © 2005 Society of Plastics Engineers