Defect dynamics in viscous fingering

We study the dynamics of Staffman-Taylor fingering in terms of topological defects of the flow field. The defects are created and/or annihilated at the interface. The route towards the single-finger steady state is characterized by a detailed mechanism for defect annihilation. For small viscosity contrast this mechanism is impeded, and creation of new defects leads the system away from a single-finger solution. Strong evidence for a drastic reduction of the basin of attraction of the Saffman-Taylor finger is presented.

Phase separation dynamics under stirring

Phase separation dynamics in the presence of externally imposed stirring is studied. The stirring is assumed independent of the concentration and it is generated with a well-defined energy spectrum. The domain growth process is either favored or frozen depending on the intensity and correlation length of this advective flow. This behavior is explained by analytical arguments.

External Fluctuations in Front Propagation

We study the effects of external noise in a one-dimensional model of front propagation. Noise is introduced through the fluctuations of a control parameter leading to a multiplicative stochastic partial differential equation. Analytical and numerical results for the front shape and velocity are presented. The linear-marginal-stability theory is found to increase its range of validity in the presence of external noise. As a consequence noise can stabilize fronts not allowed by the deterministic equation.

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described by Tanveer [Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993)] and Siegel and Tanveer [Phys. Rev. Lett. 76, 419 (1996)], as well as direct numerical computation, following the numerical scheme of Hou, Lowengrub, and Shelley [J. Comput. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (nonsingular) zero-surface-tension solutions. The effect is present even when the relevant zero-surface-tension solution has asymptotic behavior consistent with selection theory. Such singular effects, therefore, cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structurally unstable flow, restoring the hyperbolicity of multifinger fixed points.

Systematic weakly nonlinear analysis of interfacial instabilities in Hele-Shaw flows

We develop a systematic method to derive all orders of mode couplings in a weakly nonlinear approach to the dynamics of the interface between two immiscible viscous fluids in a Hele-Shaw cell. The method is completely general: it applies to arbitrary geometry and driving. Here we apply it to the channel geometry driven by gravity and pressure. The finite radius of convergence of the mode-coupling expansion is found. Calculation up to third-order couplings is done, which is necessary to account for the time-dependent Saffman-Taylor finger solution and the case of zero viscosity contrast. The explicit results provide relevant analytical information about the role that the viscosity contrast and the surface tension play in the dynamics of the system. We finally check the quantitative validity of different orders of approximation and a resummation scheme against a physically relevant, exact time-dependent solution. The agreement between the low-order approximations and the exact solution is excellent within the radius of convergence, and is even reasonably good beyond this radius.

Systematic weakly nonlinear analysis of radial viscous fingering

We present a weakly nonlinear analysis of the interface dynamics in a radial Hele-Shaw cell driven by both injection and rotation. We extend the systematic expansion introduced in [E. Alvarez-Lacalle et al., Phys. Rev. E 64, 016302 (2001)] to the radial geometry, and compute explicitly the first nonlinear contributions. We also find the necessary and sufficient condition for the uniform convergence of the nonlinear expansion. Within this region of convergence, the analytical predictions at low orders are compared satisfactorily to exact solutions and numerical integration of the problem. This is particularly remarkable in configurations (with no counterpart in the channel geometry) for which the interplay between injection and rotation allows that condition to be satisfied at all times. In the case of the purely centrifugal forcing we demonstrate that nonlinear couplings make the interface more unstable for lower viscosity contrast between the fluids.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

Lateral instability in normal viscous fingers

We study a low-amplitude, long-wavelength lateral instability of the Saffman-Taylor finger by means of a phase-field model. We observe such an instability in two situations in which small dynamic perturbations are overimposed to a constant pressure drop. We first study the case in which the perturbation consists of a single oscillatory mode and then a case in which the perturbation consists of temporal noise. In both cases the instability undergoes a process of selection.

Selection, shape and relaxation of fronts: A numerical study of the effects of inertia.

We study the problem of front propagation in the presence of inertia. We extend the analytical approach for the overdamped problem to this case, and present numerical results to support our theoretical predictions. Specifically, we conclude that the velocity and shape selection problem can still be described in terms of the metastable, nonlinear, and linear overdamped regimes. We study the characteristic relaxation dynamics of these three regimes, and the existence of degenerate (¿quenched¿) solutions.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Identification of secretory IgA, free secretory piece and serum IgA in the ovine and caprine species.

Caprine and ovine IgA were identified by cross-reaction with anti-human and anti-bovine IgA sera in colostrum, mature milk, saliva, urine and serum. Secretory component (SC) was shown in the free form and associated with polymeric serum IgA in secretions. Mean molecular weights were determined for the IgA and the free secretory components. The high IgA content of saliva suggested that it was a major secretory immunoglobulin in these species. Traces of secretory IgA were also found in normal sera but most of the serum IgA had no secretory determinant. Secretory IgA, serum IgA and free secretory component were purified. Levels of the sheep and goat immunoglobulins were measured in various fluids.

Reply to Comment on 'Two-finger selection theory in the Saffman-Taylor problem

We clarify the meaning of the results of Phys. Rev. E 60, R5013 (1999). We discuss the use and implications of periodic boundary conditions, as opposed to rigid-wall ones. We briefly argue that the solutions of the paper above are physically relevant as part of a more general issue, namely the possible generalization to dynamics, of the microscopic solvability scenario of selection.

Relevance of dynamic wetting in viscous fingering patterns

We demonstrate that wetting effects at moving contact lines have a strong impact in viscous fingering patterns. Experiments in a rotating Hele-Shaw (HS) cell, dry or prewetted, show consistent morphological differences. When the wetting fluid invades a dry region, contact angle dynamics yield a kinetic contribution to the interface pressure drop that scales with capillary number as Ca2¿3 but is significantly larger than the Park-Homsy kinetic correction. Numerical results are in very good agreement with experiments and show that standard HS equations work best for prewetted cells.

External fluctuations in a pattern-forming instability

The effect of external fluctuations on the formation of spatial patterns is analyzed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the bifurcation point controlled by the intensity of the multiplicative noise. This shift takes place in the ordering direction (i.e., produces patterns), but its magnitude decreases with that of the noise correlation length. Analytical arguments are presented to explain these facts.