Weakly nonlinear subcritical instability of visco-elastic Poiseuille flow

It is well known that the Poiseuille flow of a visco-elastic polymer fluid between plates or through a tube is linearly stable in the zero Reynolds number limit, although the stability is weak for large Weissenberg numbers. In this paper we argue that recent experimental and theoretical work on the instability of visco-elastic fluids in Taylor-Couette cells and numerical work on channel flows suggest a scenario in which Poiseuille flow of visco-elastic polymer fluids exhibits a nonlinear "subcritical" instability due to normal stress effects, with a threshold which decreases for increasing Weissenberg number. This proposal is confirmed by an explicit weakly nonlinear stability analysis for Poiseuille flow of an UCM fluid. Our analysis yields explicit predictions for the critical amplitude of velocity perturbations beyond which the flow is nonlinearly unstable, and for the wavelength of the mode whose critical amplitude is smallest. The nonlinear instability sets in quite abruptly at Weissenberg numbers around 4 in the planar case and about 5.2 in the cylindrical case, so that for Weissenberg numbers somewhat larger than these values perturbations of the order of a few percent in the wall shear stress suffice to make the flow unstable. We have suggested elsewhere that this nonlinear instability could be an important intrinsic route to melt fracture and that preliminary experiments are both qualitatively and quantitatively in good agreement with these predictions.Comment: 20 pages, 16 figures. Accepted for publication in J. of Non-Newtonian Fluid Mechanic

Coherent structures in plane channel flow of dilute polymer solutions with vanishing inertia

When subjected to sufficiently strong velocity gradients, solutions of long, flexible polymers exhibit flow instabilities and chaotic motion, often referred to as elastic turbulence. Its mechanism differs from the familiar, inertia-driven turbulence in Newtonian fluids, and is poorly understood. Here, we demonstrate that the dynamics of purely elastic pressure-driven channel flows of dilute polymer solutions are organised by exact coherent structures that take the form of two-dimensional travelling waves. Our results demonstrate that no linear instability is required to sustain such travelling wave solutions, and that their origin is purely elastic in nature. We show that the associated stress profiles are characterised by thin, filament-like arrangements of polymer stretch, which is sustained by a solitary pair of vortices. We discuss the implications of the travelling wave solutions for the transition to elastic turbulence in straight channels, and propose ways for their detection in experiments

Give growth and macroeconomic stability in Russia a chance - harden budgets by eliminating nonpayments

The authors analyze the links between Russia's disappointing growth performance in the second half of the 1990s, its costly and unsuccessful stabilization, the macroeconomic meltdown of 1998, and the spectacular rise of non-payments. Non-payments flourished in an environment of fundamental inconsistency between a macroeconomic policy geared at sharp disinflation, and a microeconomic policy of bailing enterprises out through soft budget constraints. Heavy untargeted implicit subsidies flowing through the non-payments system (amounting to 10 percent of GDP annually) have stifled growth, contributed to the August 1998 meltdown, through their impact on public debt, and have made at best a questionable contribution to equity. Dismantling this system must be a top priority, along with promoting enterprise restructuring and growth (by hardening budget constraints) and medium-term macroeconomic stability (by reducing the size of subsidies). Getting the government out of the non-payments system means settling all appropriately controlled budgetary expenditures on time, and in cash, and eschewing spending arrears, thereby setting an example for enterprises, and laying the groundwork for eliminating tax offsets at all levels of government, and insisting on cash tax payments. To stop energy-related subsidies, would require not only that the government pay its own energy bills on time, and in cash, but also that the energy monopolies be empowered to disconnect non-paying clients. This will enable the government to insist that the energy monopolies in turn pay their own taxes in full, and on time.Banks&Banking Reform,Public Sector Economics&Finance,Economic Theory&Research,Payment Systems&Infrastructure,Environmental Economics&Policies,Banks&Banking Reform,Environmental Economics&Policies,Municipal Financial Management,Public Sector Economics&Finance,Economic Theory&Research

Molecular Motors Interacting with Their Own Tracks

Dynamics of molecular motors that move along linear lattices and interact with them via reversible destruction of specific lattice bonds is investigated theoretically by analyzing exactly solvable discrete-state ``burnt-bridge'' models. Molecular motors are viewed as diffusing particles that can asymmetrically break or rebuild periodically distributed weak links when passing over them. Our explicit calculations of dynamic properties show that coupling the transport of the unbiased molecular motor with the bridge-burning mechanism leads to a directed motion that lowers fluctuations and produces a dynamic transition in the limit of low concentration of weak links. Interaction between the backward biased molecular motor and the bridge-burning mechanism yields a complex dynamic behavior. For the reversible dissociation the backward motion of the molecular motor is slowed down. There is a change in the direction of the molecular motor's motion for some range of parameters. The molecular motor also experiences non-monotonic fluctuations due to the action of two opposing mechanisms: the reduced activity after the burned sites and locking of large fluctuations. Large spatial fluctuations are observed when two mechanisms are comparable. The properties of the molecular motor are different for the irreversible burning of bridges where the velocity and fluctuations are suppressed for some concentration range, and the dynamic transition is also observed. Dynamics of the system is discussed in terms of the effective driving forces and transitions between different diffusional regimes