Polymer Maximum Drag Reduction: A Unique Transitional State

The upper bound of polymer drag reduction is identified as a unique transitional state between laminar and turbulent flow corresponding to the onset of the nonlinear breakdown of flow instabilities

Resource allocation for two source-destination pairs sharing a single relay with a buffer

In this paper, we obtain the optimal resource allocation scheme in order to maximize the achievable rate region in a dual-hop system that consists of two independent source-destination pairs sharing a single half-duplex relay. The relay decodes the received information and possesses buffers to enable storing the information temporarily before forwarding it to the respective destination. We consider both non-orthogonal transmission with successive interference cancellation at the receivers and orthogonal transmission. Also, we consider Gaussian block-fading channels and we assume that the channel state information is known and that no delay constraints are required. We show that, with the aid of buffering at the relay, joint user-and-hop scheduling is optimal and can enhance the achievable rate significantly. This is due to the joint exploitation of multiuser diversity and multihop diversity in the system. We provide closed-form expressions to characterize the average achievable rates in a generic form as functions of the statistical model of the channels. Furthermore, we consider sub-optimal schemes that exploit the diversity in the system partially and we provide numerical results to compare the different schemes and demonstrate the gains of the optimal one. © 2014 IEEE

Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow

We investigate the dynamics of the two-dimensional periodic Kolmogorov flow of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct numerical simulations. Above a critical Weissenberg number the flow displays a transition from stationary to randomly fluctuating states, via periodic ones. The increasing complexity of the flow in both time and space at progressively higher values of elasticity accompanies the establishment of mixing features. The peculiar dynamical behavior observed in the simulations is found to be related to the appearance of filamental propagating patterns, which develop even in the limit of very small inertial non-linearities, thanks to the feedback of elastic forces on the flow.Comment: 10 pages, 14 figure

Maximizing Expected Achievable Rates for Block-Fading Buffer-Aided Relay Channels

© 2002-2012 IEEE. In this paper, the long-term average achievable rate over block-fading buffer-aided relay channels is maximized using a hybrid scheme that combines three essential transmission strategies, which are decode-and-forward, compress-and-forward, and direct transmission. The proposed hybrid scheme is dynamically adapted based on the channel state information. The integration and optimization of these three strategies provide a more generic and fundamental solution and give better achievable rates than the known schemes in the literature. Despite the large number of optimization variables, the proposed hybrid scheme can be optimized using simple closed-form formulas that are easy to apply in practical relay systems. This includes adjusting the transmission rate and compression when compress-and-forward is the selected strategy based on the channel conditions. Furthermore, in this paper, the hybrid scheme is applied to three different models of the Gaussian block-fading buffer-aided relay channels, depending on whether the relay is half or full duplex and whether the source and the relay have orthogonal or non-orthogonal channel access. Several numerical examples are provided to demonstrate the achievable rate results and compare them to the upper bounds of the ergodic capacity for each one of the three channel models under consideration

System and method for confining an object to a region of fluid flow having a stagnation point

A device for confining an object to a region proximate to a fluid flow stagnation point includes one or more inlets for carrying the fluid into the region, one or more outlets for carrying the fluid out of the region, and a controller, in fluidic communication with the inlets and outlets, for adjusting the motion of the fluid to produce a stagnation point in the region, thereby confining the object to the region. Applications include, for example, prolonged observation of the object, manipulation of the object, etc. The device optionally may employ a feedback control mechanism, a sensing apparatus (e.g., for imaging), and a storage medium for storing, and a computer for analyzing and manipulating, data acquired from observing the object. The invention further provides methods of using such a device and system in a number of fields, including biology, chemistry, physics, material science, and medical science

Solitary coherent structures in viscoelastic shear flow: computation and mechanism

Starting from stationary bifurcations in Couette-Dean flow, we compute nontrivial stationary solutions in inertialess viscoelastic circular Couette flow. These solutions are strongly localized vortex pairs, exist at arbitrarily large wavelengths, and show hysteresis in the Weissenberg number, similar to experimentally observed ``diwhirl'' patterns. Based on the computed velocity and stress fields, we elucidate a heuristic, fully nonlinear mechanism for these flows. We propose that these localized, fully nonlinear structures comprise fundamental building blocks for complex spatiotemporal dynamics in the flow of elastic liquids.Comment: 5 pages text and 4 figures. Submitted to Physical Review Letter

Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A. Groisman and V. Steinberg, \sl Nature $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of width of the region available for flow to radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high molecular weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. Those include: (i)randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales; (ii) significant increase in the rates of momentum and mass transfer (compared to those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms, and parameter dependence of the elastic turbulence are compared with those of the conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure

Microdevices for extensional rheometry of low viscosity elastic liquids : a review

Extensional flows and the underlying stability/instability mechanisms are of extreme relevance to the efficient operation of inkjet printing, coating processes and drug delivery systems, as well as for the generation of micro droplets. The development of an extensional rheometer to characterize the extensional properties of low viscosity fluids has therefore stimulated great interest of researchers, particularly in the last decade. Microfluidics has proven to be an extraordinary working platform and different configurations of potential extensional microrheometers have been proposed. In this review, we present an overview of several successful designs, together with a critical assessment of their capabilities and limitations

The shear viscosity of carbon fibre suspension and its application for fibre length measurement

The viscosity of short carbon fibre suspensions in glycerol aqueous solution was measured using a bespoke vane-in-cup viscometer, where the carbon fibre has an aspect ratio from 450 to 2209. In the semi-concentrated regime, nL3 ranging from 20 to 4400, the suspensions demonstrated strong shear-thinning characteristics particularly at higher concentrations. The shear-thinning characteristic is strongly related to the crowding factor proposed by Kerekes, indicating that non-hydrodynamic interactions occur in the suspensions. The influence of fibre bending on viscosity emerges when the bending ratio is lower than 0.0028. An empirical model based on transient network formation and rupture was proposed and used to correlate the relative viscosity with fibre concentration nL3 and shear rate. Based on the model, a viscosity method is established to analyse the fibre length by measuring the viscosity of the fibre suspension using a bespoke vane-in-cup viscometer