This manuscript is the original submission to Nature. The final (published) version can be accessed at http://www.nature.com/nature/journal/v526/n7574/full/nature15701.html 1 arXiv:1510.09143v1 [physics.flu-dyn] Oct 2015Over a century of research into the origin of turbulence in wallbounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow. [1][2][3][4][5][6] At slightly higher speeds the situation changes distinctly and the entire flow is turbulent. Neither the origin of the different states encountered during transition, nor their front dynamics, let alone the transformation to full turbulence could be explained to date. Combining experiments, theory and computer simulations here we uncover the bifurcation scenario organising the route to fully turbulent pipe flow and explain the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence 7 and fully turbulent flows. 8,9 The sudden appearance of localised turbulent patches in an otherwise quiescent flow was first observed by Osborne Reynolds for pipe flow 1 and has since been found to be the starting point of turbulence in most shear flows. 2,4,[10][11][12][13][14][15] Curiously, in this regime it is impossible to maintain turbulence over extended regions as it automatically 16,17 reduces to patches of characteristic size, called puffs in pipe flow (see Fig. 1a). Puffs can decay, or else split and thereby multiply. Once the Reynolds number R > 2040 the splitting process outweighs decay, resulting in sustained disordered motion. 7 Although sustained, turbulence at these low R only consists of puffs surrounded by laminar flow (Fig. 1a) and cannot form larger clusters. 17,18 At larger flow rates, the situation is fundamentally different: once triggered, turbulence aggressively expands and eliminates all laminar motion (Fig. 1b). Fully turbulent flow is now the natural state of the system and only then do wallbounded shear flows have characteristic mean properties such as the Blasius or Prandtl-von Karman friction laws. 9 This rise of fully turbulent flow has remained unexplained despite the fact that this transformation occurs in virtually all shear flows and generally dominates the dynamics at sufficiently large Reynolds numbers.A classical diagnostic for the formation of turbulence 2-5, 19, 20 is the propagation speed of the In each case, the flow is initially seeded with localised turbulent patches and the subsequent evolution is visualised via space-time plots in a reference frame co-moving with structures. Colours indicate the value of u 2 r + u 2 θ . Further highlighting the distinction between cases, shown at the top are cross sections of instantaneous flow within the pipe. A 35D section is shown with the vertical direction str...

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Self-assembly of surfactant molecules into micelles of various shapes and forms has been extensively used to synthesize soft nanomaterials. Translucent solutions containing rod-like surfactant micelles can self-organize under flow to form viscoelastic gels. This flow-induced structure (FIS) formation has excited much fundamental research and pragmatic interest as a cost-effective manufacturing route for active nanomaterials. However, its practical impact has been very limited because all reported FIS transitions are reversible because the gel disintegrates soon after flow stoppage. We present a new microfluidics-assisted robust laminar-flow process, which allows for the generation of extension rates many orders of magnitude greater than is realizable in conventional devices, to produce purely flow-induced permanent nanogels. Cryogenic transmission electron microscopy imaging of the gel reveals a partially aligned micelle network. The critical flow rate for gel formation is consistent with the Turner-Cates fusion mechanism, proposed originally to explain reversible FIS formation in rod-like micelle solutions.

The eect of salt concentration C s on the critical shear rateγ c required for the onset of shear thickening and apparent relaxation time λ of the shear-thickened phase, has been investigated systematically for dilute CTAB/NaSal solutions. Experimental data suggest a self-similar behavior ofγ c and λ as functions of C s . Specically,γ c ∼ C s −6 whereas λ ∼ C s 6 such that an eective Weissenberg number We ≡ λγ for the onset of the shear thickened phase is only weakly dependent on C s . A procedure has been developed to collapse the apparent shear viscosity versus shear rate data obtained for various values of C s into a single master curve. The eect of C s on the elastic modulus and mesh size of the shear-induced gel phase for dierent surfactant concentrations is discussed.Experiments performed using dierent ow cells (Couette and cone-and-plate) show thatγ c , λ and the maximum viscosity attained are geometry-independent. The elastic modulus of the gel phase inferred indirectly by employing simplied hydrodynamic instability analysis of a sheared gel-uid interface is in qualitative agreement with that predicted for an entangled phase of living polymers. A qualitative mechanism that combines the eect of C s on average micelle length and Debye parameter with shearinduced congurational changes of rod-like micelles is proposed to rationalize the selfsimilarity of SIS formation.

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In pipes, turbulence sets in despite the linear stability of the laminar Hagen-Poiseuille flow. The Reynolds number (Re) for which turbulence first appears in a given experiment -the 'natural transition point'-depends on imperfections of the set-up, or more precisely, on the magnitude of finite amplitude perturbations. At onset, turbulence typically only occupies a certain fraction of the flow and this fraction equally is found to differ from experiment to experiment. Despite these findings, Reynolds proposed that after sufficiently long times, flows may settle to a steady condition: below a critical velocity flows should (regardless of initial conditions) always return to laminar while above eddying motion should persist. As will be shown, even in pipes several thousand diameters long the spatio-temporal intermittent flow patterns observed at the end of the pipe strongly depend on the initial conditions and there is no indication that different flow patterns would eventually settle to a (statistical) steady state. Exploiting the fact that turbulent puffs do not age (i.e. they are memoryless), we continuously recreate the puff sequence exiting the pipe at the pipe entrance, and in doing so introduce periodic boundary conditions for the puff pattern.This procedure allows us to study the evolution of the flow patterns for arbitrary long times, and we find that after times in excess of 10 7 advective time units, indeed a statistical steady state is reached. Though the resulting flows remain spatio-temporally intermittent, puff splitting and decay rates eventually reach a balance so that the turbulent fraction fluctuates around a well defined level which only depends on Re. In accordance with Reynolds proposition, we find that at lower Re (here 2020), flows eventually always resume to laminar while for higher Re (>= 2060) turbulence persists.The critical point for pipe flow hence falls into the interval of 2020 < Re < 2060, which is in very good agreement with the recently proposed value of Re c = 2040. The latter estimate was based on single puff statistics and entirely neglected puff interactions.Unlike in typical contact processes where such interactions strongly affect the percolation threshold, in pipe flow the critical point is only marginally influenced. Interactions on the other hand, are responsible for the approach to the statistical steady state. As shown, they strongly affect the resulting flow patterns, where they cause 'puff clustering' and these regions of large puff densities are observed to travel across the puff pattern in a wave like fashion.

Present study investigates the potential of cassava peel and rubber tree bark for the removal of Cr (VI) from aqueous solution. Removal efficiency of more than 99% was obtained during the kinetic adsorption experiments with dosage of 3.5 g/L for cassava peel and 8 g/L for rubber tree bark. By comparing popular isotherm models and kinetic models for evaluating the kinetics of mass transfer, it was observed that Redlich-Peterson model and Langmuir model fitted well (R 2 > 0.99) resulting in maximum adsorption capacity as 79.37 mg/g and 43.86 mg/g for cassava peel and rubber tree bark respectively. Validation of pseudo-second order model and Elovich model indicated the possibility of chemisorption being the rate limiting step. The multi-linearity in the diffusion model was further addressed using multi-sites models (two-site series interface (TSSI) and two-site parallel interface (TSPI) models). Considering the influence of interface properties on the kinetic nature of sorption, TSSI model resulted in low mass transfer rate (5% for cassava peel and 10% for rubber tree bark) compared to TSPI model. The study highlights the employability of two-site sorption model for simultaneous representation of different stages of kinetic sorption for finding the rate-limiting process, compared to the separate equilibrium and kinetic modeling attempts.

The recent classification of the onset of turbulence as a directed percolation (DP) phase transition has been applied to all major shear flows including pipe, channel, Couette and boundary layer flows. A cornerstone of the DP analogy is the memoryless (Markov) property of turbulent sites. We here show that for the classic case of channel flow, the growth of turbulent stripes is deterministic and that memorylessness breaks down. Consequently turbulence ages and the one to one mapping between turbulent patches and active DP-sites is not fulfilled. In addition, the interpretation of turbulence as a chaotic saddle with supertransient properties, the basis of recent theoretical progress, does not apply. The discrepancy between channel flow and the established transition model illustrates that seemingly minor geometrical differences between flows can give rise to instabilities and growth mechanisms that fundamentally alter the nature of the transition to turbulence.