Asymmetric Bifurcation Research Articles

Nonlinear Distribution of Sediment at River Diversions: Brief History of the Bulle Effect and Its Implications

AbstractOne of the fundamental units in fluvial systems is a bifurcation, where an existing channel splits into two. Diversions are a special class of asymmetric bifurcation, in which one of the ch...

Experimental investigation of particle migration in suspension flow through bifurcating microchannels

Experimental measurements of velocity and concentration profiles were carried out to study transport of non‐colloidal suspension in bifurcating micro channels for both diverging and converging flow conditions using a combination of mirco‐particle image velocimetry and particle tracking velocimetry techniques. Migration of particles across the streamline was observed and symmetric velocity and concentration profile in the inlet branch becomes asymmetric in the daughter branches. Further migration of particles toward the center of the channel in the outlet branch make the profiles again symmetric. The evolution of velocity and concentration profiles was observed to be different in the symmetric and asymmetric bifurcation channels. The comparison of the streamlines for the fluid and the particles showed significant deviation near the bifurcation region. This may explain why there is unequal flow and particle partitioning during flow of suspension in asymmetric bifurcating channels as reported in many previous studies. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2293–2307, 2018

АНАЛИЗ ЧУВСТВИТЕЛЬНОСТИ И ОПТИМИЗАЦИЯ ПОЛОГИХ СТЕРЖНЕВЫХ КОНСТРУКЦИЙ С УЧЕТОМ ГЕОМЕТРИЧЕСКОЙ НЕЛИНЕЙНОСТИ И ОГРАНИЧЕНИЙ НА УСТОЙЧИВОСТЬ

The paper addresses the issue of sensitivity and the optimization of shallow rod structures with simultaneously varying the node coordinates, dimensions, cross-section areas, and with constraints on the critical total instability load, accounting for geometric nonlinearities, strength constraints. The material of the structures undergoing large displacements is assumed linearly elastic. All the external loads are considered conservative. Total loss of stability of a structure is interpreted as a singularity of its tangential stiffness matrix in critical points. The criteria for classifying the three types of the critical points - symmetric, asymmetric bifurcation points and a limit point - have been formulated. Special attention is paid to total loss of stability in limit points, characteristic of low or shallow rod structures, such as trusses, arches, cupolas, etc. To trace a fundamental curve of equilibrium states with limit points, the method of successive increments of displacements is used. Sensitivity of the critical load corresponding to a limit point has been analytically studied, and sensitivity of displacements of geometrically nonlinear structures has been analyzed. Sensitivity was analyzed using the direct method. A method for optimizing elastic shallow rod structures, accounting for geometric nonlinearities and stability constraints is presented. An additional condition in the considered optimization problem is the condition that limit points arise earlier than bifurcation ones. The methodology has been tested on benchmark structure - the spatial symmetric thirty-element aerial. The results obtained in the АNSYS medium, accounting for the linear and nonlinear analyses of stability are in good agreement with results published by foreign researchers for the behchmark structure.

The Role of Hemodynamics in Intracranial Bifurcation Arteries after Aneurysm Treatment with Flow-Diverter Stents.

Treatment of intracranial bifurcation aneurysms with flow-diverter stents can lead to caliber changes of the distal vessels in a subacute phase. This study aims to evaluate whether local anatomy and flow disruption induced by flow-diverter stents are associated with vessel caliber changes in intracranial bifurcations. Radiologic images and demographic data were acquired for 25 patients with bifurcation aneurysms treated with flow-diverter stents. Whisker plots and Mann-Whitney rank sum tests were used to evaluate if anatomic data and caliber changes could be linked. Symmetry/asymmetry were defined as diameter ratio 1 = symmetric and diameter ratio <1 = asymmetric. Computational fluid dynamics was performed on idealized and patient-specific anatomies to evaluate flow changes induced by flow-diverter stents in the jailed vessel. Statistical analysis identified a marked correspondence between asymmetric bifurcation and caliber change. Symmetry ratios were lower for cases showing narrowing or subacute occlusion (medium daughter vessel diameter ratio = 0.59) compared with cases with posttreatment caliber conservation (medium daughter vessel diameter ratio = 0.95). Computational fluid dynamics analysis in idealized and patient-specific anatomies showed that wall shear stress in the jailed vessel was more affected when flow-diverter stents were deployed in asymmetric bifurcations (diameter ratio <0.65) and less affected when deployed in symmetric anatomies (diameter ratio ∼1.00). Anatomic data analysis showed statistically significant correspondence between caliber changes and bifurcation asymmetry characterized by diameter ratio <0.7 (P < .001). Similarly, computational fluid dynamics results showed the highest impact on hemodynamics when flow-diverter stents are deployed in asymmetric bifurcations (diameter ratio <0.65) with noticeable changes on wall sheer stress fields. Further research and clinical validation are necessary to identify all elements involved in vessel caliber changes after flow-diverter stent procedures.

Numerical design of a T-shaped microfluidic device for deformability-based separation of elastic capsules and soft beads.

We propose a square cross-section microfluidic channel with an orthogonal side branch (asymmetric T-shaped bifurcation) for the separation of elastic capsules and soft beads suspended in a Newtonian liquid on the basis of their mechanical properties. The design is performed through three-dimensional direct numerical simulations. When suspended objects start near the inflow channel centerline and the carrier fluid is equally partitioned between the two outflow branches, particle separation can be achieved based on their deformability, with the stiffer ones going "straight" and the softer ones being deviated to the "side" branch. The effects of the geometrical and physical parameters of the system on the phenomenon are investigated. Since cell deformability can be significantly modified by pathology, we give a proof of concept on the possibility of separating diseased cells from healthy ones, thus leading to illness diagnosis.

Fast-scale non-linear distortion analysis of peak-current-controlled buck–boost inverters

ABSTRACTThis paper deals with fast-scale non-linear distortion behaviours including asymmetrical period-doubling bifurcation and zero-crossing distortion in peak-current-controlled buck–boost inverters. The underlying mechanisms of the fast-scale non-linear distortion behaviours in inverters are revealed. The folded bifurcation diagram is presented to analyse the asymmetrical phenomenon of fast-scale period-doubling bifurcation. In view of the effect of phase shift and current ripple, the analytical expressions for one pair of critical phase angles are derived by using the design-oriented geometrical current approach. It is shown that the phase shift between inductor current and capacitor voltage should be responsible for the zero-crossing distortion phenomenon. These results obtained here are useful to optimise the circuit design and improve the circuit performance.

An Eulerian-Eulerian formulation of suspension rheology using the finite volume method

We have adapted a well-known constitutive model formulated by Morris and Boulay (1999) that describes the stress tensor for a mixture of particles in a Newtonian liquid into a two-phase finite-volume solver. The two-phase model treats each phase with a separate continuity and momentum equation that splits the stress of the constitutive model between the two phases, with the particle pressure applied only to the particle phase in addition to source terms related to the drag of particles in the fluid. We compare the resulting model using a variety of NMR experiments, considering the flow of neutrally buoyant monodisperse particles at low Reynolds number in the following geometries: 2D simple shear flow in a Couette device, axisymmetric and 3D pressure driven flow down a pipe and in a 2D and 3D asymmetric channel bifurcation. We find excellent agreement with velocity and volume fraction profiles in all of the comparisons with experimental data without much further numerical fitting beyond the original suspension stress model.

Self-excited oscillation of non-equilibrium condensation in critical flow nozzle

The unsteady flow with vapor condensation in critical flow nozzle includes many different self-excited periodic oscillation modes and might affect its flow field and mass flow-rate. The instability of condensation in transonic nozzle flow was discussed firstly. To investigate the phenomenon of self-excited oscillation and bifurcation induced by non-equilibrium condensation of the pure superheated steam flow in critical flow nozzle, an Eulerian viscous flow solver using SST k-ω turbulent model for vapor condensation was established and validated by experimental data of both steady and unsteady condensations, and algebraic formula. Three self-excited symmetric oscillation modes were classified by the oscillation amplitude and frequency of induced shock. The phenomenon of symmetric oscillation modes and asymmetric bifurcation were discussed in detail. Moreover, the effect of self-excited oscillation on its mass flow-rate was clarified. The maximum deviation of mass flow-rate is 1.2%, which is worthy of attention.

Nonlinear buckling behaviour of spherical shells: barriers and symmetry-breaking dimples.

The nonlinear axisymmetric post-buckling behaviour of perfect, thin, elastic spherical shells subject to external pressure and their asymmetric bifurcations are characterized, providing results for a structure/loading combination with an exceptionally nonlinear buckling response. Immediately after the onset of buckling, the buckling mode localizes into a dimple at the poles. The relations among the pressure, the dimple amplitude and the change in volume of the shell are determined over a large range of pole deflections. These results allow accurate evaluation of criteria such as the Maxwell condition for which the energies in the unbuckled and buckled states are the same and evaluation of the influences of pressure versus volume-controlled loadings. Non-axisymmetric bifurcation from the axisymmetric state, which occurs deep into the post-buckling regime in the form of multi-lobed dimples, is also established and discussed.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

Distributary channels in the fluvial to tidal transition zone

Coastal lowland plains under mixed fluvial‐tidal influence may form complex, composite channel networks, where distributaries blend the characteristics of mouth bar channels, avulsion channels, and tidal creeks. The Kapuas coastal plain exemplifies such a coastal plain, where several narrow distributaries branch off the Kapuas River at highly asymmetric bifurcations. A comprehensive geomorphological analysis shows that trends in the channel geometry of all Kapuas distributaries are similar. They consist of a short, converging reach near the sea and a nonconverging reach upstream. The two parts are separated by a clear break in scaling of geometrical properties. Such a break in scaling was previously established in the Mahakam Delta, which suggests that this may be a general characteristic in the fluvial to tidal transition zone. In contrast to the geometrical trend similarities, a clear difference in bed material between the main and side distributaries is found. In the main distributary, a continuous trend of downstream fining is established, similar to what is often found in lowland rivers. In the side distributaries, bed material coarsens in the downstream direction. This indicates an undersupply of sediment to the side distributaries, which may contribute to their long‐term stability as established from historical maps. Tides may be the main agent preventing fine sediment to settle, promoting residual transport of fine material to the coastal ocean.

Abstract WP90: The Role of Haemodynamics in a Bifurcation Vessel Narrowing or Occlusion After Aneurysm Treatment with Flow Diverter Stents

Background and Purpose: Treatment of intracranial aneurysms at bifurcations with flow-diverter stents (FDS) can lead to occlusion/narrowing of the distal vessels. This study investigated the role played by haemodynamics within different bifurcation types treated with FDS. Materials and Methods: Radiological images, demographic and outcome data were acquired for 25 bifurcating aneurysm treated with FDS. Statistical analysis was used to correlate the event of occlusion/narrowing with anatomical data. Computational Fluid Dynamics (CFD) study was performed on idealized and patient-specific anatomies to identify possible cause-effect mechanisms mediated by haemodynamics. Results: Statistical analysis identified marked correlation between asymmetric bifurcation and occlusion/narrowing (diameters ratio=DR=1 symmetric, &lt;1 asymmetric). CFD predictions in both idealized and patient-specific anatomies showed that wall shear stress (WSS) in the jailed vessel is mostly affected when FDS are deployed in non-symmetric bifurcations (DR&lt;0.65), and least affected when deployed in symmetric anatomies (DR = 1.00). Conclusion: Analysis of the anatomical data showed statistically significant correlations between occlusion/narrowing and bifurcation asymmetry characterized by DR&lt;0.7. Similarly, CFD results showed that FDS have the highest impact on haemodynamics when deployed in bifurcations with higher degrees of anatomical asymmetry (DR&lt;0.65) with strong changes induced on the WSS fields. This suggests a higher risk associated to FDS-treatment of asymmetric bifurcation together with a possible FDS-induced pathway leading to occlusion/narrowing of arteries and mediated by haemodynamics and endothelial response.

Microscale distribution and dynamic surface tension of pulmonary surfactant normalize the recruitment of asymmetric bifurcating airways.

We investigate the influence of bifurcation geometry, asymmetry of daughter airways, surfactant distribution, and physicochemical properties on the uniformity of airway recruitment of asymmetric bifurcating airways. To do so, we developed microfluidic idealized in vitro models of bifurcating airways, through which we can independently evaluate the impact of carina location and daughter airway width and length. We explore the uniformity of recruitment and its relationship to the dynamic surface tension of the lining fluid and relate this behavior to the hydraulic (PHyd) and capillary (PCap) pressure drops. These studies demonstrate the extraordinary importance of PCap in stabilizing reopening, even in highly asymmetric systems. The dynamic surface tension of pulmonary surfactant is integral to this stability because it modulates PCap in a velocity-dependent manner. Furthermore, the surfactant distribution at the propagating interface can have a very large influence on recruitment stability by focusing surfactant preferentially to specific daughter airways. This implies that modification of the surfactant distribution through novel modes of ventilation could be useful in inducing uniformly recruited lungs, aiding in gas exchange, and reducing ventilator-induced lung injury.NEW & NOTEWORTHY The dynamic surface tension of pulmonary surfactant is integral to the uniformity of asymmetric bifurcation airway recruitments because it modulates capillary pressure drop in a velocity-dependent manner. Also, the surfactant distribution at the propagating interface can have a very large influence on recruitment stability by focusing surfactant preferentially to specific daughter airways. This implies that modification of the surfactant distribution through novel modes of ventilation could be useful in inducing uniformly recruited lungs, reducing ventilator-induced lung injury.

Composite spheroidal shells under external pressure

ABSTRACTBuckling, collapse, and first ply failure pressures have been obtained for a range of spheroidal FRP shells under static external pressures. Comparisons of the load carrying capacities are made for like geometries. It is shown that some prolate ellipsoids can be stronger, for up to 70% than the equivalent spheres. The effect of boundary conditions in the equatorial plane on the buckling strength is assessed for the diameter-to-wall- thickness ratio ranging from 100 to 500. Regions where the strength (FPF) rather than asymmetric bifurcation control the failure have been identified. Small perturbations in ply orientations, ±5°, have been introduced in order to assess their influence on the buckling strength. Both symmetric and asymmetric stacking with respect to the mid-plane have been analyzed (including random stacking).Initial shape imperfection positioned at the apex of a hemispherical head has been examined. The latter aimed at assessing the sensitivity of buckling pressure to deviations from perfect geometry. Results have been obtained for the lower bound approach based on the local flattening using the increased-radius. Imperfections in ellipsoids have also been studied. Axisymmetric modeling of all shells was used throughout in this study. Only the upper half of shells was modeled, and the issue of boundary conditions at the equatorial plane was also explored.

Three Pathways of Colonic Carcinogenesis in Rats.

Colorectal cancer (CRC) is one of the more intensively studied human malignancies. For many years, the general view has been that the vast majority of CRCs in humans evolve from conventional (tubular or villous) adenomas via the adenoma-carcinoma pathway. More recently, serrated colorectal polyps (hyperplastic polyps, sessile serrated polyps and traditional serrated adenomas) have emerged as an alternative pathway of colorectal carcinogenesis in humans. Archival sections from early experiments in Sprague-Dawley (SD) rats injected with dimethylhydrazine (DMH) were reviewed and the histology of colonic neoplasias was re-evaluated. Out of 215 colonic neoplasias, 9% were serrated adenomas and 6% serrated carcinomas, 11% conventional adenomas, 39% highly differentiated carcinomas, 21% gut-associated lymphoid tissue (GALT) carcinomas, 13% signet-ring cell carcinomas, and 1% villous carcinomas. In a more recent review of archived sections from DMH-treated rats with colonic GALT follicles, dysplastic crypts exhibiting asymmetrical bifurcations in GALT mucosa were found in 49% and colonic GALT carcinomas in 53% of 276 DMH-treated rats. Histology of the 146 colonic GALT-carcinomas revealed highly differentiated carcinoma in 75%, signet-ring cell carcinoma in 20%, mucinous carcinomas in 3% and mixed in the remaining 2%. Highly differentiated carcinomas were seen to evolve from dysplastic crypts with asymmetric bifurcations and from adenomas and signet-ring cell carcinomas, and from non-dysplastic crypts having goblet cells with marked anisocytosis. It is apparent that DMH treatment in SD rats induced conventional adenomas, conventional carcinomas, serrated adenomas, serrated carcinomas and GALT carcinomas. The paradigm permits to monitor in detail the early histological steps that epitomize the three alternative pathways of colonic carcinogenesis in SD rats. This model might be useful for analyzing different molecular aberrations evolving during the conventional adenoma-carcinoma pathway, the serrated carcinoma pathway, and the GALT carcinoma pathway of colonic carcinogenesis, under standard laboratory conditions.

Branching morphogenesis in the developing kidney is governed by rules that pattern the ureteric tree.

Metanephric kidney development is orchestrated by the iterative branching morphogenesis of the ureteric bud. We describe an underlying patterning associated with the ramification of this structure and show that this pattern is conserved between developing kidneys, in different parts of the organ and across developmental time. This regularity is associated with a highly reproducible branching asymmetry that is consistent with locally operative growth mechanisms. We then develop a class of tip state models to represent elaboration of the ureteric tree and describe rules for 'half-delay' branching morphogenesis that describe almost perfectly the patterning of this structure. Spatial analysis suggests that the observed asymmetry may arise from mutual suppression of bifurcation, but not extension, between the growing ureteric tips, and demonstrates that disruption of patterning occurs in mouse mutants in which the distribution of tips on the surface of the kidney is altered. These findings demonstrate that kidney development occurs by way of a highly conserved reiterative pattern of asymmetric bifurcation that is governed by intrinsic and locally operative mechanisms.

Nonlinear buckling analysis of shallow arches with elastic horizontal supports

The stiffness of the supports has an influence on the buckling modes and buckling loads of the arch. This paper investigates the in-plane nonlinear behavior and stability of shallow circular arches with elastic horizontal supports that are uniformly subjected to a radial load by the principle of virtual work. The three limiting shallowness values and the critical flexibility of the elastic horizontal supports are derived to differentiate the buckling mode. As the flexibilities of the elastic horizontal supports of an arch increase, the buckling load of the arch decreases, and the central radial displacement increases. And the buckling mode of the arch would then be changed from asymmetric bifurcation buckling to asymmetric bifurcation buckling after the occurrence of snap-through buckling. Then, snap-through buckling occurs, and finally, there is no buckling. Then the parameters including rise-to-span ratio(f/L) and load type are further investigated. An experimental model is designed to verify the analytical results. Finally, a design method for a shallow circular arch with elastic horizontal supports is proposed with the requirement of the elastic-plastic buckling load carrying capacity and the maximum horizontal displacement of the supports for engineering reference.

Quantitative visualization of asymmetric gas flow in constricted microchannels by using pressure-sensitive paint

Asymmetric flow in constricted microchannel devices was quantitatively investigated using a pressure-sensitive paint (PSP) technique. For microchannel devices with constriction ratios of 2 : 1 and 5 : 1, detailed pressure maps for the region around the constriction structure were obtained and enabled visualization of the flow field. Symmetric flow was observed in the microchannel device with a constriction ratio of 2 : 1 at the Reynolds number range 2–165. In the microchannel with a constriction ratio of 5 : 1, a deflected flow pattern was clearly identified from PSP measurements at Reynolds numbers exceeding 107. Furthermore, PSP measurements showed a pressure difference of up to 2.5 kPa between the two lateral locations corresponding to y = ±0.15 W (W is the microchannel width) downstream of the constriction at a Reynolds number of 279. The pressure difference resulted from asymmetric bifurcation of the flow.

Free instability of channel bifurcations and morphodynamic influence

Channel bifurcations are a fundamental element of a broad variety of flowing freshwater environments worldwide, such as braiding and anabranching rivers, river deltas and alluvial fans. River bifurcations often develop asymmetrical configurations with uneven discharge partition and a bed elevation gap between the downstream anabranches. This has been reproduced by one-dimensional (1-D) analytical theories which, however, rely on the empirical calibration of one or more parameters and cannot provide a clear and detailed physical explanation of the observed dynamics. We propose a novel two-dimensional (2-D) solution for the flow and bed topography in channel bifurcations based on an innovative application to a multi-thread channel configuration of the 2-D steady linear solution developed decades ago to study river bars and meandering in single thread river settings. The resonant value of the upstream channel aspect ratio, corresponding to the theoretical resonance condition of regular river meanders (Blondeaux &amp; Seminara,J. Fluid Mech., vol. 157, 1985, pp. 449–470) is the key parameter discriminating between symmetrical and asymmetrical bifurcations, in quantitative agreement with experimental observations and numerical simulations, and qualitatively matching field observations. Only when the aspect ratio of the upstream channel of the bifurcation exceeds resonance, is the bifurcation node able to trigger the upstream development of a steady alternate bar pattern, thus creating an unbalanced configuration. Ultimately, the work provides an analytical explanation of the intrinsic legacy between bifurcation asymmetry and the phenomenon of 2-D upstream morphodynamic influence discovered by Zolezzi &amp; Seminara (J. Fluid Mech., vol. 438, 2001, pp. 183–211).

Asymmetric bifurcation of thermally and electrically actuated functionally graded material microbeam.

In this paper, we investigate the symmetric snap-through buckling and the asymmetric bifurcation behaviours of an initially curved functionally graded material (FGM) microbeam subject to the electrostatic force and uniform/non-uniform temperature field. The beam model is developed in the framework of Euler-Bernoulli beam theory, accounting for the through-thickness power law variation of the beam material and the physical neutral plane. Based on the Galerkin decomposition method, the beam model is simplified as a 2 d.f. reduced-order model, from which the necessary snap-through and symmetry breaking criteria are derived. The results of our work reveal the significant effects of the power law index on the snap-through and symmetry breaking criteria. Our results also reveal that the non-uniform temperature field can actuate the FGM microbeam and induce the snap-through and asymmetric bifurcation behaviours.

Numerical simulations of the separation of elastic particles in a T-shaped bifurcation

In this work, we study the dynamics of an elastic particle suspended in an inertialess Newtonian fluid flowing through a channel with an orthogonal side branch (asymmetric T-shaped bifurcation) by means of 2D Arbitrary Lagrangian Eulerian (ALE) Finite Element Method (FEM) direct numerical simulations.The simulations show that, when the fluid is equally partitioned in the two downstream branches and the particle starts from the inflow channel centerline, a sufficiently deformable particle is deviated into the ‘side’ branch, at variance with a rigid particle, which remains in the ‘main’ outlet. The effects of the elastic capillary number and the confinement ratio on the particle trajectory and deformation near the bifurcation are investigated. We discuss how this device can be exploited for separating particles based on their elasticity.