Holographic flow visualization as a tool for studying three-dimensional coherent structures and instabilities

Holography is capable of three-dimensional (3D) representation of spatial objects such as fluid interfaces and particle ensembles. Based on this, we adapt it into a 3D flow visualization tool called Holographic Flow Visualization (HFV). This technique provides a novel means of studying spatially and temporally evolving complex fluid flow structures marked by a disperse phase or interfaces of different fluids. This paper demonstrates that HFV is a straightforward technique, especially when the In-line Recording Off-axis Viewing (IROV) configuration is used. The technique can be applied either as a stand-alone experimental tool for studying scalar-based coherent structures, flow instabilities, interactions of different fluids driven by fluid dynamics, interfacial phenomena, or as a precursor to volumetric 3D velocity vector field measurement of complex transient flow dynamics. Experimental results in several complex fluid flows and flames demonstrate the effectiveness of HFV. Different methods are used to mark flow structures undergoing different instabilities: 1) a vortex ring grown out of a drop of polymer suspension falling in water, 2) cascade of a bag-shaped drop of milk in water, and 3) internal flow structures of a jet diffusion flame.     

Simulation of particulate-filled composite deformation diagrams on the basis of a constitutive model of large plastic deformation for a polymer matrix

Deformation diagrams of particulate-filled polymers have been calculated on the basis of specific constitutive equations [1] for large plastic deformation of the polymer. Composite structure is represented by the Hashin polydisperse model [2]. Original finite-element (FE) code with triangular elements has been elaborated and used for the numerical solution of boundary value problems. Local achievement of a critical value by the elastic main strain was used as a fracture criterion. Engineering (force-elongation) diagrams were found to exhibit maxima for arbitrary filler fraction if the interfacial bond was perfect and for low loading at zero adhesion. Stress-strain diagrams with a yield maximum and draw minimum provide macroscopic neck-type localization. Further, the loading in the case of facilitated deboading results in the diminution of the difference between maximum and minimum drawing forces and then in the disappearance of the latter, which in turn provides the transition from localized to macrouni-form deformation. Young's modulus and the yield stress increase with filling in the case of absolute adhesion and decrease in the opposite case. Ultimate elongation sharply drops with an increase in filler fraction, and embrittlement occurs at a small fraction of inorganic particles if a perfect interfacial bond is present. Contrary, a decrease in ultimate elongation is much more gradual, and composites conserve ductile properties of the matrix up to a high portion of inclusions. The laws found qualitatively coincide with what is observed for real materials.     

Time-delayed map as a model for open fluid flow

It is shown that a time-delayed map for just one (chaotic) element whose feedback is periodically interrupted can be exactly mapped to a coupled map lattice model for open fluid flow.     

Micro- and nanoscale instabilities of deformation in polymers

The rate and magnitude of the deformation in polymers under constant compressive stresses at room temperature have been measured. The use of laser interferometer has made it possible to perform measurements at small intervals of variations in the specimen length Δl = 0.325 μm, and the analysis of the form of beats has made it possible to estimate oscillations of the strain rate in nanoscale displacements. It has been shown that the average strain rate of polymers continuously varies and no creeping interval with a constant rate is observed. At all stages of smooth variations in the average rate, jumps of its current values corresponding to Δl from several nanometers to a hundred and more nanometers have been found. Changes in the structure with an increase in the deformation manifest themselves in an increase in the size of nanoscale jumps and in a complication of their shape.     

A study of Peierls instabilities for a two-dimensional t-t' model

In this paper we study Peierls instabilities for a half-filled two-dimensional tight-binding model with nearest-neighbour hopping t and next nearest-neighbour hopping t' at zero and finite temperatures. Two dimerization patterns corresponding to the same phonon vector (π,π) are considered to be realizations of Peierls states. The effect of imperfect nesting introduced by t' on the Peierls instability, the properties of the dimerized ground state, as well as the competition between two dimerized states for each t' and temperature T, are investigated. It is found: (i). The Peierls instability will be frustrated by t' for each of the dimerized states. The Peierls transition itself, as well as its suppression by t', may be of second- or first-order. (ii). When the two dimerized states are considered jointly, one of them will dominate the other depending on parameters t' and T. Two successive Peierls transitions, that is, the system passing from the uniform state to one dimerized state and then to the other may take place with decrease of temperature. Implications of our results to real materials are discussed. Received 31 July 2001     

A model for ripple instabilities in granular media

We extend the model of surface granular flow proposed in [#!bcre!#] to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We discuss in detail how this mechanism can be described in a phenomenological way, and show that a flat bed is linearly unstable against ripple formation in a certain region of parameter space. We focus in particular on the (realistic) case where the migration velocity of the instability is much smaller than the grains' velocity. In this limit, the full dispersion relation can be established. We relate the critical wave vector to the mean hopping length and to the ratio of the flight time to the `stick' time. We provide an intuitive interpretation of the instability. Received: 30 January 1998 / Revised: 12 May 1998 / Accepted: 8 June 1998     

Methodology of physical mesomechanics as a basis for model construction in computer-aided design of materials

Conclusions The basic theses concerning the methodology of physical mesomechanics considered in this review show that a deformable solid can be represented as a microlevel system of self-consistent deformation structural elements of different scales. The law of scale invariance allows us to describe the behavior of very different materials under different loading conditions based on the element base for the scale levels of a deformable solid. The motion of volume structural elements of the deformation is described by the equations of mechanics (mesolevel and macrolevel), accommodation processes within the SEDs and on their boundaries — dislocation theory (microlevel). We have formulated an algorithm for construction of models for such multilevel systems which can be used in computer-aided design of materials. Examples of the classification of different structural materials have been presented based on the proposed algorithm.This work was done with the support of the Russian Foundation for Basic Research, Project No. 9301-16498.Institute of Physics of Strength and Materials Science, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 6–25, November, 1995.     

Elastic instabilities of polymer solutions in cross-channel flow

When polymer molecules pass near the hyperbolic point of a microchannel cross flow, they are strongly stretched. As the strain rate is varied at low Reynolds number (< 10(-2)), tracer and particle-tracking experiments show that molecular stretching produces two flow instabilities: one in which the velocity field becomes strongly asymmetric, and a second in which it fluctuates nonperiodically in time. The flow is strongly perturbed even far from the region of instability, and this phenomenon can be used to produce mixing.     

Quasilinear model of deformation of a stratified three-dimensionally inhomogeneous flow above a randomly inhomogeneous surface

We study the deformation of the wind velocity profile due to resonant interactions with waves radiated by the flow over a statistically homogeneous topography. The wind whose velocity vector changes its direction within a layer of finite thickness is considered. Quasilinear equations for the velocity components of the mean flow are derived under large Richardson, numbers and small Froude numbers. It is shown that the modulus of the wind velocity is constant in time and its direction angle satisfies the Riemann equation for simple waves. The flow deformation is determined by the average wave resistance force per unit square. The deformation of the wind velocity profile takes place within the layer between the Earth’s surface and the level where the wind change its direction to the opposite one. At large time scales, the wind velocity vector in this layer approaches the direction opposite to the near-surface one. Institute of Applied Physics, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 3, pp. 255–265, March 1999.     

Thermodynamic basis for a variational model for crystal growth

Variational models provide an alternative approach to standard sharp interface models for calculating the motion of phase boundaries during solidification. We present a correspondence between objective functions used in variational simulations and specific thermodynamic functions. We demonstrate that variational models with the proposed identification of variables are consistent with nonequilibrium thermodynamics. Variational models are derived for solidification of a pure material and then generalized to obtain a model for solidification of a binary alloy. Conservation laws for internal energy and chemical species and the law of local entropy production are expressed in integral form and used to develop variational principles in which a "free energy," which includes an interfacial contribution, is shown to be a decreasing function of time. This free energy takes on its minimum value over any short time interval, subject to the laws of conservation of internal energy and chemical species. A variational simulation based on this model is described, and shown for small time intervals to provide the Gibbs-Thomson boundary condition at the solid-liquid interface.     

无碰撞电流片低频电磁模不稳定性：MHD模型

利用含无电阻广义Ohm定律的可压缩磁流体力学(MHD)理论，研究了在具有剪切磁场的无碰撞电流片中低频电磁模不稳定性，假定等离子体压力各向同性，推导出了三维扰动传播波模的色散关系.色散关系的数值求解集中在电流片中间平面(z=0)和半厚度边缘(z=1)上，并分别考虑了二维传播和三维传播，以及不同的离子惯性长度情况.主要结果如下：1)对 于二维扰动传播(k_z=0)的波，在z=0平面上，Alfven波增长率最大，不稳定的波 频率 和波数范围也更宽.离中间平面越远，增长率越小，波数区域越小.同时，随着离子惯性长度 的增大，Alfven波不稳定性的增长率变大.2)对于三维扰动传播(k_z≠0)的波， 哨声是 不稳定的.在电流片中间平面上，哨声有明显的增长率；而在离子惯性区外边，哨声的增长 率还变大.3)在电流片中间(z=0)平面上，低频波主要是电流不稳定性激发的.在离中间 平面较远处，电流、密度和压力的梯度不稳定性变得更重要. 关键词： 无碰撞电流片 磁流体力学 色散关系 不稳定性     

Fragmentation instabilities of a drop as it falls in a miscible fluid

We review here a series of experiments on the fragmentation instabilities that a liquid drop undergoes as it falls inside a fluid with which it is miscible, so called the solvent. Motivated by the original experiments initiated by Thomson and Newall in 1885, we started to investigate this subject more than one decade ago, encountering up to date a number of challenging problems in hydrodynamical instabilities, complicated by the presence of transient interfaces between the drop and the solvent. In particular, we have shown that when a drop of liquid is deposited over the surface of the same liquid, it falls down inside the solvent because the energy associated to its surface tension against air is instantaneously converted into kinetic energy. As a consequence, a very fast fluid injection takes place as the drop touches the free surface of the solvent and the drop enters inside the solvent. Due to the hydrodynamical instabilities related to the large velocity gradients, it develops into a ring that expands radially. The ring continues to go downwards inside the solvent until it stops at a certain height due to viscous dissipation. In the first stages of the ring expansion, a fluid membrane remains attached to the ring, so-called “turban" for its shape, which is concave or convex depending on the sign of the density difference between the drop and the solvent. When a small density difference is introduced between the drop and the solvent, the ring becomes unstable because of density gradients and it fragments into smaller droplets. On their turn, the secondary droplets may undergo the same instability and may fragment again, so that a cascade of fragmentation takes place. If the density difference is positive, that is, the drop is heavier than the solvent, the secondary droplets continue to go down deeper inside the solvent, until the whole process is washed out by the slow diffusion of the concentration gradients. When the density difference between the drop and the solvent is negative, then the secondary droplets rise up to the free surface of the solvent, where they are distorted by the equivalent of an impact with a rigid wall. Universal scaling laws for the cascade of fragmentation and for the dynamical behavior of the drop have been derived and accompany the experimental observations.     

Electron pairing as a source of cyclic instabilities in enzyme catalysis

Enzymatic reactions can be interpreted in terms of a thermodynamically consistent potential surface with different pathways for complex formation and decomposition. The construction suggests that unstable pairing of parallel spin electrons provides the basis for pathway switching.     

Chaotic flow in a model for repeated yielding

Chaos exhibited by a model introduced in the context of repeated yielding is studied. The model shows an infinite sequence of period-doubling bifurcations with an exponent δ = 4.67 ± 0.1. The associated one-dimensional map and the projection of the strange attractor are also studied.