Dynamics and rheology of Janus drops in a steady shear flow

The behavior and rheology of a dispersion of Janus drops (or Janus emulsion) under a steady shear flow are explored in the infinite dilution limit. To achieve analytical progress, the Janus drops are assumed to consist of a pair of fluids bounded to hemispherical domains of equal radii. At ‘freely’ suspended conditions the Janus drops undergo periodic orbits in a shear flow that are intermediate to that of a solid sphere and a disk that depend on the viscosities of the internal fluids. Non-Newtonian behavior is found for this system on account of the anisotropic hydrodynamics of the Janus drops. The viscosity of the Janus emulsion that corresponds to the minimum energy of dissipation is analogous to that derived by Taylor (1932) for a dispersion of simple drops. It is also found that an external force can induce the Janus drops to adopt a preferential orientation in a shear flow. Interestingly, a neutrally buoyant Janus drop with a displaced center of gravity can migrate lateral to the undisturbed shear flow; it is inferred that this phenomenon can lead to spatial-dependent rheology in pressure-driven flows.     

Behavior of a net of fibers linked by viscous interactions: theory and mechanical properties

This paper presents an investigation of the macroscopic mechanical behavior of highly concentrated fiber suspensions for which the mechanical behavior is governed by local fiber-fiber interactions.The problem is approached by considering the case of a net of rigid fibers of uniform length, linked by viscous point interactions of power-law type. Those interactions may result in local forces and moments located at the contacting point between two fibers, and respectively power-law functions of the local linear and angular velocity at this point.Assuming the existence of an elementary representative volume which size is small compared to the size of the whole structure, the fiber net is regarded as a periodic assembly of identical cells. Macroscopic equilibrium and constitutive equations of the equivalent continuum are then obtained by the discrete and periodic media homogenization method, based on the use of asymptotic expansions.Depending on the order of magnitude of local translational viscosities and rotational viscosities, three types of the equivalent continua are proved to be possible. One of them leads to an effective Cosserat medium, the other ones being usual Cauchy media. Lastly, formulations that enable an effective computation of constitutive equations are detailed. They show that the equivalent continuum behaves like an anisotropic power-law fluid.     

Convective magnetohydrodynamic two fluid flow and heat transfer in an inclined channel

 The problem of fully developed free convection two fluid magnetohydrodynamic flow in an inclined channel is investigated. The governing momentum and energy equations are coupled and highly nonlinear due to dissipation terms, solutions are found employing perturbation technique for small values of Pr · Ec (=ɛ) the product of Prandtl number and Eckert number. Effects of Grashof number, Hartmann number, inclination angle, the ratios of electrical conductivities, viscosities and heights of two fluids on the flow are explored. It is observed that the flow can be controlled effectively by suitable adjustment of the values for the ratios of heights, electrical conductivities and viscosities of the two fluids. Received on 10 December 1999     

A new method to determine viscosity of liquids using vibration principles

A new method for determining viscosity of liquids is examined. The method employs the principles of vibration and measures the viscous damping due to the motion of a liquid placed in a cylindrical tube. The apparatus and the test liquid are treated as a dynamic system and the measured mechanical impedances are used to calculate energy dissipation due to the viscous damping. The newly designed apparatus is able to generate shear deformations in the liquid without using moving solid surfaces. A harmonic varying force with a frequency close to the resonance frequency of the system is applied through a piston and the resulting velocities of the oscillations generated in the system are measured. Liquids with higher viscosities result in lower velocities due to the higher damping. Analytical equations are provided to relate the viscous damping of the dynamic system to the viscosity of the liquids. The viscosities obtained from the proposed method are in good agreement with the ones obtained from standard rotational viscometry using a cone and plate geometry.     

Wavelet analysis of coherent structures in a three-dimensional mixing layer

Wavelet analysis is applied to the results obtained by the direct numerical simulation of a three-dimensional (3D) mixing layer in order to investigate coherent structures in dimension of scale. First, 3D orthonormal wavelet bases are constructed, and the corresponding decomposition algorithm is developed. Then the Navier-Stokes equations are transformed into the wavelet space and the architecture for multi-scale analysis is established. From this architecture, the coarse field images in different scales are obtained and some local statistical quantities are calculated. The results show that, with the development of a mixing layer, the energy spectrum densities for different wavenumbers increase and the energy is transferred from the average flow to vortex structures in different scales. Due to the non-linear interactions between different scales, cascade processes of energy are very complex. Because vortices always roll and pair at special areas, for a definite scale, the energy is obtained from other scales at some areas while it is transferred to other scales at other areas. In addition, energy dissipation and transfer always occur where an intense interaction between vortices exists. The project supported by the Research Fund for the Doctoral Program of Higher Education and the National Natural Science Foundation for Outstanding Youth of China (19925210)     

A rheological theory for liquid crystal thin films

A macroscopic rheological theory for compressible isothermal nematic liquid crystal films is developed and used to characterize the interfacial elastic, viscous, and viscoelastic material properties. The derived expression for the film stress tensor includes elastic and viscous components. The asymmetric film viscous stress tensor takes into account the nematic ordering and is given in terms of the film rate of deformation and the surface Jaumann derivative. The material function that describes the anisotropic viscoelasticity is the dynamic film tension, which includes the film tension and dilational viscosities. Viscous dissipation due to film compressibility is described by the anisotropic dilational viscosity. Three characteristic film shear viscosities are defined according to whether the nematic orientation is along the velocity direction, the velocity gradient, or the unit normal. In addition the dependence of the rheological functions on curvature and film thickness has been identified. The rheological theory provides a theoretical framework to future studies of thin liquid crystal film stability and hydrodynamics, and liquid crystal foam rheology. Received: 9 October 2000 Accepted: 6 April 2001     

On Gear Modelling in Multistage Rotary Vane Engines

A discussion of the dynamics of a multistage rotary vane engine is given in terms of a simplified model for combustion driving torques, power dissipation, and torque transmission. Torque transmission is effected by conjugate gear pairs attached to each unit of the engine. An argument for the design of such pairs is presented so that unwanted torque fluctuations in a flywheel attached to a member of the pair can be significantly attenuated. It is suggested that a variant of simple Cosserat dynamics offers a useful modelling tool for discussing the complex interaction between interacting gear teeth. A quasi-stationary analysis is used to place bounds of a particular choice of conjugate gear coupling in the presence of such interactions. It is concluded that a multistage rotary vane engine with at least two units can be usefully coupled to a single flywheel via a well-defined conjugate gear system that attenuates unwanted torque fluctuations over a broad range of rotary speeds.     

Effect of metachronal phasing on the pumping efficiency of oscillating plate arrays

An aqueous solution of sodium iodide and zinc iodide is proposed as a fluid that matches the refractive index of a solid manufactured by rapid prototyping. This enabled optical measurements in single-phase flow through porous structures. Experiments were also done with an organic index-matching fluid (anisole) in porous structures of different dimensions. To compare experiments with different viscosities and dimensions, we employed Reynolds similarity to deduce the scaling laws. One of the target quantities of our investigation was the dissipation rate of turbulent kinetic energy. Different models for the dissipation rate estimation were evaluated by comparing isotropy ratios. As in many other studies also, our experiments were not capable of resolving the velocity field down to the Kolmogorov length scale, and therefore, the dissipation rate has to be considered as underestimated. This is visible in experiments of different relative resolutions. However, being near the Kolmogorov scale allows estimating a reproducible, yet underestimated spatial distribution of dissipation rate inside the porous structure. Based on these results, the $k-\varepsilon$ model was used to estimate the turbulent diffusivity. Comparing it to the dispersion coefficient obtained in the same porous structure, we conclude that even at $Re_p=500$ the turbulent diffusivity makes up only a small part of mass transfer in axial direction. The main part is therefore attributed to Taylor dispersion.     

Non-Newtonian behaviour of simple liquids

A new method is presented for determining essentially exact non-Newtonian behaviour of simple liquids such as liquid argon, chlorine and water, whose molecules can be roughly represented by spherically averaged Lennard-Jones pair potentials. The technique of Non-Equilibrium Molecular Dynamics, NEMD, shows that even these simple liquids shear thin, have a second-Newtonian region and shear thicken. These phenomena have been associated in the past with complex mechanisms and structures. The appearance of these effects in such simple systems demands a re-evaluation of the former approaches. As with experimental techniques the viscosities were most accurately obtained only within a certain shear rate range. As a result, literature analytical fits were sought for the data. The Carreau and Cross models fit the simple liquids' shear thinning curves at densities slightly below the normal freezing density whereas a Herschel-Bulkley expression was found most suitable at densities in excess of 15% of this. Extreme shear thinning behaviour is associated with the creation of long range order within the liquid.     

Dissipation and inter-scale transfer in fully coupled particle and fluid motions in homogeneous isotropic forced turbulence

This work examines in detail the coupling mechanism between a stationary, homogeneous and isotropic turbulent (HIT) flow and particles, including the effect of particle-particle collisions. In order to illustrate how the physics can be elucidated of four-way interactions, a series of coupled Direct Numerical Simulations (DNS) of forced HIT are performed on a 128³ periodic box at two Taylor Reynolds numbers, 35.4 and 58.0, with interacting particles of different global Stokes numbers and volume fractions. The results show that fluid dissipation decreases up to 32% with increasing global Stokes numbers and particle volume fractions. Moreover, the corresponding dissipation when ignoring particle-particle collisions is over-estimated by up to 7% compared to the fully coupled simulations. A spectral analysis of the coupling mechanism reveals that the particles transfer energy from the large to the small scales, thereby explaining the difference in dissipation. Finally, a model spectrum for the coupling between the turbulent fluid and the particles is proposed.     

Viscous flow through the swirl chamber of a pressure-swirl atomizer

We study theoretically the viscous flow through the swirl chamber of a pressure-swirl atomizer. The aim is to predict quantitatively the flow rate of a given liquid driven by a given pressure difference across the atomizer in order to explain the counter-intuitive experimental finding that, for moderate liquid dynamic viscosities, at a given driving pressure difference and atomizer geometry, a higher liquid viscosity results in a higher flow rate. The concept for the flow analysis is to subdivide the flow field in the swirl chamber into zones allowing for neglect of velocity components or boundary-layer simplification. The result is a quantitative prediction of the liquid flow rate for a given driving pressure difference and atomizer geometry, and for given liquid properties relevant for the discharge from the atomizer. Flow rates are compared to experimental data from various sources and show good agreement. Another part of the results is the diameter of the air core formed around the symmetry axis of the swirl chamber, which is of sub-millimetric order here. This result is compared to different experimental correlations and also shows very good agreement. For small values of the swirl velocity and/or very high liquid viscosities, the air core breaks down. The phenomenon of air core break down has been analysed, and it is shown that for high viscosities the air core breaks down due to weak swirl velocity.     

Surface tension models with different viscosities

Surface tension in ILB models for fluids with different viscosities and different numbers of rest populations is derived, starting from the so-called mechanical definition. It is shown that the standard perturbation, inserted into these models in order to create surface tension, should be slightly modified for models with different viscosities in order to avoid the dependence of surface tension upon the actual phase distribution. The analytical results are numerically confirmed by mechanical and bubble tests. It is demonstrated also that the perturbation of the lattice Boltzmann equation gives rise to the appearance of anisotropic terms in population solutions related to anomalous currents and density fluctuations. When particular values of the eigenvalues of the collision operators are used, these spurious currents are annihilated in the time-independent solutions of the mechanical tests in arbitrarily inclined channels when bounce-back conditions are imposed at the solid boundaries.     

Finite volume scheme for the solution of fluid flow problems on unstructured non‐staggered grids

A recently developed non‐staggered methodology which uses the principle of applying fourth‐order dissipation to the governing pressure‐correction equation is developed so it can be applied to unstructured grids. A finite volume methodology is used for discretization. The fourth‐order dissipation term is found using second‐order gradient operators. This makes it straightforward to incorporate the dissipation term on unstructured grids. The new methodology is compared with solutions from a standard finite volume second‐order flow solver and is also tested for a standard laminar driven‐lid flow problem with grids systems that do not have a uniform structure. Finally, we demonstrate how the new methodology can be used to predict flow over a wavy boundary. Copyright © 2002 John Wiley & Sons, Ltd.     

Reflection and transmission of regular waves at a surface-pitching slotted barrier

The interactions between regular surface waves and a surface-pitching slotted barrier are investigated both analytically and experimentally.A quasi-linear theory is developed using the eigenfunction expansion method.The energy dissipation within the barriers is modeled by a quadratic friction factor,and an equivalent linear dissipation coefficient,which is depth-varying,wave-height dependent,is introduced to linearize the matching condition at the surface-pitching barrier.By comparing the theoretical results with laboratory experiments,it is shown that the present method can satisfactorily predict the variation of the reflection and transmission coefficients with wave height.     

Thermal dispersion and viscous dissipation effects on non-darcy mixed convection in a fluid saturated porous medium

Mixed convection flow and heat transfer about an isothermal vertical wall embedded in a fluid saturated porous medium with uniform free stream velocity is considered and the effects of thermal dispersion and viscous dissipation in both aiding and opposing flows are analysed. Similarity solution is not possible due to the inclusion of the viscous dissipation term, series solution is obtained, first and second order effects of dissipation revealed that viscous dissipation lowers the heat transfer rate. Observations also revealed that the thermal dispersion effect enhances the heat transfer rate and the effect of viscous dissipation is observed to increase with increasing values of the dispersion parameter. Received on 21 March 1997     

Numerical assessment of a shock‐detecting sensor for low dissipative high‐order simulation of shock–vortex interactions

Considering the importance of high‐order schemes implementation for the simulation of shock‐containing turbulent flows, the present work involves the assessment of a shock‐detecting sensor for filtering of high‐order compact finite‐difference schemes for simulation of this type of flows. To accomplish this, a sensor that controls the amount of numerical dissipation is applied to a sixth‐order compact scheme as well as a fourth‐order two‐register Runge–Kutta method for numerical simulation of various cases including inviscid and viscous shock–vortex and shock–mixing‐layer interactions. Detailed study is performed to investigate the performance of the sensor, that is, the effect of control parameters employed in the sensor are investigated in the long‐time integration. In addition, the effects of nonlinear weighting factors controlling the value of the second‐order and high‐order filters in fine and coarse non‐uniform grids are investigated. The results indicate the accuracy of the nonlinear filter along with the promising performance of the shock‐detecting sensor, which would pave the way for future simulations of turbulent flows containing shocks. Copyright © 2014 John Wiley & Sons, Ltd.     

基于能量耗散分析的混凝土随机疲劳损伤模型

基于微-细观随机断裂模型(MMSF)发展了一类混凝土随机疲劳损伤模型。该模型将MMSF中的微弹簧视为一能量耗散单元并考察了其跨尺度的能量耗散过程。在纳观尺度,引入速率过程理论描述裂纹的扩展速度,并基于裂纹层级模型和自相似假定完成从纳观尺度到微观尺度的过渡。由此建立了微弹簧在疲劳荷载作用下的多尺度耗能描述。此外,为了考虑疲劳加载中混凝土多条裂纹的相互影响,引入了包含损伤扩展效应和损伤愈合效应的疲劳损伤因子来修正耗能表达。通过与相关试验的对比,证明了该模型能反映疲劳荷载作用下混凝土的主要力学行为,如疲劳损伤三阶段特点、疲劳寿命的离散性和疲劳寿命随加载频率的变化趋势等。     

Constraint-induced restriction and extension operators with applications

The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show that, through the Hodge orthogonal decomposition, a pair of bounded linear operators, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence, we use it to calculate the eigenvalues of the Stokes operator.     

Investigation of droplet collisions for solutions with different solids content

The collision behaviour of droplets and the collision outcome are investigated for high viscous polymer solutions. For that purpose, two droplet chains produced by piezoelectric droplet generators are directed towards each other at a certain angle so that individual droplet pairs collide. For recording the collision event, one double-image and one high-speed CCD camera were used. One camera is positioned perpendicular to the collision plane recording the outcome of the collision, and the second camera is aligned parallel to the collision plane to assure that the droplet chains are exactly in one plane. A new approach for tracking droplets in combination with an extended particle tracking velocimetry algorithm has been developed. Time-resolved series of pictures were used to analyse the dynamics of droplet collisions. The three different water soluble substances were saccharose and 1-Ethenyl-2-pyrrolidone (PVP) with different molecular weights (K17, K30). The solvent was demineralised water. The solids contents ranged from 20 to 60 %, 5 to 25 % and 5 to 35 %, yielding dynamic viscosities in the range of 2–60 mPa s. Results were collected for different pairs of impact angles and Weber numbers in order to establish common collision maps for characterising the outcomes. Here, relative velocities between 0.5 and 4 m/s and impact parameters in the interval from 0 to 1 for equal-sized droplets (Δ = 1) have been investigated. Additionally, satellite formation will be discussed exemplarily for K30. A comparison with common models of different authors (Ashgriz and Poo in J Fluid Mech 221:183–204, 1990; Estrade et al. in Int J Heat Fluid Flow 20:486–491, 1999) mainly derived for low viscous droplets revealed that the upper limit of their validity is given by an Ohnesorge number of Oh = 0.115 and a capillary number of Ca = 0.577. For higher values of these non-dimensional parameters and hence higher dynamic viscosities, these models are unable to predict correctly the boundaries between collision scenarios. The model proposed by Jiang et al. (J Fluid Mech 234:171–190, 1992), which includes viscous dissipation, is able to predict the boundary between coalescence and stretching separation for higher viscosities (i.e. Oh > 0.115 and Ca > 0.577). However, the model constants are not identical for different solution properties. As a conclusion, an alteration of the collision appearance takes place because of the relative importance between surface tension and viscosity.     

AN ARTIFICIAL DISSIPATION FORMULATION FOR A SEMI-IMPLICIT,PRESSURE BASED SOLUTION SCHEME FOR VISCOUS AND INVISCID FLOWS

The formulation of artificial dissipation terms for a semi-implicit, pressure based flow solver, similar to SIMPLE type formulations, is presented and is applied to both the Euler and the Navier-Stokes equations. The formulation uses generalized coordinates and a non-staggered grid. This formulation is compared to some SIMPLE and time marching formulations. The relationship between SIMPLE and time marching formulations is discussed briefly. The artificial dissipation inherent in some commonly used semi-implicit formulations, e.g. upwind differencing, powerlaw, QUICK and pressure weighting, is investigated. The scheme used here includes these dissipation terms directly, but retains the ability to mimic previous schemes. The potential for errors introduced by the simultaneous use of artificial dissipation in the continuity equation and central differencing of convective terms, is revealed. The effect of the amount of dissipation on the accuracy of the solution and the convergence rate is quantitatively demonstrated for two-dimensional inviscid flow in a mildly curved duct, three-dimensional laminar flow in a square cross section elbow with strong secondary flows, and two-dimensional turbulent flow through a turbine nozzle. The spurious effects of artificial dissipation, particularly second order dissipation, inherent in some commonly used algorithms, is clearly shown. The effect of artificial dissipation on the convergence rate is also demonstrated. The main conclusion drawn from the results is that the minimum amount of artificial dissipation that gives the required accuracy, but also an adequate convergence rate for a particular case, has to be used. This amount of dissipation is case dependent. The direct inclusion of artificial dissipation terms provides control over the amount of dissipation used.