Drop formation in liquid-liquid systems

Conclusion An experimental method for determining the momentum flux on a drop for a nozzle with an arbitrary fluid velocity profile at the exit has been described. I t was observed that the variation of drop volume with flow rate can differ some-what from that conceived in previous drop formation models, in that drop volume does not necessarily vary smoothly with flow rate. High-speed motion pictures of drop formation and detachment show that the drop oscillates as it grows. I t is believed that this oscillation is related to the observed unsteady variation of drop volume with flow rate. Presently with General Dynamics Space Systems Division, San Diego/CA, USA     

Motions of elastic solids in fluids under vibration

Motion of a rigid or deformable solid in a viscous incompressible fluid and corresponding fluid–solid interactions are considered. Different cases of applying high frequency vibrations to the solid or to the surrounding fluid are treated. Simple formulas for the mean velocity of the solid are derived, under the assumption that the regime of the fluid flow induced by its motion is turbulent and the fluid resistance force is nonlinearly dependent on its velocity. It is shown that vibrations of a fluid’s volume slow down the motion of a submerged solid. This effect is much pronounced in the case of a deformable solid (i.e., gas bubble) exposed to near-resonant excitation. The results are relevant to the theory of gravitational enrichment of raw materials, and also contribute to the theory of controlled locomotion of a body with an internal oscillator in continuous deformable (solid or fluid) media.     

On a stress-power-based characterization of second-gradient elastic fluids

An algebraic characterization of fluidity applicable to second-gradient materials is argued, individuating a collection of deformations from a reference placement that entail no pointwise stress-power expenditure. For simplicity, the characterization in question is developed in the context of elastic materials, within which general representations for the stress response, both Cauchy-like and Piola-like, of elastic second-gradient fluids are derived.     

Ideal elastic fluids of different viscosity and elasticity levels

Four constant viscosity, highly elastic fluids of different viscosity and elasticity levels are presented. The viscosity ranges from 4 × 10^?3 to 5.0 Pa s and the Maxwell relaxation time varies from 0.09 to 4.5 s. The steady and dynamic shear properties are determined. These fluids comply with the requirements of the simple fluid theory except for theG′ andN ₁/2 data where a slight deviation is observed. The results suggest the possibility of preparing a wide range of constant viscosity elastic fluids with specific values of viscosity and relaxation time by manipulating polymer molecular parameters as well as polymer concentration, solvent viscosity and salt addition. The effects of each of these parameters on the rheological behaviour are examined.     

Finite deflection dynamics of elastic beams

Solutions are obtained for the problem of an infinite elastic beam subjected to essentially constant velocity boundary conditions at one point of the beam. The effects of finite deflections, normal force, rotatory inertia and shear deformation are included. The equations of the problem are converted into non-dimensional form and a perturbation approach is used to obtain a consistent approximation. Numerical solutions are obtained for the bending moment, shear force and the normal force for different velocities of impact. It is shown that the solution to the problem depends on a combined geometrical and material parameter which does not vary significantly for compact sections and a loading parameter which determines the amplitude of the response. Finally the linear Timoshenko beam theory is shown to predict the bending moment and shear force extremely well even when the deflections are large enough to cause appreciable stretching of the centroidal axis.     

Nonlinear dynamics of oriented elastic solids

Based on a continuum model for oriented elastic solids the set of nonlinear dispersive equations derived in Part I of this work allows one to investigate the nonlinear wave propagation of the soliton type. The equations govern the coupled rotation-displacement motions in connection with the linear elastic behavior and large-amplitude rotations of the director field. In the one-dimensional version of the equations and for two simple configurations an exhaustive study of solitons is presented. We show that the transverse and/or longitudinal elastic displacements are coupled to the rotational motion so that solitons, jointly in the rotation of the director and the elastic deformations, are exhibited. These solitons are solutions of a system of linear wave equations for the elastic displacements which are nonlinearly coupled to a sine-Gordon equation for the rotational motion. For each configuration, the solutions are numerically illustrated and the energy of the solitions is calculated. Finally, some applications of the continuum model and the related nonlinear dynamics to several physical situations are given and additional more complex problems are also evoked by way of conclusion.     

Purely elastic interfacial instabilities in superposed flow of polymeric fluids

Purely elastic interfacial stability of superposed plane Poiseuille flow of polymeric liquids has been investigated utilizing both asymptotic and numerical techniques. It is shown that these instabilities are caused by an unfavorable jump in the first normal stress difference across the fluid interface. To determine the significance of these instabilities in finite experimental geometries, a comparison between the maximum growth rates of purely elastic instabilities with instabilities driven primarily by a viscosity or a combined viscosity and elasticity difference is made. Based on this comparison, it is shown that purely elastic interfacial instabilities can play a major role in superposed flow of polymeric liquids in finite experimental geometries.     

Shear motions of elastic fluids for a given tangential stress

Stationary and nonstationary modes of elastic fluid motion for a given constant strain rate =const were studied under simple shear conditions, theoretically in [1, 2] as compared with experiment; time dependences of the normal and tangential stresses were examined for the emergence into stationary flow and their relaxation from steady flow. These results permitted a study of the relaxation characteristics of elastic fluids. However, no less interesting are the lagging (retardation) effects in elastic fluids, which can be studied in modes giving the shear stress ₁₂(). In this paper, the two most widespread shear modes in practice are examined theoretically and experimentally for a given ₁₂: the mode of arrival at the stationary flow from the state of rest for ₁₂=const and the mode of retardation (elastic recovery) from stationary flow. Theoretical computations are performed on a model describing large elastic strains. The experiment was performed on a concentrated polymer solution. Quantitative correspondence between theory and experiment is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 9–13, July–August, 1976.     

Flow visualization of the elastic Taylor-Couette instability in Boger fluids

Flow visualization is performed on an elastically-dominated instability in several similar Boger fluids in Taylor-Couette flow. The onset and evolution of secondary flow are observed over a range of shear rates using reflective mica platelet seeding. Sequences of ambiently and sheet-illuminated images were digitally processed. Rotation of the inner cylinder was ramped from rest to its final value over a time on the order of a polymer relaxation time. Dilute solutions of high molecular weight polyisobutylene in oligomeric polybutene manifest a flow transition at a Deborah number, De _s = _s 1.5 with a Taylor number of 0.00022 in a cell with dimensionless gap ratio = 0.0963. At this transition, simple azimuthal shearing is replaced by steady, roughly square, axisymmetric counter-rotating vortices grossly similar to the well-known Taylor vortex flow that is observed at De _s = 0, Ta = 3612. At De _s = 3.75, Ta = 0.0014, an axisymmetric oscillatory secondary flow develops initially but is replaced by the steady vortices. At De _s = 7.5, Ta = 0.0054, the oscillatory and vortex flow coexist and possess an irregular cellular cross-section. A wide span of growth rates is observed: the ratio of onset to polymer relaxation time ranges from 170000 at De _s = 1.5 to O(10) at De _s > 5. The role of inertia was explored through changing the solvent viscosity. A transition similar to the one that occurs at De _s = 3.75, Ta = 0.0014, from the base azimuthal shearing flow to axisymmetric vortices, was also observed with a much lower viscosity fluid at De _s = 3.3, Ta = 74.     

弹性动力学的多变量响应问题的解法

基于瞬时混合变分原理与乘积型二元三次 B样条函数 ,以板壳为例 ,建立样条动力方程。引入样条参数及其对时间的导数作为状态变量 ,导出状态方程。对空间域采用混合样条元法 ,对时间域采用现代控制论中的状态空间法。文末数值算例表明 ,计算精度与效率是令人满意的。本文方法对计算多输入与多输出 ,时不变与时变系统和线性与非线性系统等多变量动力响应问题 ,有广阔的应用与发展前景     

Anomalous dynamics response of nonlinear elastic bar

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Turbulent flow of mildly elastic fluids through rotating straight circular tubes

The turbulent flow of mildly elastic drag reducing fluids through a straight tube rotating around an axis perpendicular to its own is analysed using boundary layer approximations. The momentum integral approach is used and the governing equations have been solved numerically using the Runge-Kutta-Merson method. The influence of the Deborah number on the velocity distribution and the boundary layer thickness has been exemplified through the analysis. NCL Communication No. 3354.     

A contour integral approach to some cavity flows of elastic fluids

This papers considers a contour integral approach to some cavity flows of elastic fluids. The fluids are described by integral constitutive equations and therefore require consideration of strain history. Strain calculations can consume a large amount of computer resource and so we develop an efficient approach to this aspect. Both slider and calender driven flows are considered.     

Small vibrations of a linearly elastic body surrounded by heavy,incompressible, non-Newtonian fluids with free surfaces

We consider the small transient motions of a coupled system constituted by a linearly elastic body and two heavy, incompressible, non-Newtonian fluids.Through a formulation in terms of non-linear evolution equations in Hilbert spaces of possible states with finite mechanical energy, we obtain existence and uniqueness results and study the influence of gravity. To cite this article: C. Licht, Tran Thu Ha, C. R. Mecanique 333 (2005).     

Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids

Wave propagation in a porous elastic medium saturated by two immiscible fluids is investigated. It is shown that there exist three dilatational waves and one transverse wave propagating with different velocities. It is found that the velocities of all the three longitudinal waves are influenced by the capillary pressure, while the velocity of transverse wave does not at all. The problem of reflection and refraction phenomena due to longitudinal and transverse wave incident obliquely at a plane interface between uniform elastic solid half-space and porous elastic half-space saturated by two immiscible fluids has been analyzed. The amplitude ratios of various reflected and refracted waves are found to be continuous functions of the angle of incidence. Expression of energy ratios of various reflected and refracted waves are derived in closed form. The amplitude ratios and energy ratios have been computed numerically for a particular model and the results obtained are depicted graphically. It is verified that during transmission there is no dissipation of energy at the interface. Some particular cases have also been reduced from the present formulation.