Instability interaction with flow

Electric fields may interact with flows fed by hydrostatic or pumping action [91]. Flows driven by electroosmotic means may be mixed as well by the action of fluctuating electric fields, which creates oscillating electroosmotic flows and has been termed electrokinetic instability (EKI) [25, 93], In this way, rapid stretching and folding of material lines are induced, not unlike the effect of stirring. In one realized example, comparatively low frequencies, below -100 Hz, and electric field strengths in excess of 100 V mm1 are applied for channels with dimensions of about 50 pm [25],... 

Turing patterns interacting with flow Recently the influence of a flow field on the Turing instability and the patterns that result have been considered [105-108]. In order not to scramble the Idring patterns only flows with very weak mixing properties may be considered. A low Reynolds number flow in a tubular reactor may provide an experimental realization [109]. If the chemical reaction is passive to the flow (i.e. it does not perturb the imposed... 

This chapter considers the first group of instabilities and introduces the analysis of processes implying an interaction with external flow-field perturbahons. This is exemplified by investigations of coupling between pressure waves and plane flames and also between an external acceleration field and flame fronts. The coupling between flow perturbations and flames giving rise to heat release unsteadiness and coupling with acoushc modes is considered in Chapter 5.2, which deals with the relationship between perturbed flame dynamics and radiated acoustic field, a fundamental process of thermo-acoustic instabilities. 

Next, one performs the normal mode analysis, i.e. the flow instabilities are governed by discrete eigenmodes those do not interact with each other and are studied separately. Equations (2.3.8) to (2.3.11) are variable coefficient linear partial differential equations but, they do not admit analytic solutions. However, with the help of normal mode analysis, this can be further simplified. As the coefficients of these equations are functions of the wall normal co-ordinate, it is natural to expand the disturbance quantities in the following manner,... 

Tube vibrations in a tube bundle are caused by oscillatory phenomena induced by fluid (gas or liquid) flow. The dominant mechanism involved in tube vibrations is the fluidelastic instability or fluidelastic whirling when the structure elements (i.e., tubes) are shifted elastically from their equilibrium positions due to the interaction with the fluid flow. The less dominant mechanisms are vortex shedding and turbulent buffeting. 

Particles elevate the viscosity of the medium (water) through viscous interaction with the water. Thermal or Brownian motion of the particles contributes to this at low rates of shear, but this contribution diminishes with increasing shear rate. At very high rates of shear and with high particle volume fraction, instabilities in the tendency of particles to align in layers with the flow field can result in dilatency. The rheology of hard sphere dispersions has become quite well understood and quantified by theory and experiment, especially in the last decade. 

Droplet production by droplet stream generators takes place by pinch-off of liquid portions from jets. A trivial prerequisite for the application of this technique of drop production is, therefore, the formation of a laminar liquid jet from a round orifice or nozzle. The conditions of liquid flow through the orifice required to form a laminar jet are discussed in Sect. 26.3 below. Once the laminar jet is formed, its linear temporal instability against a disturbance with a non-dimensional wave number ka = 2nalX (with the wavelength X of the disturbance and the jet radius a) in a gaseous ambient medium under the action of surface tension, neglecting both the liquid viscosity and the dynamic interaction with the ambient gas, is described by the dispersion relation... 

The mechanisms by which freely rising bubbles interact with each other in relatively low-viscosity liquids and, specifically, how they approach, contact, and coalesce or break up are important aspects of multi-phase flow. Coalescence and breakup can control the interfacial area and mass transfer rate in bubble columns and gas-sparged chemical and biological reactors. Bubble interaction is fundamental in two-phase flow instability that plagues boilers and oil and gas wells. But bubble interaction remains a relatively mysterious area. 

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