Flow instabilities types

Deviation from laminar shear flow [88,89],by calculating the material functions r =f( y),x12=f( Y),x11-x22=f( y),is assumed to be of a laminar type and this assumption is applied to Newtonian as well as viscoelastic fluids. Deviations from laminar flow conditions are often described as turbulent, as flow irregularities or flow instabilities. However, deviation from laminar flow conditions in cone-and-plate geometries have been observed and analysed for Newtonian and viscoelastic liquids in numerous investigations [90-95]. Theories have been derived for predicting the onset of the deviation of laminar flow between a cone and plate for Newtonian liquids [91-93] and in experiments reasonable agreements were found [95]. 

The properties of liquid metals can cause flow instability (oscillation) because of vapor pressure—temperature relationship. Most liquid metals, especially alkali metals, show a greater change in saturation temperature, corresponding to a given change of pressure, than does water. In a vertical system under gravitational force, the change of static pressure could appreciably alter the saturation temperature such that explosion -type flow oscillation would occur that would result in liquid... 

The following parametric effects on density wave instability are summarized, as these effects have been often observed in the most common type of two-phase flow instability (Boure et al., 1973) ... 

When the part is of sandwich type there is a potential for a flow instability that will push the core toward one of the sides. The resulting part will have a thicker skin on one of the sides. 

Fig. 1. Typical flow curve of commercial LPE. There are five characteristic flow regimes (i) Newtonian (ii) shear thinning (iii) sharkskin (iv) flow discontinuity or stick-slip transition in controlled stress, and oscillating flow in controlled rate (v) slip flow. There are three leading types of extrudate distortion (a) sharkskin like, (b) alternating bamboo like in the shaded region, and (c) spiral like on the slip branch. Industrial extrusion of polyethylenes is most concerned with flow instabilities occurring in regimes (iii) to (v) where the three kinds of extrudate distortion must be dealt with. The unit shows the approximate levels of stress where the sharkskin and flow discontinuity occur respectively. There is appreciable molecular weight and temperature dependence of the critical stress for the discontinuity. Other highly entangled melts such as 1,4 polybutadienes also exhibit most of the features illustrated herein...

Many polymers exhibit neither a measurable stick-slip transition nor flow oscillation. For example, commercial polystyrene (PS), polypropylene (PP), and low density polyethylene (LDPE) usually do not undergo a flow discontinuity transition nor oscillating flow. This does not mean that their extrudate would remain smooth. The often observed spiral-like extrudate distortion of PS, LDPE and PP, among other polymer melts, normally arises from a secondary (vortex) flow in the barrel due to a sharp die entry and is unrelated to interfacial slip. Section 11 discusses this type of extrudate distortion in some detail. Here we focus on the question of why polymers such as PS often do not exhibit interfacial flow instabilities and flow discontinuity. The answer is contained in the celebrated formula Eqs. (3) or (5). For a polymer to show an observable wall slip on a length scale of 1 mm requires a viscosity ratio q/q equal to 105 or larger. In other words, there should be a sufficient level of bulk chain entanglement at the critical stress for an interfacial breakdown (i.e., disentanglement transition between adsorbed and unbound chains). The above-mentioned commercial polymers do not meet this criterion. 

Linear polyethylenes (PE) are one polymer that possess an important ingredient necessary for a display of interfacial stick-slip transition. In the past, the coincidence that PE is both the most widely used polymer and most prone to suffer from melt flow instabilities has challenged the PE industry. Today we still face the task of how to effectively remove instabilities that result in various types of extrudate distortions. 

The term melt fracture has been applied from the outset [9,13] to refer to various types of visible extrudate distortion. The origin of sharkskin (often called surface melt fracture ) has been shown in Sect. 10 to be related to a local interfacial instability in the die exit region. The alternating quasi-periodic, sometimes bamboo-like, extrudate distortion associated with the flow oscillation is a result of oscillation in extrudate swell under controlled piston speed due to unstable boundary condition, as discussed in Sect. 8. A third type, spiral like, distortion is associated with an entry flow instability. The latter two kinds have often been referred to as gross melt fracture. It is clearly misleading and inaccurate to call these three major types of extrudate distortion melt fracture since they do not arise from a true melt fracture or bulk failure. Unfortunately, for historical reasons, this terminology will stay with us and be used interchangeably with the phase extrudate distortion. ... 

In stud dng stability of flows, it is convenient to pose the problem either as a temporal or as a spatial instability problem. While it is numerically expedient to take a temporal approach, many practical flows are known to follow spatial route. For example in lab experiments for external wall-bounded flows, it is noted that the disturbances grow in space as they travel downstream. This was established unambiguously through the experiments of Schubauer Skramstad (1947) for flat plate boundary layer and is an excellent example of spatial instability problems. However, there are many flows where the instability grows both in space and time. These type of problems to identify whether the flow suffers temporal and/ or spatial instability arise in linear stability analysis. Flow instability studied following descriptions of two independent routes, is an artificial way of treating general instability problems. 

For different systems, we have different signs of the real and imaginary part of Landau coefficient /. Here, we will keep our attention focused to flow past a circular cylinder, that works as a prototypical model for bluff-body flow instability. This instability begins as a linear temporal instability and its first appearance with respect to the Reynolds number is referred to as Hopf bifurcation. Thus, the Reynolds number at which the first bifurcation occurs is given by Rccr- Thus, above Rccr the value of <7 > 0 signifies linear instability. One of the most important aspect of this linear instability is the subsequent non-linear saturation that can be adequately explained by the Landau s equation, if only R is positive. We will focus upon this type of flow only in the next. 

The problems of combining flow instabilities with a description of reservoir heterogeneities in a realistic unified treatment is currently of great interest for all types of EOR. Chapter 3 of this book describes the beginnings for new methods of introducing the heterogeneities of a reservoir into simulations of the fluid flow. Treatment of the fully coupled problem, i.e., flow instabilities with three fluids in a field-scale natural reservoir, will require many years of research. 

Our main concern here is to present the mass transfer enhancement in several rate-controlled separation processes and how they are affected by the flow instabilities. These processes include membrane processes of reverse osmosis, ultra/microfiltration, gas permeation, and chromatography. In the following section, the different types of flow instabilities are classified and discussed. The axial dispersion in curved tubes is also discussed to understand the dispersion in the biological systems and radial mass transport in the chromatographic columns. Several experimental and theoretical studies have been reported on dispersion of solute in curved and coiled tubes under various laminar Newtonian and non-Newtonian flow conditions. The prior literature on dispersion in the laminar flow of Newtonian and non-Newtonian fluids through... 

Chaotic mixing based on viscoelastic flow instability in rather simple microfluidic channel geometries was successfully demonstrated. These viscoelastic micromixers bypass the limitation of low Reynolds number in microfluidic flows and could potentially be implemented in a Lab-on-a-Chip platform with minimum requirements for design and fabrication. However, this type of micromixer is yet to be optimized. 

One interesting benefit that can be obtained with coextrusion is a more uniform temperature distribution in the material. This can be realized by coextruding a thin, low-viscosity outer layer over a high-viscosity inner layer. The highest shear rate and heat generation normally occurs at the wall. By having a low-viscosity material at the location of maximum shear rate, the heat generation is reduced at this point and a more even temperature profile is obtained. This is a useful technique for thermally unstable polymers. As discussed before in Section 7.5.3, this technique can also avoid the occurrence of shark skin and melt fracture type flow instabilities. 

Viscosities of non-Newtonian polymers are dependent on extrusion temperature and shear rate, both of which may vary within the coextrusion die. The shear rate dependence is further complicated in that it is determined by the position and thickness of a polymer layer in the melt stream. A polymer used as a thin surface layer in a coextruded product experiences higher shear rate than it would if it were positioned as a central core layer. There are several types of flow instabilities that have been observed in coextrusion. 

Two types of flow instabilities are observed when polymer fluid flows through a cylindrical path and is extmded from... 

This type of actuator platform relies on contactless pneumatic actuation, where the objects are kept away from the actuator surface by means of airflow. This allows simultaneous levitation and conveyance of parts. Generally, these platforms offer high velocities and absence of friction problems, but in return, they require a greater level of complexity control. The main problems are flow instabilities and turbulences, which necessitate the use of sensors and imaging in order to minimise their effect. 

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