Interfacial instability oscillating

Liquid Interfacial Systems Oscillations and Instability, Rudoiph V. Birikh, Vladimir A. Briskman, Manuei G. Veiarde, and Jean-Claude Legros... 

In a recent work [69], we were able to reveal that the sharkskin merely originates from a local interfacial instability of the boundary condition near the die exit wall. Specifically, the oscillation of adsorbed chains between their coil and stretch states produces a small scale periodic perturbation on the overall die swell and makes the extrudate surface appear rough or sharkskin like. 

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. ... 

Liquid Interfacial Systems Oscillations and Instability, Rudolph V. Birikh,... 

Birikh, Rudolph V. Liquid Interfacial Systems Oscillations and Instability. Surfactant Science Series, vol. 113. New York Marcel Dekker, 2003. 

Interfacial instability is a common phenomenon since in most cases the events occurring at the interface are in the region far from equilibrium [40, 41]. A typical example is Marangoni instability [44-47]. Electric potential oscillations have been observed in biphasic systems [48, 49], Self-induced oscillations in similar systems have also been observed [10]. Theoretical efforts have also been made to understand the mechanism in some cases [23, 27],... 

In the remainder of this book, we present information on phenomena where dynamic interfacial effects are important. We begin in this chapter with interfacial stability and the closely related subject of interfacial oscillation or wave motion. It is frequently of great interest to know the conditions for interfacial instability. We may ask, for instance, how far a fluid jet leaving a circular orifice travels before it breaks up into drops. Or when we can expect spontaneous convection to arise near an interface across which one or more species diffuse. 

Birikh, R.V., Briskman, V.A., Verlarde, M.G., and Legros, i.-C., Liquid Interfacial Systems, Oscillations and Instability, Marcel Dekker, New York, 2003. 

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. 

One leading explanation attributes the anomalous melt flow behavior (i.e., flow discontinuity and oscillation) to constitutive instabilities [65]. In other words, the anomalies would be constitutive in nature and non-interfacial in origin. Such an opinion has not only been expressed phenomenologically by Tordella [9b] and many other rheologists but found support from several theoretical studies [65-67]. However, these theories only attempt to describe inherent bulk flow behavior. Thus, a connection between the anomalous flow phenomena and constitutive instabilities was often explored without any account for possible molecular processes in the melt/wall interfacial region. 

Extrudate distortion has been viewed as explicit evidence for melt flow instabilities or melt fracture. This is another calamitously misleading assertion in the massive literature of over 3000 papers on the subject. Because extrudate distortion was also observed even without any signature of slip, it was concluded by Blyler and Hart [32] that the slip process is not an essential part of the flow instability. This dilemma, that the flow anomalies including flow oscillation cannot be accounted for in terms of either a constitutive instability or interfacial slip mechanism, has persisted until very recently. Denn coined this plight the paradox [10b]. 

As discussed in more detail below, recent experiments convincingly showed that the flow oscillation in capillary extrusion of LPE is interfacial in nature due to a reversible coil-stretch transition at the melt/die wall boundary. Pressure oscillation phenomenon has also been reported in extrusion of other polymer melts. In particular, there are well-defined oscillations in controlled-rate capillary flow of PB that were found to arise from the same interfacial molecular instability [62]. 

It is simplest to think of sharkskin as a result of a quasi-periodic perturbation on the overall extrudate swell. This small amplitude fluctuation of extrudate swell arises from the oscillation of the boundary condition at the exit wall that produces an oscillation of the local stress level as the interfacial chains suffer a conformational instability. The local boundary condition oscillates between noslip and slip, resulting in the fluctuation of the stress level at the die exit. To determine whether some sort of melt fracture occurs, we need to know not only the... 

Monodisperse melts appear to exhibit a plateau region in the stress vs shear rate flow curve [51,62,65]. The capillary flow behavior actually closely resembles the oscillatory shear behavior in the sense that the flow curve essentially overlaps on the absolute value of complex modulus G vs the oscillation frequency (0 [62]. Thus.it appears that the transition-like capillary flow behavior of highly entangled monodisperse melts reflects constitutive bulk properties of the melts and is not interfacial in origin. It remains to be explored whether this plateau indeed manifests a real constitutive instability, i.e., whether it is double-valued. 

We have surveyed the most recent progress and presented a new molecular level understanding of melt flow instabilities and wall slip. This article can at best be regarded as a partial review because it advocates the molecular pictures emerging from our own work over the past few years [27-29,57,62,69]. Several results from many previous and current workers have been discussed to help illustrate, formulate and verify our own viewpoints. In our opinion, the emerging explicit molecular mechanisms have for the first time provided a unified and satisfactory understanding of the two major classes of interfacial melt flow instability phenomena (a) sharkskin-like extrudate distortion and (b) stick-slip (flow discontinuity) transition and oscillating flow. 

A variant, with reminiscences to sec. 1.5, is based upon the capillary instability of jets, a topic that has drawn recent interest because of the increasing application of ink jet printers. Such printers are based on the deflection of a liquid jet in an electric field. The idea goes back to Sweet ), and has given rise to much printing technology. For the present purpose, oscillations in the jet are not produced by an elliptic orifice, but applied externally, say piezo-electrically. Dynamic surface or interfacial tensions can be obtained from, for Instance, the (quadrupole) oscillations of drops that have just broken away from the jet, or from the oscillations in the jet just before breaking. Measurements can be carried out down to lO" s" l... 

In the case of an inviscid liquid (v = 0), we obtain p = +/ p as before, and the interface oscillates without damping. There is no instability because, with the liquid below the gas, both gravity and interfacial traision act to restore the deformed interface to its initial planar configuration. But with no viscous resistance to flow, the momentnm developed during the return carries the interface beyond the flat configuration to a new deformation of opposite sign to the original one. 

In the examples of interfacial stability considered thus far, the systems have been at rest in their initial states. Hence the predictions of when instability can be expected are, in fact, conditions for thermodynamic stability. We have chosen not to emphasize this point and to carry out the analyses in terms of perturbations of the general equations of change because we obtain in this way not only the stability condition but also the rates of growth of unstable perturbations and the appropriate frequencies of oscillation and damping factors for stable perturbations. Also, the basic method of analysis used above is applicable to systems not initially in equilibrium, as we shall see later in this chapter and in Chapter 6. 

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