Dilational elasticity

In a dilatational experiment, where the surface is periodically expanded and contracted, is a function of the angular frequency (co) of the dilatation as ia equation 3 where is the dilatational elasticity and Tj is the dilatational viscosity. 

It has been shown (16) that a stable foam possesses both a high surface dilatational viscosity and elasticity. In principle, defoamers should reduce these properties. Ideally a spread duplex film, one thick enough to have two definite surfaces enclosing a bulk phase, should eliminate dilatational effects because the surface tension of an iasoluble, one-component layer does not depend on its thickness. This effect has been verified (17). SiUcone antifoams reduce both the surface dilatational elasticity and viscosity of cmde oils as iUustrated ia Table 2 (17). The PDMS materials are Dow Coming Ltd. polydimethylsiloxane fluids, SK 3556 is a Th. Goldschmidt Ltd. siUcone oil, and FC 740 is a 3M Co. Ltd. fluorocarbon profoaming surfactant. 

Ed is the dilatational elasticity, and rid is the dilatational viscosity. It is characteristic for a stable foam to exhibit a high surface dilatational elasticity and a high dilatational viscosity. Therefore effective defoamers should reduce these properties of the foam. 

Dilatational Elasticities and Viscosities of Crude Oil at 1 mHz with Polydimethylsiloxanes (PDMS) [300]... 

This has been verified for polydimethylsiloxanes added to crude oils. The effect of the dilatational elasticities and viscosities on crude oil by the addition of polydimethylsiloxanes is shown in Table 21-1. Under nonequilibrium conditions, both a high bulk viscosity and a surface viscosity can delay the film thinning and the stretching deformation, which precedes the destruction of a foam. There is another issue that concerns the formation of ordered structures. The development of ordered structures in the surface film may also stabilize the foams. Liquid crystalline phases in surfaces enhance the stability of the foam. 

A study on a commonly used demulsifier, namely, a phenol-formaldehyde resin, elucidated how various parameters such as interfacial tension, interfacial shear viscosity, dynamic interfacial-tension gradient, dilatational elasticity, and demulsifier clustering affect the demulsification effectiveness [1275]. 

Our goal is to develop a property-performance relationship for different types of demulsifiers. The important interfacial properties governing water-in-oil emulsion stability are shear viscosity, dynamic tension and dilational elasticity. We have studied the relative importance of these parameters in demulsification. In this paper, some of the results of our study are presented. In particular, we have found that to be effective, a demulsifier must lower the dynamic interfacial tension gradient and its ability to do so depends on the rate of unclustering of the ethylene oxide groups at the oil-water interface. 

Other experiments performed by Bergeron [34] on air foams stabilized with ionic surfactants reveal that the so-called Gibbs or dilatational elasticity e may play an important role in the coalescence process. The Gibbs elasticity measures the variation of surface tension yi t associated to the variation of the surfactant surface concentration F ... 

Figure 24. A comparison of the data obtained from a range of surface rheological measurements of samples of /3-lg as a function of Tween 20 concentration. ( ), The surface diffusion coefficient of FITC-jS-lg (0.2 mg/ml) at the interfaces of a/w thin films (X), the surface shear viscosity of /3-lg (0.01 mg/ml) at the o/w interface after 5 hours adsorption ( ), the surface dilational elasticity and (o) the dilational loss modulus of /3-lg (0.2 mg/ml).

The surface rheological properties of the /3-lg/Tween 20 system at the macroscopic a/w interface were examined by a third method, namely surface dilation [40]. Sample data obtained are presented in Figure 24. The surface dilational modulus, (E) of a liquid is the ratio between the small change in surface tension (Ay) and the small change in surface area (AlnA). The surface dilational modulus is a complex quantity. The real part of the modulus is the storage modulus, e (often referred to as the surface dilational elasticity, Ed). The imaginary part is the loss modulus, e , which is related to the product of the surface dilational viscosity and the radial frequency ( jdu). 

Experiments with the /3-lg/Tween 20 system were performed at a macroscopic a/w interface at a /3-lg concentration of 0.2 mg/ml [40]. The data obtained relate to the properties of the interface 20 minutes after formation. Up to R = 1, the storage modulus (dilational elasticity) was large and relatively constant, whereas the loss modulus (dilational viscosity) increased with increasing R. As R was increased to higher values there was a marked decrease in the storage modulus (dilational elasticity) and a gradual increase in the loss modulus (dilational viscosity). In summary, the data show the presence of a transition in surface dilational behavior in this system at a solution composition of approximately R = 1. At this point, there is a transformation in the adsorbed layer properties from elastic to viscous. 

The dilational rheology behavior of polymer monolayers is a very interesting aspect. If a polymer film is viewed as a macroscopy continuum medium, several types of motion are possible [96], As it has been explained by Monroy et al. [59], it is possible to distinguish two main types capillary (or out of plane) and dilational (or in plane) [59,60,97], The first one is a shear deformation, while for the second one there are both a compression - dilatation motion and a shear motion. Since dissipative effects do exist within the film, each of the motions consists of elastic and viscous components. The elastic constant for the capillary motion is the surface tension y, while for the second it is the dilatation elasticity e. The latter modulus depends upon the stress applied to the monolayer. For a uniaxial stress (as it is the case for capillary waves or for compression in a single barrier Langmuir trough) the dilatational modulus is the sum of the compression and shear moduli [98]... 

At equilibrium, the surface elasticity, or surface dilational elasticity, EG, is defined [15,25] by ... 

Keywords Monolayers Surface light scattering Capillary waves Dispersion equation Dilational elastic modulus Dilational loss modulus Scaling exponent... 

Fig. 4 General solution for the dispersion equation on water at 25 °C. The damping coefficient a vs. the real capillary wave frequency o> , for isopleths of constant dynamic dilation elasticity ed (solid radial curves), and dilational viscosity k (dashed circular curves). The plot was generated for a reference subphase at k = 32431 m 1, ad = 71.97 mN m-1, /i = 0mNsm 1, p = 997.0kgm 3, jj = 0.894mPas and g = 9.80ms 2. The limits correspond to I = Pure Liquid Limit, II = Maximum Velocity Limit for a Purely Elastic Surface Film, III = Maximum Damping Coefficient for the same, IV = Minimum Velocity Limit, V = Surface Film with an Infinite Lateral Modulus and VI = Maximum Damping Coefficient for a Perfectly Viscous Surface Film...

Fig. 5 Wave motion at maximum damping and infinite dilational elasticity. A Motion at the maximum damping coefficient where optimal resonant mode coupling implies that a surface fluid element moves at a 45° angle to the direction of wave propagation. B Wave Motion at infinite dilational elasticity, where the same element is only able to move in the transverse direction...

Figure 31 shows (a) and /< (b) - / plots for sample II, 10R5 (PPO-PEO-PPO). Dynamic dilational elasticities s at different temperatures reach their asymptotes at the same concentration ( 0.5 mgm 2) but a bit higher than r (0.4 mg nr2). Corresponding viscosities /< at three different temperatures reach the minima at the same value of r as the static elasticities of this poly-... 

In the presence of liquid flow, the situation becomes more complicated due to the creation of surface tension gradients [17]. These gradients, described by the Gibbs dilational elasticity [17], e, initiate a flow of mass along the interface in direction of a higher surface or interfacial tension (the Marangoni effect), e is given by the... 

The earliest available hydrodynamic theory of water wave damping by elastic surface films was published by Lamb (1895). He refers to Reynolds (1880) and the experiments by Aitken (see Scott 1979, Giles and Forrester 1970), but prior publication of the detailed theory is not indicated. All but the outline of the theory was omitted from later editions of this book, and it is likely that Lamb assumed that damping was greatest with an inextensible film, and that intermediate elasticities, therefore, had less effect (cited after Scott 1979). This conclusion was shown by Dorrestein (1951) to be incorrect. The paper by Levich (1940) was the first to present in detail the linearised hydrodynamics of waves on a water surface with surface dilational elasticity. The only cases considered in detail concern insoluble films, and represent the clean and incompressible-film-covered surface. A detailed treatment of the hydrodynamic theory of surface waves, including the effect of an elastic surface film, was published by Levich in 1962. In addition, the damping caused by dissolved surface-active material was considered. Further laboratory experiments performed until 1978 were briefly reviewed by Scott (1979). 

Figure 9 Dilational elasticity ( ) and viscosity (B)/or fi-LG in buffer at 22° C at a frequency of0.002 Hz...

A second more detailed type of investigation is the determination of the dilational elastic modulus at a given frequency during the adsorption process. This allows us to determine the variation of e with the surface pressure. 

We have also measured y(t) and e(t) during polymer adsorption for a given concentration. In Figure 6, the e-n curve, the equation state of the layer during the adsorption process, is presented. At low surface pressure, one observes a linear increase of the dilational elastic modulus with the surface pressure n. From the slope of the linear part of the e-n curve, a value of 0.66 was found for the excluded volume critical exponent. The same value has been measured elsewhere with another technique.12 This result indicates that, unlike the excluded volume chain behaviour in the bulk, the air water interface is not a good solvent for MeC. At intermediate surface pressures, the modulus levels off and then increases again until the equilibrium surface pressure is reached. 

MeC adsorbs at the air water interface leading to a decrease in the surface tension. An equilibrium state is only reached at very long times, due to the high molecular mass of methylcellulose. The layer which is present at the interface at equilibrium is almost purely elastic with a large dilational elastic modulus. The value of the excluded volume critical exponent extracted from the E-n curve indicates that the air-water interface is not a good solvent for the polymer. 

Entropy decrease (for entropy-elasticity) of the network chains as a result of the dilation (elastic deformation term). 

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