Viscoelastic Film

Similar instability is caused by the electrostatic attraction due to the applied voltage [56]. Subsequently the hydrodynamic approach was extended to viscoelastic films apparently designed to imitate membranes (see Refs. 58-60, and references therein). A number of studies [58, 61-64] concluded that the SQM could be unstable in such models at small voltages with low associated thinning, consistent with the experimental results. However, as has been shown [60, 65-67], the viscoelastic models leading to instability of the SQM did not account for the elastic force normal to the membrane plane which opposes thickness... 

Effect of Viscoelastic Film on Coupling, and Inner Slip... 

We now turn our attention to the interstitial viscoelastic film between the solid and liquid, and we discuss its effect on coupling and boundary conditions. 

Martin, S. J. and Frye, G. C. (1990). Surface acoustic wave response to changes in viscoelastic film properties. Appl. Phys. Lett. 57,1867-9. [218]... 

Two additional stabilizing influences will be summarized next that of viscoelastic films and that of solid-particle films. In general, where electrical surface charge is an important determinant of stability, it is easier to formulate a very stable O/W emulsion than a W/O emulsion because the electric double layer thickness is much greater in water than in oil. (This is sometimes incorrectly stated in terms of greater charge being present on droplets in an O/W emulsion.) However, there are ways to effectively stabilize W/O emulsions. 

The modern resurgence in interest in capillary wave hydrodynamics, which started in the early 1950s, centers around the damping effects and the presence of a viscoelastic film between two fluids [37,49-56]. All are more or less similar, in the assumptions invoked and the hydrodynamic theory used. The Lucassen-Reynders-Lucassen [55] and Kramer s [56] dispersion equations are essentially identical except Kramer ignores the gravity wave at the outset which is consistent with the wave vector range often used experimentally, and this is seen in Fig. 3. 

The state of a pure liquid without any viscoelastic film coverage is designated as I when e = 0 and /< = 0. Al this point, the frequency a>0 agrees with Eq. 10 while the damping coefficient a is given by the Stokes equation [64] with a correction similar to the one used for the Kelvin equation ... 

Since the transverse shear wave may penetrate the damping surface layer and the viscous liquid, additivity of the equivalent electrical elements in the BVD circuit is only valid under certain particular conditions. Martin and Frye [53] studied the impedance near resonance of polymer film coated resonators in air with a lumped-element BVD model, modified to account for the viscoelastic properties of the film. In addition to the elements shown in Fig. 12.3 to describe the quartz crystal and the liquid, L/ and Rf were added to describe the viscoelastic film overlayer. For a small... 

Etchenique and Calvo [75, 76] developed a fast real time measurement of R and XL element of the electroacoustic impedance applied the LEM model of Martin to measure the rheological properties of poly(allylamine)-GOx hydrogels under fast electrochemical perturbations and derived the viscoelastic properties of the film from the quartz equivalent parameters. For thin viscoelastic films, this method was able to separate the mass due to ions and solvent exchange and the viscosity changes, when the density and the elasticity of the overlayer was known. 

These correspond, respectively, to polymer or electrolyte entrapped within surface features, the polymer film, and the solution. The first of these is a minor effect when using polished crystals the surface mechanical impedance of this contribution is Z, = wp where j = V-l, o> = 2nf0, and p is the areal mass density of the entrapped material. For finite and semiinfinite viscoelastic layers, the surface mechanical impedance is given by Z, = (GPf)m and Zv = (Gpf)1/2 tanh(y/i/), respectively, where prf and hf are the film density and thickness and y = /w(p/G)l/2. For the solution, Zs = (tapsT]J2)m (1 + j), where p, and tj, are the density and viscosity of the solution. When rigid mass, finite viscoelastic film and semi-infinite liquid loadings are all present, as in the experiment of Fig. 13.7, one can show that [42] ... 

The formalism outlined above will be applied to determine equivalent-circuit models for a TSM resonator with (1) an ideal mass layer, (2) a contacting semiinfinite liquid, and (3) a viscoelastic film. By determining the mechanical impedance Zj associated with each perturbation, the equivalent-circuit model arising from each can be obtained. In cases where the perturbation cannot be easily modeled, the procedure can be reversed the resonator response is used to determine Zg and thereby characterize the perturbation. 

This section examines the dynamic behavior and the electrical response of a TSM resonator coated with a viscoelastic film. The elastic properties of viscoelastic materials must be described by a complex modulus. For example, the shear modulus is represented by G = G + yG", where G is the storage modulus and G" the loss modulus. Polymers are viscoelastic materials that are important for sensor applications. As described in Chapter S, polymer films are commmily aj lied as sorbent layers in gas- and liquid-sensing applications. Thus, it is important to understand how polymer-coated TSM resonators respond. 

ELECTRICAL CHARACTERISTICS OF A TSM RESONATOR COATED WITH A VISCOELASTIC FILM... 

The equivalent circuit model of Figure 3.7 can be used to describe the near-resonant electrical characteristics of the quartz resonator coated by a viscoelastic film. The surface film causes an increase in the motional impedance, denoted by the complex element Zg. From Equation 3.19, this element is proportional to the ratio of the surface mechanical impedance Zj contributed by the film to the characteristic shear wave impedance Zq of the quartz. 

Equations 3.19 and 3.36 can be combined to find the change in (electrical) motional impedance that arises from a viscoelastic film on a thickness-shear mode resonator [40] ... 

While Equation 3.59 does not apply to viscoelastic films, the velocity and attenuation arising from acoustically thin, viscoelastic films can be determined from Equation 3.58 by inserting complex moduli (e.g., K and G) into the 0 expressions. 

From the aforementioned considerations, a perturbational formula can be derived for the SAW velocity and attenuation changes, applying to either acoustically thin or thick viscoelastic films [50] ... 

HPMCs were all able to generate viscoelastic films after adsorption. F4M formed the most elastic films, because of a higher content of methyl groups in the molecule which favor the formation of hydrophobic bonds at the interface. 

Another important use of the PHS-PEO-PHS block copolymer is the formation of a viscoelastic film around water droplets [11, 12] this results from the dense packing of the molecule at the W/O interface, which leads to an appreciable interfacial viscosity. The viscoelastic film prevents transport of water from the internal water droplets in the multiple emulsion drop to the external aqueous medium, and this ensures the long-term physical stability of the multiple emulsion when using polymeric surfactants. The viscoelastic film can also reduce the transport of any a.i. in the internal water droplets to the external phase. This is desirable in many cases when protection of the ingredient in the internal aqueous droplets is required and release is provided on application of the multiple emulsion. 

It should be emphasised that polymeric surfactants prevent the coalescence of water droplets in the multiple emulsion drops, as well as coalescence of the latter drops themselves. This is due to the interfacial rheology of the polymeric surfactant films. As a result of the strong lateral repulsion between the stabilising chains at the interface (PHS chains at the W/O interface and PEO chains at the O/W interface), these films resist deformation under shear and hence produce a viscoelastic film. On approach of the two droplets, this film prevents deformation of the interface so as to prevent coalescence. 

Figure 4 represents a (zoomed) part of the y( t ) data of Figure 3, together with the (synchronous) surface area data. In this case, the phase angle between response and perturbation is almost zero. In other words, the film appears as purely elastic. In contrast, a viscoelastic film shows an anticipating response, as Figure 5 illustrates for example. 

C. Maldarelli and R. K. Jain, The linear, hydrodynamic stability, of an interfacially perturbed, transversely isotropic, thin, planar viscoelastic film. I. General formulation and a derivation of the dispersion equation, J. Colloid Interface Sci. 90, 233-62 (1982). 

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