Viscosity dilational

Another important property is the surface dilational viscosity, k... 

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. 

Hsu and Berger [43] used the maximum bubble pressure method (MBP) to study the dynamic surface tension and surface dilational viscosity of various surfactants including AOS and have correlated their findings to time-related applications such as penetration and wetting. A recent discussion of the MBP method is given by Henderson et al. [44 and references cited therein]. 

Figure 12a gives the surface dilatational viscosities for a nonionic surfactant, namely, nonylphenol 10 EO, and for C12-C14 AOS. Both products were ad-... 

There is good correlation between the concentration giving the maximum surface dilatational viscosity and that giving the best foam performance. The nonylphenol 10 EO is a low-foaming nonionic surfactant with a maximum foam height of 150 ml in this test, whereas AOS produced 670 ml of foam. Figure 12 clearly shows that there is an optimum surfactant concentration for a dynamic process such as foam generation. 

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. 

The imaginary component, "(f), is the dilational viscosity modulus. This arises when the demulsifier in the monolayer is sufficiently soluble in the bulk liquid, so that the tension gradient created by an area compression/expansion can be short circuited by a transfer of demulsifiers to and from the surface. It is 90° out of phase with the area change. 

The dynamic surface tension of a monolayer may be defined as the response of a film in an initial state of static quasi-equilibrium to a sudden change in surface area. If the area of the film-covered interface is altered at a rapid rate, the monolayer may not readjust to its original conformation quickly enough to maintain the quasi-equilibrium surface pressure. It is for this reason that properly reported II/A isotherms for most monolayers are repeated at several compression/expansion rates. The reasons for this lag in equilibration time are complex combinations of shear and dilational viscosities, elasticity, and isothermal compressibility (Manheimer and Schechter, 1970 Margoni, 1871 Lucassen-Reynders et al., 1974). Furthermore, consideration of dynamic surface tension in insoluble monolayers assumes that the monolayer is indeed insoluble and stable throughout the perturbation if not, a myriad of contributions from monolayer collapse to monomer dissolution may complicate the situation further. Although theoretical models of dynamic surface tension effects have been presented, there have been very few attempts at experimental investigation of these time-dependent phenomena in spread monolayer films. 

The rheological properties of a fluid interface may be characterized by four parameters surface shear viscosity and elasticity, and surface dilational viscosity and elasticity. When polymer monolayers are present at such interfaces, viscoelastic behavior has been observed (1,2), but theoretical progress has been slow. The adsorption of amphiphilic polymers at the interface in liquid emulsions stabilizes the particles mainly through osmotic pressure developed upon close approach. This has become known as steric stabilization (3,4.5). In this paper, the dynamic behavior of amphiphilic, hydrophobically modified hydroxyethyl celluloses (HM-HEC), was studied. In previous studies HM-HEC s were found to greatly reduce liquid/liquid interfacial tensions even at very low polymer concentrations, and were extremely effective emulsifiers for organic liquids in water (6). 

Since there is no change in surface tension with a change in the rate of a pure liquid surface (i.e., d A/d II = infinity), the elasticity is zero. The interfacial dilational viscosity, ks, is defined as... 

Boussinesq (B4) proposed that the lack of internal circulation in bubbles and drops is due to an interfacial monolayer which acts as a viscous membrane. A constitutive equation involving two parameters, surface shear viscosity and surface dilational viscosity, in addition to surface tension, was proposed for the interface. This model, commonly called the Newtonian surface fluid model (W2), has been extended by Scriven (S3). Boussinesq obtained an exact solution to the creeping flow equations, analogous to the Hadamard-Rybczinski result but with surface viscosity included. The resulting terminal velocity is... 

We can distinguish between two types of stresses on an interface a shear stress and a dilatational stress. In a shear stress experiment, the interfacial area is kept constant and a shear is imposed on the interface. The resistance is characterized by a shear viscosity, similar to the Newtonian viscosity of fluids. In a dilatational stress experiment, an interface is expanded (dilated) without shear. This resistance is characterized by a dilatational viscosity. In an actual dynamic situation, the total stress is a sum of these stresses, and both these viscosities represent the total flow resistance afforded by the interface to an applied stress. There are a number of instruments to study interfacial rheology and most of them are described in Ref. [1]. The most recent instrumentation is the controlled drop tensiometer. 

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. 

Unlike in three dimensions, where liquids are often considered incompressible, a surfactant monolayer can be expanded or compressed over a wide area range. Thus, the dynamic surface tension experienced during a rate-dependent surface expansion, is the result of the surface dilational viscosity, the surface shear viscosity, and elastic forces. Often, the contributions of shear and/or the dilational viscosities are neglected during stress measurements of surface expansions. Isolating interfacial viscosity effects is difficult because, since the interface is connected to the substrate on either side of it, the interfacial viscosity is coupled to the two bulk viscosities. 

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...

On the basis of our experimental results presented so far, the overall viscoelastic behavior of these triblock copolymers shows an elasticity-dominance over the viscosity. After reaching the critical mass density, where the static elasticity es reaches the maximum, these triblock copolymers collapse into the subphase and form hydrated brushes and these anchored brushes may be responsible for the result that the surface viscosities drop to around the 0 value at r. A distinctive difference between two types of polymers, sample I (PEO-PPO-PEO) and sample II (PPO-PEO-PPO), is the temperature dependence of r where both static elasticity and dilational viscosity show kinds of transitions. V of sample I increases with increasing temperature while that of sample II does not change with temperature. 

Dilatant. Viscosity goes up with shear. If you pour sand, it pours like a liquid. If you punch sand hard with your fist, it hurts. The sand feels like a continuous solid. 

The generalization in Eq. (2.15) involves the viscosity, fi, and the dilatational viscosity, k, to characterize a fluid. Usually it is not necessary to know the value of k in fluid mechanics problems. For gases we often assume it to be close... 

The theoretical analysis indicated that asymmetric drainage was caused by the hydrodynamic instability being a result of surface tension driven flow. A criterion giving the conditions of the onset of instability that causes asymmetric drainage in foam films was proposed. This analysis showed as well that surface-tension-driven flow was stabilised by surface dilational viscosity, surface diffusivity and especially surface shear viscosity. 

Hoffman, R. L. 1972. Discontinuous and dilatant viscosity behavior in concentrated suspensions. 1. Observation of a flow instability. Trans. Soc. Rheol. 16 155-173. 

By way of introduction, consider the dilational experiment of fig. 3.49. At t = t the monolayer is instantaneously subjected to a stress r° = r = r°, which is kept constant till t = t, after which it is suddenly removed. Panels (b) and (c) refer to the strain response AA/A for a purely elastic and a purely viscous monolayer, respectively, The elastic monolayer directly follows the applied stress after cessation it relaxes instantaneously. The viscous one starts to flow after cessation of the stress the flow stops. The height of the block in panel (b) is equal to r / K (compare [3.6,18]) whereas in panel (c) the interfacial (dilational) viscosity follows from the slope as... 

Dilational interfacial properties can be determined in various ways both at small and at large strains. In the former case results are normally interpreted in terms of interfacial dilational storage moduli, interfacial dilational loss moduli or dynamic interfacial dilational viscosities and the loss tangents as a function of applied deformation frequency, see sec. 3.6f. For large strains one obtains the Interfacial dilational viscosity. Various techniques have been discussed In the reviews by Miller et al. and Prins, mentioned in sec. 3. lOd. For the wave behaviour, see fig. 3.45. 

Dilatant viscosity behavior comes about, because under shear stress the particles are pressed apart, whereupon large cavities are formed, which are less lubricated . This flow behavior is to be avoided in the chemical industry and should be circumvented e.g. by changing the recipe. 

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