Solution viscosity, shear rate micelles

The 3 1 LDAO/SDS mixture becomes viscoelastic and rheo-pectic when a small amount of NaCl Is added. Its viscosity shows a reversible Increase with time of shearing at constant shear rate. The rheopectic behavior Is probably due to long thread-like micelles that are aligned parallel to the flow In weakly bound clusters, as In the case of cetyltrlmethyl ammonium bromide and monosubstituted phenol mixed solutions (21). 

If rj is independent of the shear rate y a liquid is called Newtonian. Water and other low molecular weight liquids typically are Newtonian. If rj decreases with increasing y, a liquid is termed shear thinning. Examples for shear thinning liquids are entangled polymer solutions or surfactant solutions with long rod-like micelles. The zero shear viscosity is the value of the viscosity for small shear rates ij0 = lim,> o tj y). The inverse case is also sometimes observed rj increases with increasing shear rate. This can be found for suspensions and sometimes for surfactant solutions. In surfactant solutions the viscosity can be a function of time. In this case one speaks of shear induced structures. 

Here T 0 means the viscosity of the solution at zero shear rate, r g the viscosity of the pure solvent, 6 the number of rods per unit volume and L the lengths of the rods. As long as L is still shorter than the mean spacing between the aggregates, the viscosity of the detergent solution is still very low and always small in comparison with the solvent viscosity. As a consequence, very accurate measurements are necessary to get some informations on the dimensions of the rodlike micelles. The Zimm-Crothers viscometer is a very sensitive instrument and it was possible to measure the viscosity of the dust-and airfree solutions with an accuracy of 0,2% at very low shear rates (15). 

Polysaccharides with Surfactant Micelles. Consider a solution of a fairly hydrophobic polysaccharide, such as a cellulose ether. The hydrophobic groups cause a weak attractive interaction, leading to a somewhat increased viscosity at low shear rates. If an anionic small-molecule surfactant is added, say SDS (sodium dodecyl sulfate), at a concentration above the CMC (critical micellization concentration), micelles are formed that interact with the polymer more specifically, one or a few polymer chains can pass through a micelle. In this way, polymer chains can be cross-linked. If now the polymer concentration c is below c (the chain overlap concentration), mainly intramolecular junctions are formed. If c > c, however, a gel results. In this manner, viscoelastic gels can be made with a modulus of the order of 10 Pa. 

Viscosity Maxima. The low-shear-rate viscosities of both commercial and model associative thickeners below their c /, values will increase with the addition of conventional low molecular weight surfactants or coalescing aid (22). With HEUR polymers, solution viscosities are observed to increase, achieve a maximum value, and then decrease with continued increase in surfactant concentration (23). This type of behavior is illustrated (Figure 5) for four commercial HEURs with a nonionic surfactant (typical of that used in coating formulations). A similar behavior has been observed (24) with a classical anionic surfactant and hydrophobically modified (hydroxy-ethyl)cellulose (HMHEC) and is reviewed in Chapter 18. Intermicellar networks, formed by the participation of one or more hydrophobes from different polymers in the micelles of conventional surfactants, were again recently suggested (25) to affect viscous solutions. 

Fig. 26 Variation of the apparent shear viscosity r] = C7st(7)/7 as a function of the shear rate for a solution of CPCl/Hex wormlike micelles in 0.2 M NaCl brine. The total concentration is c = 36 wt. % and the molar ratio [Hex]/[CPC1] = 0.49. The continuous line between the data points is a guide for the eyes. At high shear rates, the viscosity decreases according to a power law with exponent —0.73...

Fig. 2. Experimental data (points) for the non-Newtonian shear stress versus the shear rate of a dilute solution of wormlike micelles (Delgado Castillo, 2005 2007). Fit of the data using the isotropic friction model (hne) in Eqs. (35), (36) and (38). Notice that the dependence of the effective viscosity as a function of the shear rate is not simply a power law. Figure taken from Ref. (Malaga, 2006).

In shear measurements one expects the described solutions behave like normal Newtonian aqueous solutions. This is in fact the case for small shear rates (Fig. 11.32). In Fig. 11.32 the shear viscosity, which was measured in a capillary viscometer, is plotted vs.the shear rate. One observes a sudden rise of the viscosity at a characteristic shear rate and for y> % the solutions show some shear thickening behaviour. Obviously something dramatic has happened to the micelles in the solutions. Some conclusions about what has happened can be drawn from flow birefringence measurements. Some typical results of flow measurements from a Couette system are shown in Fig. 11.33. We note a sudden increase of the flow birefringence at a critical shear rate. For y < yc no flow birefringence could be detected. 

Shear-Rate-Dependent Solution Viscosities of Polymers Crosslinked by Micelles. 

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