Viscosity zero-shear suspension

The rheological behavior of storage XGs was characterized by steady and dynamic shear rheometry [104,266]. Tamarind seed XG [266] showed a marked dependence of zero-shear viscosity on concentration in the semi-dilute region, which was similar to that of other stiff neutral polysaccharides, and ascribed to hyper-entanglements. In a later paper [292], the flow properties of XGs from different plant species, namely, suspension-cultured tobacco cells, apple pomace, and tamarind seed, were compared. The three XGs differed in composition and structural features (as mentioned in the former section) and... 

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. 

Rheological measurements Two instruments were used to investigate the rheology of the suspensions. The first was a Haake Rotovisko model RV2(MSE Scientific Instruments, Crawley, Sussex, England) fitted with an MK50 measuring head. This instrument was used to obtain steady state shear stress-shear rate curves. From these curves information can be obtained on the viscosity as a function of shear rate. The yield value may be obtained by extrapolation of the linear portion of the shear stress-shear rate curve to zero shear rate. The procedure has been described before (3). 

The increase in gel strength with increase in bentonite concentration above the gel point is consistent with the increase in yield value and modulus. On the other hand, the limited creep measurements carried out on the present suspension showed a high residual viscosity Oq of the order of 9000 Nm s when the bentonite concentration was 45g dm. As recently pointed out by Buscall et al (27) the settling rate in concentrated suspensions depends on 0. With a model system of polystyrene latex (of radius 1.55 vim and density 1.05 g cm ) which was thickened with ethyl hydroxy ethyl cellulose, a zero shear viscosity of lONm was considered to be sufficient to reduce settling of the suspension with = 0.05. The present pesticide system thickened with bentonite gave values that are fairly high and therefore no settling was observed. 

Brenner (1974) has presented numerical results for the suspension stresses in various flows. Figure 6-14 plots the intrinsic viscosity [defined in Eq. (6-6)] for oblate and prolate spheroids of various aspect ratios as functions of the Peclet number. Note that as the aspect ratio of the spheroid increases, the zero-shear viscosity increases, and the suspension shows more shear thinning. The suspension also becomes more elastic when the aspect ratio p for prolate or 1/ for oblate spheroids) is large see Fig. 6-15, which plots Ni N2 versus Pe for prolate spheroids of various aspect ratios p. Typically, N2 is roughly an order of magnitude less than Ni, so this plot of Nj, mainly reflects the behavior of V,. 

The effective enlargement of the diameter of charged spheres leads to enhancement of the low-shear-rate viscosity. According to Russel (1978 Russel et al. 1989), the zero-shear viscosity out to second order in 0 of a disordered suspension of charged spheres is... 

Figure 6.29 Zero-shear relative viscosity versus particle volume fraction for aqueous suspensions of charged polystyrene spheres (a = 34 nm) in 5 x lO " M NaCl ( ) (Buscall et al. 1982a). The line is calculated by using Eq. (6-66) for the viscosity, with 0eff given by Eq. (6-64), and d ff by Eq. (6-67a) or (6-67b). The potential 1T(/ ) is given by Eq. (6-58) or (6-59) with k given by Eq. (6-61) the constant K is 0.10, and is in the range 50-90 mV. (From Buscall 1991, reproduced with permission of the Royal Society of Chemistry.)...

Stable particle suspensions exhibit an extraordinarily broad range of rheological behavior. which depends on particle concentration, size, and shape, as well as on the presence and type of stabilizing surface layers or surface charges, and possible viscoelastic properties of the suspending fluid. Some of the properties of suspensions of spheres are now reasonably well understood, such as (a) the concentration-dependence of the zero-shear viscosity of hard-sphere suspensions and (b) the effects of deformability of the steric-stabilization layers on the particles. In addition, qualitative understanding and quantitative empirical equations... 

Problem 6.1 (Worked Example) Estimate the zero-shear viscosity of a suspension of hard spheres 100 nm in diameter at a volume fraction of [Pg.318]

Figure 7.10 The effect of poly-isobutylene (PIB) concentration on the zero-shear viscosity of the suspensions described in Fig. 7-9. The lines were calculated assuming / r,o(0) = K exp(—atTniin/A er), with values of the second virial coefficient A2 of 6 X 10 8 X 10 and 10 ". (From Buscall et al. 1993, with permission from the Journal of Rheology.)...

The system shows a (dynamic) yield stress cr that can be obtained by extrapolation to zero shear rate [8]. Clearly, at and below cr the viscosity ri-roo. The slope of the hnear curve gives the plastic viscosity ri i- Some systems, such as clay suspensions, may show a yield stress above a certain clay concentration. 

In this section we investigate some of the properties of mixtures undergoing steady shearing flow. Specifically we consider the viscosity and normal stress functions for suspensions of rigid dumbbells of various lengths which have the same zero shear rate viscosity as a solution containing dumbbells of length L only. 

Particle Shape Effect. To this point, we have been dealing only with spherical particle suspensions. When the particles have irregular shapes, the rheological properties are expected to be very different from those of the spherical particle suspensions. Consider, for example, a simple system of cylindrical fibre suspensions. Because the particles are expected to align in the direction of the flow or shear, the viscosity needs to be treated as a second-order tensor, that is, the values of the viscosity under the same condition are different when different directions are referred. Only at the low (zero) shear limit may the particles be randomly distributed and have an isotropic rheological behavior. 

For colloidal particles, the dimensionless parameters are generally small and non-Newtonian effects dominate. Considering the same example as above, but with particles of radius a = 1 /xm, the parameters take on the values Pe = y, N y = 10 y, and N = 10 y so that for shear rates of 0.1 s or less they are all small compared to unity. The limit where the values of the dimensionless forces groups are very small compared to unity is termed the low shear limit. Here the applied shear forces are unimportant and the structure of the suspension results from a competition between viscous forces. Brownian forces, and interparticle surface forces (Russel et al. 1989). If only equilibrium viscous forces and Brownian forces are important, then there is well defined stationary asymptotic limit. In this case, there is an analogue between suspensions and polymers which is similar to that for the high shear limit, wherein the low shear limit for suspensions is analogous to the zero-shear-rate viscosity limit for polymers. 

We studied the dependence of spin modes on viscosity in the HDDA/persulfate system. Determining the viscosity is complicated by the shear-thinning behavior of silica gel suspensions. Figure 6 shows the apparent viscosity vs. shear rate for different percentages of silica gel in HDDA. The linear stability analysis assumes Newtonian behavior so we need to estimate the viscosity at zero shear, which is something we can not reliably estimate with our viscometer. We used the viscosities at the lowest shear rate we could measure and recognize that we are underestimating the true value. Fortunately, this does not affect the qualitative trends. 

The viscosity of a dilute suspension of solid spheres depends solely on the volume fraction of the spheres. Hence, the zero-shear viscosity r/o of a dilute suspension can be given... 

The flow behavior of silicone oils [5] and silicone oil/glass sphere suspensions [14] was studied by several authors. One of the most used rheological material parameters to characterize the flow behavior is the zero-shear-rate viscosity tIq. The t]o value of the linear silicone oils studied are correlated with the relevant weight-average molecular weight Af by Eq. 3 [16], where a = 3.58. 

Zero-Shear Viscosity The flow of dilute suspensions ( < 0.05) of rigid spheres in Newtonian liquid was described by Einstein in an article of 1906 on a new method for estimation of molecular dimension [37], and then corrected in 1911 [38] ... 

These data are presented in Table 3. What is immediately evident from these data is that the closest correlation occurred when particle settling rates were compared to the apparent viscosity measured at shear rates of 1 sec . The xanthan polymer solution showed a greater ability to suspend the solids and had a higher apparent viscosity in the low shear rate range. In contrast the HEC solution had higher apparent viscosities at shear rates above 10 sec but exhibited lower particle suspension properties. The dependence on low shear rate apparent viscosity is not entirely unexpected. Roodhart has shown emperically that the zero shear viscosity must be factored into a Stokes law type calculation before settling velocities can be calculated for HPG solutions. Thus, reliance on viscosity measurements at the customary shear rates would not have selected the more efficient fluid for particle suspension. 

The polymer concentration (c) dependence of the zero-shear-rate viscosity (r]o) for aqueous poly(acrylamide) solutions of various viscosity-average molecular weights does not seem to follow the entanglement model, wherein polymer chain interpenetration would dominate the viscometric behavior, and a master curve should result when rjo is plotted against cM,. Instead, the data can be better described using a suspension model, wherein c[r]] correlates the r]o data on a master plot. A concise presentation of the relationship between r]Q, Af, and c for poly(acrylamide) in water at 25°C has been made (12). 

Figure 19 Relative zero shear viscosity of PNIPAM microgels obtained at different concentrations and different temperatures vs. the effective volume fraction. The line represents the mastercurve of hard sphere suspensions. Reproduced with permission from Senff, H. Richtering, W. J. Chem. Phys. 1999, fff, 1705. 2...

The above systems show a yield value , xp, and a high viscosity at low shear rates [residual or zero shear viscosity //(o)]. Providing xp is higher than a certain value (> 0.1 Pa) and //(o) > 1000 Pa s, no sedimentation occurs with most suspensions. 

For more concentrated suspensions, other parameters should be taken into consideration, such as the bulk (elastic) modulus. Clearly, the stress exerted by the particles depends not only on the particle size but on the density difference between the partide and the medium. Many suspension concentrates have particles with radii up to 10 pm and a density difference of more than 1 g cm . However, the stress exerted by such partides will seldom exceed 10 Pa and most polymer solutions will reach their limiting viscosity value at higher stresses than this. Thus, in most cases the correlation between setfling velocity and zero shear viscosity is justified, at least for relatively dilute systems. For more concentrated suspensions, an elastic network is produced in the system which encompasses the suspension particles as well as the polymer chains. Here, settling of individual partides may be prevented. However, in this case the elastic network may collapse under its own weight and some liquid be squeezed out from between the partides. This is manifested in a dear liquid layer at the top of the suspension, a phenomenon usually... 

Rheological measurements are used to investigate the bulk properties of suspension concentrates (see Chapter 7 for details). Three types of measurements can be applied (1) Steady-state shear stress-shear rate measurements that allow one to obtain the viscosity of the suspensions and its yield value. (2) Constant stress or creep measurements, which allow one to determine the residual or zero shear viscosity (which can predict sedimentation) and the critical stress above which the structure starts to break-down (the true yield stress). (3) Dynamic or oscillatory measurements that allow one to obtain the complex modulus, the storage modulus (the elastic component) and the loss modulus (the viscous component) as a function of applied strain amplitude and frequency. From a knowledge of the storage modulus and the critical strain above which the structure starts to break-down , one can obtain the cohesive energy density of the structure. 

Viscosity is defined as the ratio of shear stress to shear rate. The viscosity of a Newtonian fluid is a material constant that depends on temperature and pressure but is independent of the rate of shear that is, the shear stress is directly proportional to the shear rate at fixed temperature and pressure. Low molar-mass liquids and aU gases are Newtonian. Complex liquids, such as polymers and suspensions, tend to be non-Newtonian in that the shear stress is a nonlinear function of the shear rate. Some typical melt viscosities are shown in Figure 1.7. The viscosity approaches a constant value at low shear rates, known as the zero-shear viscosity and denoted... 

Hard spheres suspensions of narrow size distribution are Newtonian at low volume fraction and then shear thin between a zero shear rate viscosity ( jo) and a high shear rate plateau viscosity ( oo)-Numerous studies (Russel, 1989 Dhont, 1989 Vanderwerff, 1989 Bergenholz, 2001, 2002 Dekruif, 1985 Fuchs, 2002 Lionberger, 1998, 2000)... 

Figure 19-13. Relative zero shear stress viscosities of hard sphere silica suspensions as a function of volume fraction. The symbols represent the data of different researchers. The solid line is the Doolittle Eq. (19-13) with 0m = 0.638, and the dashed line is the Quemada equation with 4>m = 0.638 (Marshaall, 1990). Good agreement with the Doolittle equation suggests an exponential increase in viscosity in the glassy regime ( > 0.5).

Thus, one measures creep curves as a function of the applied stress (starting from a very small stress of the order of 0.01 Pa). This is illustrated in Fig. 3.45. The viscosity Pu (which is equal to the reciprocal of the slope of the straight portion of the creep curve) is plotted as a function of the applied stress. This is schematically shown in Fig. 3.46. Below a critical stress the viscosity reaches a limiting value, p(o) namely the residual (or zero shear) viscosity. Above a , p decreases rapidly with a further increase in the shear stress (the shear thinning regime). It reaches another Newtonian value Poo, which is the high shear limiting viscosity. 0, may be identified as the critical stress above which the structure of the suspension is broken down . Ucr is denoted as the true yield stress of the suspension. 

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