Viscosity concentration relation

Lines are characteristic of the concentration-viscosity relation observed for carrageenin. 

It should be emphasized also that the viscosity relation applies to infinitely dilute solution. In a network swollen to equilibrium the segment concentration is far from being infinitely small. 

Since the width of this zone is significantly greater than the length of the molecular mean free path, we should speak not of energy transfer by direct impact, but of heat conduction and other dissipative processes in the gas—diffusion and viscosity—related to the gradients of the temperature, concentration and the velocity along the normal to the wave front. 

The effective volume fraction can be obtained from the intrinsic viscosity (rj) of the dispersion. According to Einstein s viscosity relation, the product of (ijl and the mass concentration c is proportional to the particle volume fraction, which is bigger for covered particles than for bare ones. The ratio (t 1 / n. where (rjlg is the intrinsic viscosity of the dispersion of bare particles, is therefore equal to the ratio between the volume of a covered pcutlcle and that of a bare one, l.e., it equals (l + d /a) . This method has been used by several authorsespecially in older work. 

Quemada (1978a, 1978b) examined the rheology and modelling of concentrated dispersions and described simple viscosity models that incorporate the effects of shear rate and concentration of filler and separate effects of Brownian motion (or aggregation at low shear) and particle orientation and deformation (at high shear). The ratio of structure-build-up and -breakdown rates is an important parameter that is influenced by the ratio of the shear rate to the particle diffusion. A simple form of viscosity relation is given here ... 

Harper and El Sahrigi (AS), Rao et al. (IS)/ and Tanglertpaibul and Rao (AS) found that the apparent viscosity and concentration were related by a power relationship the magnitude of the exponent ranged between 2.0 and 2.5. This general relationship is important because it can be used to estimate the viscosity of tomato concentrates at one concentration from the known value at another concentration. 

Rice 32) and Rose and Cook 3J ) in Canada have made a thorough study of concentration-viscosity relationships. It is not surprising that their data follow a different relation than that just shown, as most measurements were made in salt solutions at, or near, room temperature, in most cases with instruments reflecting variations in consistency by altering the rate of shear. Under these conditions they... 

Both solution viscosity and concentration are related by the Beriy number,... 

Mooney equation (M. Mooney) n. An empirical modification of the Einstein equation applicable to higher solids concentrations, and relating the viscosity of a suspension of monodisperse spheres to that of the pure liquid r]o. 

In viscosimetry, the (d5mamic) viscosity of a diluted solution of a special solvent and HDPE resin is determined, e.g. by capillary viscosimetry as per EN ISO 1628-3 2003 Plastics - Determination of Viscosity of Polymers in Dilute Solution Using Capillary Viscometers - Part 3 Polyetl l-enes and Polypropylenes. The flow time of the solution t and of the pure solvent to is measured in a capillary immersed in a hot bath at an elevated temperature. The coefficient of viscosity J is determined from this flow times. It is defined as the relative change of the viscosity of the solution p (proportional to t) with the concentration c related to the viscosity of the solvent rjQ (proportional to to) ... 

The viscosity of a polymer solution is related to the size and extension of the polymer molecule in that particular solution larger molecular species are generally associated with higher solution viscosities. In this section, the issue of the molecular size of the polymer is discussed mainly in the light of viscosity-related properties of the polymer solution. Relationships are developed that apply to both random coil molecules, such as HPAM, and more rigid macromolecules like xanthan. A number of other quantities are related to viscosity these include the relative viscosity, specific viscosity, reduced viscosity and inherent viscosity, which are defined in Table 3.1. (Billmeyer, 1971 Rodriguez, 1983). Clearly, all of these quantities are related to the polymer concentration in solution, and a more fundamental quantity which will be defined is the intrinsic viscosity, [ ]. The intrinsic viscosity is the limit of the reduced viscosity or inherent viscosity as the solution concentration of polymer tends to zero as shown below. 

The compatibility/screening tests are, in a sense, prerequisites for a polymer solution to be selected and involve polymer/brine compatibility, filterability, sensitivity to other additives, etc. If a given polymer, or polymer type, fails such screening tests, then it should be excluded from the candidate polymer list unless there is a simple technical solution which remedies the problem. The polymer core flood data are essentially the information that is collected in the laboratory that may be used directly (or indirectly) in the polymer simulations to assess the viability of the polymer pilot flood. Information such as concentration/viscosity behaviour, adsorption/retention levels, degree of permeability reduction, and in-situ rheology would come under this category. The importance of controlling the exact experimental conditions under which this type of data is collected will be discussed below. The third type of experiment relates to the oil displacement efficiency of the polymer solution and is usually only carried out in short linear systems. This type of experiment is of somewhat limited value for the reasons discussed below. 

The dependence of viscosity on volume fraction sohds is shown in Fig. 8.88. At high particle concentrations, viscosity of the suspension increases more rapidly than predicted by the above equation due to interparticle interactions. Several empirical equations are available to relate viscosity to the solid concentration behavior of suspensions. As the volume fraction of solids is increased further, a stage will be reached where the particles will be interlocked and no flow will occur (i.e., viscosity approaches infinity). The volume fraction of sohds at which this occurs is called the maximum packing fraction and its... 

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (02.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation (02.6.2) can be used to define an apparent viscosity, happ, at a given shear rate. If q pp decreases witli increasing shear rate, tire dispersion is called shear tliinning (pseudoplastic) if it increases, tliis is known as shear tliickening (dilatant). The latter behaviour is typical of concentrated suspensions. If a finite shear stress has to be applied before tire suspension begins to flow, tliis is known as tire yield stress. The apparent viscosity may also change as a function of time, upon application of a fixed shear rate, related to tire fonnation or breakup of particle networks. Thixotropic dispersions show a decrease in q, pp with time, whereas an increase witli time is called rheopexy. 

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

The viscosity of hydiochloiic acid solutions, T], incieases slightly with incieasing concentration and is related to the molar concentration c by... 

Of the three worldwide manufacturers of poly(ethylene oxide) resins. Union Carbide Corp. offers the broadest range of products. The primary quaUty control measure for these resins is the concentrated aqueous solution viscosity, which is related to molecular weight. Specifications for Polyox are summarized in Table 4. Additional product specifications frequendy include moisture content, particle size distribution, and residual catalyst by-product level. 

Controlled stress viscometers are useful for determining the presence and the value of a yield stress. The stmcture can be estabUshed from creep measurements, and the elasticity from the amount of recovery after creep. The viscosity can be determined at very low shear rates, often ia a Newtonian region. This 2ero-shear viscosity, T q, is related directly to the molecular weight of polymer melts and concentrated polymer solutions. 

With appropriate caUbration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to 2ero concentration yield the intrinsic storage and loss moduH [G ] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instmment provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 H2. High frequency (20 to 500 K H2) viscoelastic properties can be measured with another instmment, the high frequency torsional rod apparatus (HFTRA) (294). 

Some concerns directly related to a tomizer operation include inadequate mixing of Hquid and gas, incomplete droplet evaporation, hydrodynamic instabiHty, formation of nonuniform sprays, uneven deposition of Hquid particles on soHd surfaces, and drifting of small droplets. Other possible problems include difficulty in achieving ignition, poor combustion efficiency, and incorrect rates of evaporation, chemical reaction, solidification, or deposition. Atomizers must also provide the desired spray angle and pattern, penetration, concentration, and particle size distribution. In certain appHcations, they must handle high viscosity or non-Newtonian fluids, or provide extremely fine sprays for rapid cooling. 

An estimation of the multiphase viscosity is a preliminary necessity for convenient particle processing. For particle-doped liquids the classical Einstein equation [20] relates the relative viscosity to the concentration of the solid phase ... 

Pisarzhevski-Walden equation to measured values of the dynamic viscosity. However, use of this relation is only correct for solutions in the limit of zero concentration and no change in solution mechanism. 

The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

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