Colloid Sci Research Articles

Parametric analysis of the transient back extrusion flow to determine instantaneous viscosity

Rotational rheometers are extremely sensitive instruments that are able to provide very accurate measurements of low values of different material functions, such as viscosity and viscoelastic moduli, under certain ideal flow conditions. Nevertheless, they fail in providing reliable data for the viscosity when measured at short time scales due to either instrument or fluid inertia. In 1948, Bikerman [“A penetroviscometer for very viscous liquids,” J. Colloid Sci. 3, 75 (1948)] proposed the penetroviscometer device as an instrument to measure the viscosity of highly viscous (102–104 Pa · s) Newtonian fluids under steady shear conditions. In the penetroviscometer, the fluid sample undergoes a kind of flow, which is currently known as back extrusion flow, and it is nowadays used to characterize the rheological properties of foodstuff under steady flow conditions. In this study, we perform a parametric analysis (blockage ratio, initial position, velocity profile of the inner cylinder, and viscosity of Newtonian fluids) of the back extrusion flow to determine its potential to provide reliable viscosity measurements at short time scales. Three-dimensional numerical simulations including free surface effects and inertial terms allowed us to determine its limits of operation. We additionally provide an analytical expression to calculate the time-resolved viscosity, relating the force and velocity of the inner cylinder by means of a geometric factor.

Corrigendum to “Superhydrophobic antibacterial cotton textiles” [J. Colloid and Interface Sci. 351 (1) (2010) 293–298

The authors regret three mistakes exist: ‘‘octyltrithoxysilane” must be replaced by ‘‘octyltriethoxysilane” on page 2, column 1, line 4 and page 2, column 2, line 1. ‘‘Tetraethylorthosilicate (TEOS)” should be deleted from page 2, second column, line 1. ‘‘G40” must be replaced by ‘‘G10” on line 3, in section ‘‘Characterization techniques”. The authors would like to apologise for any inconvenience caused.

The rheology of suspensions of solid particles

We present data for the rheology of suspensions of monodisperse particles of varying aspect ratio, from oblate to prolate, and covering particle volume fractions ϕ from dilute to highly concentrated. Rheology is characterized by fitting the experimental data to the model of Herschel & Bulkley (Herschel & Bulkley 1926 Kolloid Z. 39 , 291–300 ( doi:10.1007/BF01432034 )) yielding three rheometric parameters: consistency K (cognate with viscosity); flow index n (a measure of shear-thinning); yield stress τ 0 . The consistency K of suspensions of particles of arbitrary aspect ratio can be accurately predicted by the model of Maron & Pierce (Maron & Pierce 1956 J. Colloid Sci. 11 , 80–95 ( doi:10.1016/0095-8522(56)90023-X )) with the maximum packing fraction ϕ m as the only fitted parameter. We derive empirical relationships for ϕ m and n as a function of average particle aspect ratio r p and for τ 0 as a function of ϕ m and a fitting parameter τ *. These relationships can be used to predict the rheology of suspensions of prolate particles from measured ϕ and r p . By recasting our data in terms of the Einstein coefficient, we relate our rheological observations to the underlying particle motions via Jeffery’s (Jeffery 1922 Proc. R. Soc. Lond. A 102 , 161–179 ( doi:10.1098/rspa.1922.0078 )) theory. We extend Jeffery’s work to calculate, numerically, the Einstein coefficient for a suspension of many, initially randomly oriented particles. This provides a physical, microstructural explanation of our observations, including transient oscillations seen during run start-up and changes of rheological regime as ϕ increases.

Online study of the formation of PA6 droplets in PP matrix under shear flow

Breakup process of polyamide 6 (PA6) in polypropylene (PP) matrix under shear flow was online studied by using a Linkam CSS 450 stage equipped with op- tical microscopy. Both tip streaming and fracture breakup modes of PA6 droplets were observed in this study. It was reported that the droplet would break up by tip streaming model when the radio of the droplet phase viscosity to the matrix phase viscosity (Zr ¼ Zd/Zm) is smaller than 0.1 (Taylor, Proc R Soc London A 1934, 146, 501; Grace, Chem Eng Commun 1982, 14, 225; Bartok and Mason, J Colloid Sci 1959, 14, 13; Rumscheidt and Mason, J Colloid Sci 1961, 16, 238; de Bruijn, Chem Eng Sci 1993, 48, 277). However, the tip streaming model was observed even when the viscosity ra- tio was much greater than 0.1 (Zr ¼ 1.9). In this study for the tip streaming mode, small droplets were ruptured from the tip of the mother droplet. On the other hand, the mother droplet was broken into two or more daughter droplets with one or several satellite droplets between them for the frac- ture mode. It was found that PA6 droplet was much elon- gated at first, and then broke up via tip streaming or fracture to form daughter droplets or small satellite droplets with the shape of fiber or ellipse. Stopping shearing, those elongated droplets began to shrink, and finally became spheres. More- over, it was found that the average domain size of those PA6 spheres considerably decreased with increasing shear time. 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 2690- 2695, 2007

Viscosity of ‘live’ water-in-crude-oil emulsions: experimental work and validation of correlations

A method for measuring emulsion viscosity under pressurized (1–100 bar) and temperature-controlled flow conditions is described. It makes use of a flow simulator shaped as a hollow wheel. As the wheel is rotating, the liquid inside will have a relative motion in the opposite direction of the rotation. The torque acting on the wheel shaft is measured and transformed, via a calibration model, into the viscosity of the fluid. The method has been applied to water-in-oil emulsions with several live North Sea crude oils with saturation pressures up to 100 bar and water cuts in the range 0–90%. The method is shown to be a useful way of obtaining estimates of emulsion viscosity for live oil systems in a relatively small scale apparatus. Even though the crude oils studied were rather different and had very different viscosities, the relative viscosities as a function of water cut up to at least 60% showed small variation and might be represented by a general ‘master curve’. The relative viscosities obtained experimentally have been compared to a temperature-dependent Richardson-type correlation [Rønningsen, H.P., 1995. Correlations for predicting viscosity of W/O-emulsions based on North Sea crude oils. Proc. SPE Int. Symp. Oil Field Chem., Houston, TX, USA, SPE 28968], and three other correlations proposed by Mooney [J. Colloid Sci. 6 (1951) 162], Pal and Rhodes [J. Rheol. 337 (1989) 1021] (P&R) and Pal [J. Colloid Interface Sci. 231 (2000) 168], respectively. Overall, when being tuned to measured data, the P&R correlation gives the best match, closely followed by the Mooney correlation, but for low and medium water cuts, the Rønningsen correlation is comparable. This correlation does not require any measurements for tuning. Although it may be slightly conservative at low to medium water cuts, and somewhat optimistic at very high water cuts, for practical purposes in design of flow lines, it provides a reasonably accurate first estimate of the effective liquid phase viscosity. The recent correlation of Pal [J. Colloid Interface Sci. 231 (2000) 168] was found to be extremely sensitive to the choice of tuning point and, thus, to be rather inaccurate either at low water cuts or high water cuts.

The coalescence cascade of a drop

When a drop is deposited gently onto the surface of a layer of the same liquid, it sits momentarily before coalescing into the bottom layer. High-speed video imaging reveals that the coalescence process is not instantaneous, but rather takes place in a cascade where each step generates a smaller drop. This cascade is self-similar and we have observed up to six steps. The time associated with each partial coalescence scales with the surface tension time scale. The cascade will, however, not proceed ad infinitum due to viscous effects, as the Reynolds number of the process is proportional to the square root of the drop diameter. Viscous effects will therefore begin to be important for the very smallest drops. This cascade is very similar to the one observed previously by Charles and Mason [J. Colloid Sci. 15, 105 (1960)] for two immiscible liquids, where one of the liquids replaces the air in our setup.

Self-Preservation of the Drop Size Distribution Function and Variation in the Stability Ratio for Rapid Coalescence of a Polydisperse Emulsion in a Simple Shear Field

Coalescence of oil-in-water emulsion droplets in a simple shear flow produced by a Couette device is considered. A phase Doppler anemometer was used to measure the droplet size distribution as a function of time for shear rates ranging from 55 to 213 s−1and for sodium chloride salt concentrations from 0.095 to 0.6 M. The initial droplet size distribution was log-normal. During the coalescence process, the size distribution was self-preserving in accordance with D. L. Swift and S. K. Friedlander's analysis [J. Colloid Sci.19,621 (1964)]. In the limiting case of negligible repulsive force due to the electric double layer, the calculated stability ratios, corrected for droplet polydispersity, agree well with the theoretical analyses of G. R. Zeichner and W. R. Schowalter [AIChE J.23,243 (1977)] and D. L. Feke and W. R. Schowalter [J. Fluid Mech.133,17 (1983)] for the case of solid particle aggregation. The good agreement between the stability ratios for the case of coalescence of droplets in the present study and those for aggregation of solid particles indicates that resistance to film deformation and thinning present in the case of coalescence is not important compared with the collision process.

Measurement of the thermophoretic force by electrodynamic levitation: Microspheres in air

The thermophoretic force on single microspheres has been measured over a wide range of Knudsen numbers and particle thermal conductivities for solid and liquid spheres in air. The microspheres were dioctyl phthalate (DOP) droplets, metallic nickel, polystyrene latex (PSL), and glass. This covers a thermal conductivity ratio (gas to particle) range of 2 × 10 −4−0.17. In a companion paper, results are reported for monatomic (helium) and polyatomic gases (carbon dioxide and air) to examine the effects of gas properties. The measurements were accomplished by levitating the particle between heated and cooled plates mounted in a vacuum chamber. Light-scattering phase functions were used to determine the size of all materials except the nickel spheres, and for the highly absorbing metallic spheres the size was obtained by measuring the marginal stability limit of the particle. The apparatus developed for the research and the experimental techniques are discussed, and the experimental results in the Knudsen number range 0.05–20 are compared with previously proposed theories. For particle Knudsen numbers greater than about 10, the effects of the temperature jumps (thermal slip) at the heated and cooled plates become significant. The data in the transition regime overlap Loyalka's (1992, J. Aerosol Sci. 23, 291–300) solution of the linearized Boltzmann equation for hard-sphere molecules, and the data in the slip regime agree with Brock's (1962, J. Colloid Sci. 17, 768–780) theory. The effects of particle thermal conductivity are shown to be nearly negligible in the Knudsen regime, for the data for particles having greatly different thermal conductivities overlap.

An Experimental Study of the Radial Penetration of Liquids in Thin Porous Substrates

We present the results of an experimental study of the radial capillary penetration of liquids in thin porous substrates. In particular, we examine the effect of the size of the liquid reservoir on the rate of radial spreading. For capillary penetration from an infinite reservoir, the experimental data are found to be in good qualitative agreement with Marmur's model (J. Colloid Interface Sci.124, 301 (1988)). In the case of spreading liquid drops, both phases of spreading seem to follow Gillespie's prediction (J. Colloid Sci. 13, 32 (1958)) of a t-5/6 dependence of spreading rate on time.

The influence of food emulsifiers on fat and sugar dispersions in oils. II. Rheology, colloidal forces

The influence of food emulsifiers on the viscoelastic properties (storage modulus and yield value) of fat and sugar dispersions in vegetable oils has been investigated. It was found that almost all of the emulsifiers tested influence the rheology of the dispersions. The magnitude and the direction of the rheological changes depend on both the type and the amount of emulsifier. In most cases the changes are relatively small, especially for fat crystals. Generally speaking, the largest changes are caused by lecithins and saturated monoglycerides. The magnitudes of colloidal forces and equilibrium distances between the particles have been estimated from the rheological network model of van den Tempel [J. Colloid Sci. 16:284 (1964)] and from the correlation of the yield value to the interaction energy by Gillespie [J. Colloid Sci. 15:219 (1960)] and Tadros [Langmuir 6:28 (1990) andChemistry and Industry 7:210 (1985)]. The results indicate that van der Waals forces alone cannot be responsible for the interparticle interaction in fat or sugar dispersions. The formation of water bridges is discussed as a probable source of interaction in both cases. Furthermore, the validity of the network model for fat and sugar dispersions in oils is questionable.

Measurements of the complex dynamic shear compliance and loss tangent of pilot whale blubber and the role of blubber in flow-noise reduction

The complex dynamic shear compliances and loss tangents of pilot whale blubber (BLB), pork-belly fat (PBF), and beef-belly fat (BBF) have been measured over a frequency range of ≃ 45 to 4500 Hz, using the Fitzgerald apparatus [E. R. Fitzgerald and J. D. Ferry, J. Colloid Sci. 8, 1–34 (1953)]. Representative values at 100 Hz for J* and tan ζ PBF, J* = 3 × 10−9 cm2/dyn, tan ζ = 0.5; BLB, J* = 2 × 10−6 cm2/dyn, tan ζ = 0.7; BBF, J* = 2 × 10−8 cm2/dyn, tan ζ = 0.1. Thus beef-belly fat is ≃ 100 times stiffer (less compliant) and pork-belly fat is ≃ 15 times less stiff (more compliant) than whale blubber. The general shape of the compliance curves are similar except for a frequency shift in the peak values. The broad peak in J* and tan ζ implies a relaxation mechanism in all three fats. The high loss tangent in blubber and its intermediate value of compliance suggests that it plays a role in reducing flow noise by acting as a “matched load” to the boundary layer “turbulence generator.” A polyvinyl gel, with dynamic shear properties closely matched to those of blubber, is proposed as a “synthetic blubber: for studies of turbulent flow over compliant surfaces.” [Work had fragmentary support from NUSC/NLON.]

The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration

A one-dimensional ultrafiltration problem of fluid flow through a soft permeable tissue or gel under high pressure and compressive strain is solved. A finite deformation biphasic theory is used to model the behavior of the soft porous permeable solid matrix. This theory includes a Helmholtz free energy function which depends on the three principal invariants (I, II, III) of the right Cauchy-Green tensor and which satisfies the Baker-Ericksen inequalities on the principal stresses and strains. The dependence of the porosity φ f and the solidity φ s on deformation is deduced and a generalization of the exponential strain-dependent functional form for the permeability, k = k 0exp( Mϵ), of Lai and Mow ( Biorheology 103, 111–123, 1980) is proposed. In this one-dimensional problem, we show that the dependence of the permeability on φ f , φ s , and III is equivalent to its dependence on hydration as proposed by Fatt and Goldstick ( J. Colloid Sci. 20, 962–988, 1965). The exact solution of the ultrafiltration problem is derived and asymptotic and numerical methods are used to evaluate it. For high pressures and finite strains, the solution provides some suprising effects. The theory predicts that a material starting with a homogeneous porosity will have a strongly non-homogeneous porosity throughout the column during ultrafiltration. The resulting change in pore size through the filtration column may be very important in understanding its filtration characteristics. It is also found that there is a long delay time, up to 10 to 15 min, before the filtration velocity reaches an equilibrium. In filtration experiments where the rate of mass transport across the tissue or column of gel is important, sufficient time must be allowed for the steady state to be reached.

Surface diffusion in monomolecular films: II. Experiment and theory

Surface diffusion in myristic acid monolayers at the air—water interface was investigated using a radiotracer technique. Surface self-diffusion coefficients ( D s) were determined at various surface concentrations in the liquid-expanded state at 20, 25, and 30°C with an improved experimental apparatus. D s values as much as two orders of magnitude smaller than those reported earlier for the liquid-expanded state were obtained because we were able to minimize the confounding problem of extraneous surface convective flows by stringent temperature (±0.02°C) and humidity (saturation) control. The equilibrium density fluctuation model of M. Blank and J. S. Britten [ J. Colloid Sci. 20, 789 (1965)] was extended to liquid-expanded monolayers, and the theoretical predictions were found to agree well with experimental results. Agreement between experiment and theory, however, requires that the entropy changes associated with the density fluctuations be properly evaluated. There appears to be two regimes of surface diffusion: one strongly surface concentration dependent and the other only weakly dependent on surface concentration. In the latter regime, our findings clearly provide support for a “free area” mechanism of surface diffusion due to thermal fluctuations in the surface density of the monomolecular film. On the other hand, the measured lateral mobility is much faster in the former regime; presumably multiple exchange of the film molecules or another transport mechanism becomes significant.

Chain-axis invariant and chain-axis rotation twins in polymer crystals

A detailed treatment is presented of the crystallography of twinning shears which cause the polymer chain axes in polymer crystals to be invariant or to be rotated but undistorted. These chain-axis invariant and rotation twins in polyethylene are considered in detail. The polyethylene twinning mode with twinning elements $$\begin{gathered} K_1 = \{ 102\} ;\eta _1 = \left\langle {20\bar 1} \right\rangle ; K_2 = \{ 100\} ; \hfill \\ \eta _2 = \left\langle {001} \right\rangle and magnitude of shear{\mathbf{ }}g = 0.34 \hfill \\ \end{gathered} $$ is proposed as the twinning mode which is most likely to cause a marked chain axis rotation without causing a change in the orientation of theb axis and only a small change in thickness of crystalline lamellae. These are the requirements ofc-twinning which was used byPietralla (Colloid & Polymer Sci.254, 249–257 (1976) to explain some aspects of the orientation behaviour of polyethylene.

Floc density, porosity and void ratio in colloidal systems and aerosols

An enclosing volume is defined for the flocs formed from very fine particles in colloidal systems and aerosols, and a computerized procedure for its calculation is developed. Two model flocculation schemes, i.e., the Uniformly Sized Particles Model [Sutherland and Goodarz-Nia, Chem. Eng. Sci., 26, 2071 (1971)] and the Nonuniformly Sized Particles Model [Goodarz-Nia and Sutherland, Chem. Eng. Sci. 30, 407 (1975)], are carried out to form a large number of flocs. Applying the above computerized procedure to these flocs, important morphological parameters such as density, porosity, and void ratio are calculated. The results of these calculations are compared with the corresponding results computed on the basis of the volume of the radius equivalent ellipsoid, the volume estimate from the silhouette area proposed by Medalia [ J. Colloid Interface Sci. 32, 115 (1970)], and core and shell densities as proposed by Vold [ J. Colloid Sci. 18, 684 (1963)]. On the basis of the so obtained results correlations are developed for the prediction of the above morphological parameters as functions of the number of particles in the floc and the floc particle size distribution.

Acoustic Streaming as a Mechanism in the Treatment of Suspensions

Hydrodynamical shearing of droplets occurs when sufficiently high-velocity gradients exist [F. D. Rumscheidt and S. G. Mason, J. Colloid Sci. 16, 238–245 (1961)]. Theory for acoustic microstreaming near a gas bubble indicates that large velocity gradients can exist in the boundary layer. Comparison of such gradients with hydrodynamic theory leads to the prediction that acoustic streaming can be an important mechanism in the disruption of suspensions. For example hydrodynamic theory predicts that a velocity gradient of 2.5 × 104 sec−1 existing in a fluid with a viscosity of 20 cP is sufficient to shear a droplet of radius 10 μ and a surface tension of 10 dyn/cm. A velocity gradient of this magnitude exists near a resonant 20-kHz bubble oscillating with an amplitude of 20 μ. Under suitable experimental conditions, such amplitudes can be achieved using a single controlled oscillating bubble. Data obtained from such an arrangement substantiate aspects of the theory. [This investigation was supported by a National Institutes of Health Fellowship.]

The effect of electrolyte content on synthetic latex flow behavior

Usually a synthetic latex contains inorganic salts from the water-soluble initiator used in polymerization and from the impurities in the surfactant used to stabilize the latex. Upon removal of this electrolyte, by dialysis, the viscosity of the latex increases and becomes markedly shear thinning, i.e., non-Newtonian. When an electrolyte such as sodium chloride is added, the viscosity decreases immediately and may even become less than the viscosity of the original latex, and the flow behavior becomes Newtonian. Measurements show that the only significant change in the latex system is in the gegenion concentration. The particle size distribution measured on diluted latices does not change through all these viscosity changes and only a small fraction of the adsorbed surfactant is desorbed and lost upon dialysis. Upon addition of sufficient electrolyte a minimum viscosity is obtained which is that which would have been predicted by Mooney's equation.( J. Colloid Sci. 6, 162 (1951)) The use of Mooney's equation to obtain effective volume fractions from viscosities shows that the experimental data are consistent with the viewpoint that the effective volume fraction is given by the polymer volume plus the volume excluded to particles by the interaction of the charged double layers. Thus, the observed phenomenon is also consistent with a large body of colloidal theory and experiment.

Cylindrical diffusion with a discontinuous boundary

AbstractIn continuation of the article of HermansJ. J. Hermans. J. Colloid Sci. 2, 387 (1947). the theory is treated of the cylindrical diffusion in a medium with immobile “holes”, in which the diffusing particles are caught. This theory gives a better description of Hermans's observations than a formula of Bungenberg de Jong applied by him.