Generation of inkjet droplet of non-Newtonian fluid

In this study, the generation of inkjet droplets of xanthan gum solutions in water–glycerin mixtures was investigated experimentally to understand the jetting and drop generation mechanisms of rheologically complex fluids using a drop-on-demand inkjet system based on a piezoelectric nozzle head. The ejected volume and velocity of droplet were measured while varying the wave form of bipolar shape to the piezoelectric inkjet head, and the effects of the rheological properties were examined. The shear properties of xanthan gum solutions were characterized for wide ranges of shear rate and frequency by using the diffusive wave spectroscopy microrheological method as well as the conventional rotational rheometry. The extensional properties were measured with the capillary breakup method. The result shows that drop generation process consists of two independent processes of ejection and detachment. The ejection process is found to be controlled primarily by high or infinite shear viscosity. Elasticity can affect the flow through the converging section of inkjet nozzle even though the effect may not be strong. The detachment process is controlled by extensional viscosity. Due to the strain hardening of polymers, the extensional viscosity becomes orders of magnitude larger than the Trouton viscosities based on the zero and infinite shear viscosities. The large extensional stress retards the extension of ligament, and hence the stress lowers the flight speed of the ligament head. The viscoelastic properties at the high-frequency regime do not appear to be directly related to the drop generation process even though it can affect the extensional properties.     

Rheology of oil-in-water emulsions

The effect of interfacial tension on the steady-flow and dynamic viscoelastic behavior of emulsions are studied experimentally. At very low inter-facial tensions and low volume fractions, the viscosity decreases with increasing shear rate and becomes constant at high shear rates. The high-shear-rate Newtonian viscosity is not affected by interfacial tension, but the transition from pseudoplastic to Newtonian flow shifts to lower shear rates as the interfacial tension decreases. At an interfacial tension of 5 × 10^–3 Nm^–1, the viscosity decreases, passes through a minimum, and then increases as the shear rate is increased. The dilatant behavior may be attributed to elastic responses of interfaces during collision of drops. At high volume fractions, the emulsions show remarkable elasticity resulting from the interfacial energy associated with deformation of liquid films. The modulus and viscosity are proportional to interfacial tension and inversely proportional to drop size.     

Droplet deformation of a strongly shear thinning dense suspension of polymeric micelles

We investigated the deformation of a strong shear thinning droplet undergoing simple shear flow in a Newtonian liquid. The droplet was an aqueous solution of poly(ethylene oxide) end capped with an alkyl group that forms spherical micelles in aqueous solution. At high concentrations and below a critical temperature, the jammed micelles showed strong shear thinning behaviour, and neither a yield stress nor a Newtonian viscosity was observed. At small shear rates, the droplet rotated and aligned in the flow, but did not deform or only very weakly. At high shear rates, the droplet deformation increased with increasing shear rate. The deformed droplet did not relax after the shear was stopped except for a modest rounding of the edges. For each shear rate, an apparent viscosity, η _ad, of the equivalent Newtonian droplet was calculated assuming affine deformation. η _ad showed a power law dependence on the capillary number Ca with an exponent of − 1.8 and was larger than the shear viscosity of the micelle suspension at the same shear rates. The results were explained by the existence of a strong gradient of the viscosity inside the droplet leading to a very low viscosity fluid layer near the droplet/matrix interface.     

Spreading of inkjet droplet of non-Newtonian fluid on solid surface with controlled contact angle at low Weber and Reynolds numbers

The dynamics of inkjet droplet of non-Newtonian fluid on glass substrates was investigated experimentally and compared with that of Newtonian fluid. The non-Newtonian fluids used here were 100 ppm solutions of polyethylene oxide (300k, 600k and 900k) dissolved in the 1:1 mixture of water and glycerin. Weber number (We) was 2–35 and Ohnesorge number was fixed at 0.057 ± 0.003. The wettability of solid substrate was also varied. The diameter of inkjet droplets in the present study was about 50 μm and was much smaller than the size of the previous studies on drop impact. Due to the development of a thin and long thread at the rear of the main drop the jetting window of polymer solution was much narrower than that of Newtonian fluid, and hence the experimental range of Weber number was restricted. The impact scenarios of non-Newtonian inkjet droplets were found to be qualitatively different from those of Newtonian droplets during the receding phase while they were almost the same as the Newtonian fluid case during the kinematic phase. The spreading diameter at the equilibrium was well correlated with the modified Weber number (We′ = We/(1 − cos θ_eq)) as in the case of Newtonian fluid, where θ_eq is the equilibrium contact angle. The similarity or disparity between the Newtonian and non-Newtonian cases was discussed considering the conformation of polymer chains during each stage of drop deformation.     

Breakup of a capillary bridge of suspensions

The breakup of liquid bridges under the action of capillary forces is used for studying the rheology of suspensions under stretching. The experiments were performed with suspensions of finegrained (3–30 μm) sand in glycerin for sand volume fractions up to 0.465. The bridge thinning process was registered using an electro-optical measuring device and videofilming. The results were analyzed on the basis of a theory developed earlier for the thinning of a liquid bridge under the action of capillary forces. It is found that, for fairly slow stretching realized in the initial stage of the thinning, the rheological behavior of the suspensions considered agrees with the model of a Newtonian viscous fluid. Along with this, the measured effective viscosity of the suspension turned out to be approximately two-fold greater than the suspension viscosity under shear. The origin of this discrepancy is analyzed. With increase in the stretching rate, in the final stage of the thinning, the weakening of the suspension occurs, which is manifested in the formation of a local rapidly thinning neck in the bridge, similar to that observed in the breakup of plastic materials.     

Microstructure of shear-thickening concentrated suspensions determined by flow-USANS

Reversible shear thickening in colloidal suspensions is a consequence of the formation of hydroclusters due to the dominance of short-ranged lubrication hydrodynamic interactions at relatively high shear rates. Here, we develop and demonstrate a new method of flow-ultra small angle neutron scattering to probe the colloidal microstructure under steady flow conditions on length scales suitable to characterize the formation of hydroclusters. Results are presented for a model near hard-sphere colloidal suspension of 260 nm radius (10% polydisperse) sterically stabilized silica particles in poly(ethylene glycol) at shear rates in the shear thinning and shear thickening regime for dilute, moderately concentrated, and concentrated (ordered) suspensions. Hydrocluster formation is observed as correlated, broadly distributed density fluctuations in the suspension with a characteristic length scale of a few particle diameters. An order–disorder transition is observed to be coincident with shear thickening for the most concentrated sample, but the shear-thickened state shows hydrocluster formation. These structural observations are correlated to the behavior of the shear viscosity and discussed within the framework of theory, simulation, and prior experiments.     

Bulk rheology of dilute suspensions in viscoelastic liquids

A theoretical relation is derived for the bulk stress in dilute suspensions of neutrally buoyant, uniform size, spherical drops in a viscoelastic liquid medium. This is achieved by the classic volume-averaging procedure of Landau and Lifschitz which excludes Brownian motion. The disturbance velocity and pressure fields interior and exterior to a second-order fluid drop suspended in a simple shear flow of another second-order fluid were derived by Peery [9] for small Weissenberg number (We), omitting inertia. The results of the averaging procedure include terms up to orderWe ². The shear viscosity of a suspension of Newtonian droplets in a viscoelastic liquid is derived as $$\eta _{susp} = \eta _0 \left[ {1 + \frac{{5k + 2}}{{2(k + 1)}}\varphi - \frac{{\psi _{10}^2 \dot \gamma ^2 }}{{\eta _0^2 }}\varphi f_1 (k, \varepsilon _0 )} \right],$$ whereη ₀, andω ₁₀ are the viscosity and primary normal stress coefficient of the medium,ε ₀ is a ratio typically between ?0.5 and ?0.86,k is the ratio of viscosities of disperse and continuous phases, and \(\dot \gamma \) is the bulk rate of shear strain. This relation includes, in addition to the Taylor result, a shear-thinning factor (f ₁ > 0) which is associated with the elasticity of the medium. This explains observed trends in relative shear viscosity of suspensions with rigid particles reported by Highgate and Whorlow [6] and with drops reported by Han and King [8]. The expressions (atO (We ²)) for normal-stress coefficients do not include any strain rate dependence; the calculated values of primary normal-stress difference match values observed at very low strain rates.     

In situ observations of unusual drop deformation and wobbling in simple shear flow

Deformation and wobbling of a liquid drop immersed in a liquid matrix were studied under mild shear conditions for various viscosity ratios. In situ visualization experiments were conducted on a homemade transparent Couette cell incorporated to the Paar Physica MCR500 shear rheometer. The effect of drop or matrix elasticity was examined and was found to play a major role in both deformation and wobbling processes. Experimental results were compared to Jackson and Tucker (J Rheol 47:659–682, 2003), Maffettone and Minale (J Non-Newton Fluid Mech 78:227–241, 1998) and Yu and Bousmina (J Rheol 47:1011–1039, 2003) ellipsoidal models. It was found that the agreement between the Newtonian models and the experimental results required an increase in the drop viscosity. Such increment in viscosity was found to scale with the first normal stress difference.     

Phase split of nitrogen/non-Newtonian fluid two-phase flow at a micro-T-junction

An experimental investigation has been undertaken to understand the phase split of nitrogen gas/non-Newtonian liquid two-phase flow passing through a 0.5 mm T-junction that oriented horizontally. Four different liquids, including water and aqueous solutions of carboxymethyl cellulose (CMC) with different mass concentrations of 0.1, 0.2 and 0.3 wt%, were employed. Rheology experiments showed that different from water, CMC solutions in this study are pseudoplastic non-Newtonian fluid whose viscosity decreases with increasing the shear rate. The inlet flow patterns were observed to be slug flow, slug–annular flow and annular flow. The fraction of liquid taken off at the side arm for nitrogen gas/non-Newtonian liquid systems is found to be higher than that for nitrogen gas/Newtonian liquid systems in all inlet flow patterns. In addition, with increasing the pseudoplasticity of the liquid phase, the side arm liquid taken off increases, but the increasing degree varies with each flow pattern. For annular flow, the increasing degree is much greater than those for slug and slug–annular flows.     

Bimodal model of slurry viscosity with application to coal-slurries. Part 1. Theory and experiment

The rheological behavior of stable slurries is shown to be characterized by a bimodal model that represents a slurry as made up of a coarse fraction and a colloidal size fine fraction. According to the model, the two fractions behave independently of each other, and the non-Newtonian behavior of the viscosity is solely caused by the colloidal fraction, while the coarse fraction increases the viscosity level through hydrodynamic interactions. Data from experiments run with colloidal coal particles of about 2–3 µm average size dispersed in water show the viscosity of these colloidal suspensions to exhibit a highly shearrate-dependent behavior and, in the high shear limit, to match very closely the viscosity of suspensions of uniform size rigid spheres although the coal volume fraction must be determined semi-empirically. Different amounts of coarse coal particles are added to the colloidal suspension and the viscosity of the truly bimodal slurries measured as a function of shear rate. In agreement with the bimodal model, the measured shear viscosities show the coarse fraction to behave independently of the colloidal fraction and its contribution to the viscosity rise to be independent of the shear rate. It is shown that the shear rate exerted on the colloidal fraction is higher than that applied by the viscometer as a result of hydrodynamic interactions between the coarse particles, and that it is this effective higher shear rate which is necessary to apply in the correlations. For determining the coal volume fraction a relatively simple and quite accurate measurement technique is developed for determining the density and void fraction of coarse porous particles; the technique directly relates volume fraction to mass fraction.     

Newtonian drop in a Newtonian matrix subjected to large amplitude oscillatory shear flows

The dynamics of a single Newtonian drop immersed in a Newtonian matrix subjected to large-amplitude oscillatory shear flow is investigated. The ratio of the drop and matrix viscosity is above criticality, and thus break-up is absent under constant shear flow. At small forcing amplitudes the drop shape follows a regular oscillation. As the forcing amplitude increases, multipeaked oscillations of drop shape and orientation are observed. Experimental results are compared with predictions obtained with a phenomenological model. Model predictions are in qualitative good agreement with experimental data. The model suggests that the appearance of higher harmonics in the drop response is mainly due to flow nonaffinity.     

A parametric study of droplet deformation through a microfluidic contraction: Shear thinning liquids

Numerical simulations of a droplet passing through an axisymmetric microfluidic contraction are presented, focusing on systems where one of the two liquids present is shear thinning. The simulations are performed using a transient Volume of Fluid (VOF) algorithm. When the droplet is shear thinning and the surrounding phase Newtonian, droplets deform in a similar way to Newtonian droplets that have a viscosity equal to the average viscosity of the shear thinning fluid while it is within the contraction. When the surrounding phase is shear thinning and the droplet Newtonian, droplets deform in a similar way to droplets contained within a Newtonian liquid that has a viscosity that is lower than that of the droplet. In both cases the behaviour of the shear thinning fluid can be broadly described in terms of a ‘characteristic’ Newtonian viscosity: However, determining the exact value of this viscosity without performing a full shear thinning simulation is not possible.     

Viscous oil–water flows in a microchannel initially saturated with oil: Flow patterns and pressure drop characteristics

Immiscible viscous liquid–liquid two-phase flow patterns and pressure drop characteristics in a circular microchannel have been investigated. Water and silicone oil with a dynamic viscosity of 863 mPa s were injected into a fused silica microchannel with an inner diameter of 250 μm. As the microchannel was initially filled with the silicone oil, an oil film was found to always form and remain on the microchannel wall. Different flow patterns were observed and classified over a wide range of water and oil flow rates. A flow pattern map is presented in terms of Re, Ca, and We numbers. Two-phase pressure drop data have also been collected and analyzed to develop a simple correlation for slug, annular and annular-droplet flow patterns in terms of superficial water and oil velocities.     

Size prediction of drops formed by dripping at a micro T-junction in liquid-liquid mixing

In the present work, the formation of liquid drops by dripping at a micro-scale T-junction with a square cross-section (90 × 90 μm²) was examined. The drop formation process consists of three stages: X-Y and X-growth stages and a detachment stage. In the X-Y growth stage, the tip of the disperse phase grows both in the longitudinal (X) and lateral (Y) directions to form a bulged shape until a maximum value of Y is reached. Then, in the X-growth stage, the bulged part continues to grow but only in X-direction, followed by the detachment stage to be separated out a single drop through a rapid necking process. The entire process is repeated at regular intervals. The volume of the drop is determined by the Y-directional size of the bulged part at the end of the X-growth stage (S_E) and the detaching time (Δt_Detach). Based on the measurement and a simple scale analysis, a correlation to represent the drop size was proposed with the flow rates and fluid properties taken as parameters, and physical interpretations on the correlation were provided as well.     

Approximate elongation flow properties utilising the opposed orifice technique – Correction for shear and inertia

Mackay et al. (1995) have presented an approximate technique to determine the elongation viscosity from pressure drop measurements in a simple stagnation flow device. In the present paper we describe experiments using a high viscosity Newtonian oil, aimed at probing some of the assumptions made by Mackay et al. We find that Trouton ratios calculated using the original analysis are well above the value of three expected for Newtonian fluids. Finite element simulations of the flow field show this is due to the net pressure drop having a substantial shear contribution, which should be corrected for before the Trouton ratios are evaluated. Interestingly, most of the shear correction is due to shear on the inside of the orifice near the exit from the central flow region. The shear contribution to the pressure drop occurs for all flow rates, however, at large flow rates there is also an inertial correction to the pressure drop. In this paper we describe an approximate method that corrects for both shear and inertial effects. With these effects recognised and corrected for, the measured Trouton ratios are reduced to around three. Received: 15 December 1997 Accepted: 16 March 1998     

Hydrodynamic diffusivity of spherical particles in polymer solution

In this research experiments were performed to examine the hydrodynamic diffusion of spherical particles in a highly filled suspension. The suspension consisted of nearly monodisperse polymethylmethacrylate spheres in a density matched polymer solution. The polymer solution was prepared by dissolving 0–700 ppm of polyacrylamide in a mixture of ethyleneglycol and glycerine. The polymer solution did not show appreciable shear thinning. The particle loading was varied from 30 to 55%. The hydrodynamic diffusivity was estimated by measuring the time-dependent viscosity when the suspension was subjected to a circular Couette flow with an air bubble trapped under the rotor of the Couette apparatus. The results show that the dimensionless diffusivity (D/γ˙a ²) of particles in polymer solution is not proportional to shear rate (γ˙), as in the case of a Newtonian fluid, but that it decreases with increasing shear rate. The diffusivity also decreases with increasing polymer concentration. It is suggested that the elongational thickening behaviour and the increased lubrication force due to the first normal stress difference may be responsible for the reduction of diffusivity in the polymer solution. Received: 18 January 2000 Accepted: 6 April 2000     

Terminal velocity of a Taylor drop in a vertical pipe

A scaling analysis based on the field equations for two phases and the jump conditions at the interface is carried out to deduce a balance of forces acting on a Taylor drop rising through stagnant liquid in a vertical pipe. The force balance is utilized to deduce a functional form of an empirical correlation of terminal velocity of the Taylor drop. Undetermined coefficients in the correlation are evaluated by making use of available correlations for two limiting cases, i.e. extremely high and low Reynolds number Taylor bubbles in large pipes. Terminal velocity data obtained by interface tracking simulations are also used to determine the coefficients. The proposed correlation expresses the Froude number Fr as a function of the drop Reynolds number Re_D, the Eötvös number Eo_D and the viscosity ratio μ^*. Comparisons between the correlation, simulations and experimental data confirm that the proposed correlation is applicable to Taylor drops under various conditions, i.e., 0.002 < Re_D < 4960, 4.8 < Eo_D < 228, 0 ? μ^* ? 70, 1 < N < 14700, −12 < log M < 4, and d/D < 1.6, where N is the inverse viscosity number, M the Morton number, d the sphere-volume equivalent drop diameter and D the pipe diameter.     

The constitutive equation of a dilute suspension of spherical microcapsules

This paper studies the rheological behavior of a dilute suspension of spherical microcapsules, i.e. spherical thin elastic membranes filled with an incompressible liquid. Previous results obtained for the motion of such capsules freely suspended in a simple shear flow are first extended to general linear shear flows. Then the stresslet term in the external flow is computed to order ?², where ?, assumed to be small with respect to unity, is the ratio of viscous to elastic forces acting on the particle. The resulting constitutive equation is of the viscoelastic type and is similar to the one obtained for liquid droplets. It predicts that the microcapsule suspension exhibits a shear dependent viscosity and normal stress effects. The exact dependency of these phenomena on the microscopic parameters of the suspension is explicitly provided by the model.