Power-law non-Newtonian Liquid Research Articles

Modeling and Experimental Investigation of Bubble Formation in Shear-Thinning Liquids

This investigation presents both theoretical and experimental studies on the size of a growing bubble in power-law non-Newtonian liquids. At first, some previous works on the prediction of bubble size in Newtonian liquids have been extended by considering the balance of forces acting on the bubble at the moment of separation. Predicted bubble sizes were validated against the experimental results for a wide range of operating conditions, including different gas flow rates and needle diameters as well as a wide range of physical properties of the Newtonian liquids. Furthermore, in order to determine the size of the bubbles formed in power-law non-Newtonian liquids with a similar analysis, the effective shear rate of bubble growth was calculated in which the rheological properties of fluid were taken into account and subsequently the viscosity of the fluid was modified. Theoretically obtained bubble sizes for non-Newtonian liquids are in a good agreement with our experimental high-speed video observations of three carboxyl methyl cellulose (CMC) solutions.

Foams built up by non-Newtonian polymeric solutions: Free drainage

A mathematical model of free drainage of foam built up by a power-law non-Newtonian liquid is developed. The theory predictions are compared with the experimental data on the drainage of foams formed using commercially available Aculyn™22 and Aculyn™33 polymeric solutions. The rheological parameters of the polymeric solutions were independently measured and used in the calculations. The deduced dimensionless equations were solved using finite element method with appropriate boundary conditions. The numerical simulations show that the decrease in the foam height and liquid content is very fast in the very beginning of the drainage; however, it reaches a steady state at longer time. The predicted values of the time evolution of the foam height and liquid content are in good agreement with the measured experimental data.

SPRAY OF POWER-LAW FLUID FROM A SWIRL INJECTOR WITH NONTANGENTIAL INLET CHANNELS

The spray formation of power-law non-Newtonian liquids from swirl injectors with nontangential inlet channels was described by carrying out experiments in a spray test facility and compared with the spray behavior from common swirl injectors. The most evident difference between the two types of injectors is that the spray cone pulsated for the swirl injectors with nontangential inlets. The pulsation is caused by the compressible air remaining in the swirl chamber, which can reduce the sheet breakup length under high pressure drop. The nontangential entry of liquids into the swirl chamber eventually reduces the fluid swirl radius, and the equivalent geometric characteristics constant decreases. As a result, the spray angle would decrease, and the mass flow rate would increase.

Dynamic scaling of unsteady shear-thinning non-Newtonian fluid flows in a large-scale model of a distal anastomosis

Dimensional analysis has been applied to an unsteady pulsatile flow of a shear-thinning power-law non-Newtonian liquid. An experiment was then designed in which both Newtonian and non-Newtonian liquids were used to model blood flow through a large-scale (38.5 mm dia.), simplified, rigid arterial junction (a distal anastomosis of a femorodistal bypass). The flow field within the junction was obtained by Particle Imaging Velocimetry and near-wall velocities were used to calculate the wall shear stresses. Dimensionless wall shear stresses were obtained at different points in the cardiac cycle for two different but dynamically similar non-Newtonian fluids; the good agreement between the measured dimensionless wall shear stresses confirm the validity of the dimensional analysis. However, blood exhibits a constant viscosity at high-shear rates and to obtain complete dynamic similarity between large-scale experiments and life-scale flows, the high-shear viscosity also needs to be included in the analysis. How this might be done is discussed in the paper.

Capillary Flow of Power-Law Non-Newtonian Liquids in Circular Tubes

The penetration rate of power-law non-Newtonian liquids in a circular tube driven by the capillary pressure is derived. The dimensionless fractional height of liquid in the tube relative to the equilibrium height, χ = h(t)/h(∞), is calculated as a function of an appropriately chosen dimensionless time, permitting expression of the height-time dependence as a function of the reciprocal of the exponent in the power-law model, s = 1/n. It is found that the rate of penetration and, therefore, also withdrawal of liquid is dramatically retarded as the liquid becomes more strongly shear-thinning, i.e., as n becomes small relative to unity.

Effect of the Surfactant Concentration on the Rise of Gas Bubbles in Power-Law Non-Newtonian Liquids

The effect of the surfactant concentration on the terminal velocity, shape, and drag coefficient of freely rising bubbles in a non-Newtonian, pseudoplastic liquid was studied. It is known that surfactants affect the bubble terminal velocity by changing both the shape and surface mobility of the bubble. In this work we studied separately the effect of surfactants on the shape and surface mobility by using the recently obtained drag curves for freely rising bubbles with and without surface mobility. It was shown that, within the range of surfactant concentrations studied, the latter had no effect on the bubble shape. However, the effect on the bubble surface mobility was significant. It was shown that the transition from a bubble with an immobile surface to a bubble with a mobile one is a function of the surfactant concentration, terminal Reynolds number, and rheological properties of liquid. The values of these parameters at which transition occurs were determined.

Relative Shear Deformation of Non-Newtonian Liquidsin Impeller Induced Flow

Flow induced by rotating bodies is studied from the viewpoint of the shear of liquid particles. By solution of the boundary layer equations for Newtonian and power-law non-Newtonian liquids at a rotating disc, a typical velocity field was obtained. The shear distribution of particles leaving the disc edge shows that the most important deformation occurs in the boundary layer. Distribution of shear from the viewpoint of the volume flow rate is also presented. Application of the results to the prediction of particle-breakup dynamics at rotating impellers is discussed.

Theoretical and experimental studies on the formation of an air core in a swirl spray pressure nozzle using a power law non-Newtonian liquid

An extension of the recent work [15] has been made to evaluate the air core diameter both theoretically and experimentally in the case of a swirl nozzle using a time independent pure viscous power law non-Newtonian fluid. The theoretical predictions have been made through an approximated analytical solution of the hydrodynamics of flow inside the nozzle. A series of experiments has been carried out with solutions of CMC (carboxymethyl cellulose sodium salt) powder in water with different concentrations as the working fluids. The rheological properties of the working fluids were measured by a capillary tube viscometer. Finally it has been recognised from both the theory and experiment that, regarding the injection condition and the fluid properties, the generalised Reynolds number \(\operatorname{Re} _{G_i } \) at the inlet to the nozzle and the flow behaviour index n of the fluid become the pertinent independent input parameters in non-dimensional forms. The air core diameter increased with \(\operatorname{Re} _{G_i } \) and decreases with n. The effect of nozzle geometry on the air core diameter is similar to that in the case of Newtonian fluids [15].

Conversion in chemical reactions for isothermal laminar flow of non-Newtonian liquids in a tubular reactor of circular cross-section

The residence time distribution for the flow of power-law non-Newtonian liquids in a tubular reactor of circular cross section has been derived. Assuming totally segregated flow, expressions for the fractional conversion calculation for isothermal conditions and simple irreversible reactions of any order have been established. Based on a numerical computer integration of these relations general charts have been worked out for the determination of reactor performance. An approximate solution may also be obtained by applying a simple empirical correction to reactor performance calculated for Newtonian liquids.