A photographic study of shapes of bubbles and coalescence in non-Newtonian polymer solutions

This communication reports (photographically) on the shapes of bubbles of different gases in several Newtonian and polymer solutions, encompassing a wide range of rheological behavior. Effects of a surface active agent are mentioned and bubble coalescence in viscoelastic solutions is visualized.     

Models for the formation of gas bubbles at a single submerged orifice in a non-Newtonian fluid

Nitrogen bubbles were emitted by a single horizontal orifice submerged in an aqueous solution of sodium carboxymethylcellulose (C.M.C.). Their behaviour follows the Ostwald Dé Waele rheological model: τ = mE_oⁿ; τ is the shear stress and E_o the shear rate.     

Interaction between Taylor bubbles rising in stagnant non-Newtonian fluids

The interaction between Taylor bubbles rising in stagnant non-Newtonian solutions was studied. Aqueous solutions of carboxymethylcellulose (CMC) and polyacrylamide (PAA) polymers were used to study the effect of different rheological properties: shear viscosity and viscoelasticity. The solutions studied covered a range of Reynolds numbers between 10 and 714, and Deborah numbers up to 14. The study was performed with pairs of Taylor bubbles rising in a vertical column (0.032 m internal diameter) filled with stagnant liquid. The velocities of the leading and trailing bubbles were measured by sets of laser diodes/photocells placed along the column. The velocity of the trailing bubble was analysed together with the liquid velocity profile in the wake of a single rising bubble (Particle Image Velocimetry data obtained from the literature). For the less concentrated CMC solutions, with moderate shear viscosity and low viscoelasticity, the interaction between Taylor bubbles was similar to that found in Newtonian fluids. For the most concentrated CMC solution, which has high shear viscosity and moderate viscoelasticity, a negative wake forms behind the Taylor bubbles, inhibiting coalescence since the bubbles maintain a minimum distance of about 1D between them. For the PAA solutions, with moderate shear viscosity but higher viscoelasticity than the CMC solutions, longer wake lengths are seen, which are responsible for trailing bubble acceleration at greater distances from the leading bubble. Also in the PAA solutions, the long time needed for the fluid to recover its initial shear viscosity after the passage of the first bubble makes the fluid less resistant to the trailing bubble flow. Hence, the trailing bubble can travel at a higher velocity than the leading bubble, even at distances above 90D.     

Injection and coalescence of bubbles in a quiescent inviscid liquid

Time periodic generation and coalescence of bubbles by injection of a gas at a constant flow rate through an orifice at the bottom of a quiescent inviscid liquid is investigated numerically using a potential flow formulation. The volume of the bubbles is determined for different values of a Weber number and a Bond number. Single bubbling and different regimes of coalescence are described by these computations. The numerical results show qualitative agreement with well-known experimental results for liquids of low viscosity, suggesting that bubble interaction and coalescence following gas injection is to a large extent an inviscid phenomenon for these liquids, many aspects of which can be accounted for without recourse to wake effects or other viscosity-dependent ingredients of some current models.     

非牛顿流体力学实验的开发

介绍了在所研制的非牛顿流体力学实验装置上,进行的基础性-提高性-研究性实验. 基础性实验包括爬杆、射流胀大、无管虹吸演示实验;提高性实验包括流变特性、出口压力测试实验;在以非牛顿流体润滑脂为例的流变特性实验时,发现存在壁滑移,进行了存在壁滑移时的流变特性和在管道流动中的壁滑移减阻研究性实验.     

Moving boundary in a non-Newtonian fluid

Moving boundary value problem in non-Newtonian fluid is considered. Exact analytical solution for the flow of second-grade fluid for a rigid moving plate oscillating in its own plane, is obtained. The Doppler effect has been observed due to the motion of the plate. The shearing stress on the plate is also calculated. It is concluded that the solutions for stationary porous boundaries can be obtained from the solutions of moving rigid boundaries.     

Extended thermodynamics of a non-Newtonian fluid

Thermodynamics restrictions are calculated upon the constitutive equations of a non-Newtonian fluid. The fluid is of the rate type and the proper thermodynamic theory for such materials is seen to be extended thermodynamics. Thermodynamic stability conditions lead to the proper sign of the normal-stress coefficient, i.e. the sign that is compatible with experiment. Wave speeds for shear waves are calculated and the treatment of incompressible fluids is discussed.     

Peristaltic motion of a non-Newtonian fluid

Summary To understand theoretically the flow properties of physiological fluids, we have considered as a model the peristaltic motion of a power law fluid in a tube, with a sinusoidal wave of small amplitude travelling down its wall. The solution for the stream function is obtained as a power series in terms of the amplitude of the wave. The stream function and the velocity components are evaluated by solving numerically two point boundary value problems with a singular point at the origin. The influence of the applied pressure gradient along with non-Newtonian parameters on the streamlines and velocity profiles are discussed in detail.     

Variational principles in hydrodynamics of a non-Newtonian fluid

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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.     

A modified SPH method to model the coalescence of colliding non-Newtonian liquid droplets

This paper develops a modified smoothed particle hydrodynamics (SPH) method to model the coalescence of colliding non-Newtonian liquid droplets. In the present SPH, a van der Waals (vdW) equation of state is particularly used to represent the gas-to-liquid phase transition similar to that of a real fluid. To remove the unphysical behavior of the particle clustering, also known as tensile instability, an optimized particle shifting technique is implemented in the simulations. To validate the numerical method, the formation of a Newtonian vdW droplet is first tested, and it clearly demonstrates that the tensile instability can be effectively removed. The method is then extended to simulate the head-on binary collision of vdW liquid droplets. Both Newtonian and non-Newtonian fluid flows are considered. The effect of Reynolds number on the coalescence process of droplets is analyzed. It is observed that the time up to the completion of the first oscillation period does not always increase as the Reynolds number increases. Results for the off-center binary collision of non-Newtonian vdW liquid droplets are lastly presented. All the results enrich the simulations of the droplet dynamics and deepen understandings of flow physics. Also, the present SPH is able to model the coalescence of colliding non-Newtonian liquid droplets without tensile instability.     

The oscillation of a spheroid along its axis in a non-Newtonian fluid

Summary The present paper investigates the nature of the fluid flow when a spheroid is suspended in an infinitely extending elastico-viscous fluid defined by the constitutive equations given byOldroyd orRivlin andEricksen, and is made to perform small amplitude oscillations along its axis. The solution of the vector wave equation is expressed in terms of the solution of the corresponding scalar wave equation, without the use ofHeine's function or spheroidal wave functions. Two special cases (i) a sphere and (ii) a spheroid of small ellipticity, are studied in detail.Née MissRenuka Rajagopalan.     

The dynamics and dissolution of gas bubbles in a viscoelastic fluid

This paper reports an experimental study of the motion of dissolving and non-dissolving gas bubbles in a quiescent viscoelastic fluid. The objective of the investigation was to determine the influence of the abrupt transition in bubble velocity, which had been observed at a critical radius of approx. on the rate of mass transfer. Thus, a range of bubble sizes from an equivalent (spherical) radius of 0.2–0.4 cm was employed using CO₂ gas, and five different fluids, including one Newtonion glycerine/water solution and four viscoelastic solutions of Separan AP30 in water (0.1, 0.5, 1% by weight) and in a water/glycerine mixture.The experimental data on bubble velocity shows that the discontinuous increase with bubble volume observed previously for air bubbles in viscoelastic fluids, does not occur for dissolving CO₂ bubbles—presumably due to the continuous decrease in bubble volume. Instead, a very steep but definitely continuous transition is found. Mass transfer rates are found to be significantly enhanced by viscoelasticity, and comparison with available theoretical results shows that the increase is greater than expected for purely viscous, power-law fluids. We conclude that a fully viscoelastic constitutive model would be necessary for a successful analysis of the dissolution of a gas bubble which is translating through a (high molecular weight) polymer solution.     

Magnetohydrodynamic transient flows of a non-Newtonian fluid

Some exact solutions of the time-dependent partial differential equations are discussed for flows of an Oldroyd-B fluid. The fluid is electrically conducting and incompressible. The flows are generated by the impulsive motion of a boundary or by application of a constant pressure gradient. The method of Laplace transform is applied to obtain exact solutions. It is observed from the analysis that the governing differential equation for steady flow in an Oldroyd-B fluid is identical to that of the viscous fluid. Several results of interest are obtained as special cases of the presented analysis.     

Stability of steady-state non-Newtonian fluid layer flow

The stability of the steady-state plane-parallel flow of a non-Newtonian fluid layer in the gravity field along an inclined rigid surface is investigated. It is shown that the most dangerous are the long-wave perturbations propagating over the free surface. The stability maps are plotted for such perturbations in the Reynolds number — gravity parameter plane. With increase in the gravity number the layer flow becomes less stable. The layer deviation from the vertical lines stabilizes the flow.     

The Rayleigh and Stokes problems with an incompressible non-Newtonian fluid

Summary The Rayleigh problem or impulsive motion of a flat plate has been solved using a perturbation scheme when the surrounding fluid is representable by the constitutive equations of Oldroyd or Coleman and Noll. The shear stress and normal stress at the wall were expressed analytically for this unsteady motion. Further, an exact solution of the equations was found for a special case of the constitutive equations.The motion of the fluid above a harmonically oscillating plate or the Stokes problem has been determined for a special non-Newtonian fluid. The penetration of the shear wave into the fluid, the energy dissipation, the velocity profiles and the shear and normal stresses at the wall were expressed and compared to an equivalent Newtonian fluid.Some of the features of these non-Newtonian fluids were examined in simple shearing flows, and techniques to calculate some of the material constants discussed.