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Non-Viscometric Flows of Viscoelastic Fluids in Round Tubes Driven by Transversal Boundary Waves
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The unsteady transversal flow field in the tube flow of a memory integral fluid of order type driven by rotational boundary waves is investigated. A perturbation in terms of the amplitude of the sinusoidal boundary waves is used. Qualitative conclusions are independent of the explicit forms of the constitutive functions. Quantitative results are obtained by assuming Maxwell type of behavior for the latter. It is shown that transversal steady flows is a possibility if several rotational waves with frequencies in a certain ratio are imposed on the boundary. As a result helical steady flows may be possible in the longitudinal direction in a round tube. A parametrical study of the oscillating transversal field is presented for highly elastic and shear thinning liquids.
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Flow enhancement effects due to different waveforms in the tube flow of rheologically complex fluids driven by a pulsating pressure gradient are investigated. It is found that the squarer the waveform the larger the enhancement. In each case the enhancement is strongly dependent on the viscosity function, but the elastic properties also play an important role. We determine that considerable energy savings may be obtained in the transport of viscoelastic liquids if an oscillatory gradient is superposed on a mean gradient. The closer the oscillation to the square wave the larger the energy savings.
The unsteady non-viscometric motion of a memory integral fluid of order three in a rigid, circular, straight tube has been investigated. The motion is driven by a constant longitudinal pressure gradient and a periodic forcing from the boundary made up of superposed sinusoidal, rotational boundary waves. A regular perturbation is used to study the time-periodic longitudinal field for a range of viscoelastic liquids and driving parameters. Qualitative results obtained are independent of the explicit forms of the constitutive functions, the kernels of the memory integral fluid of order three, which are needed only for quantitative predictions. It is shown that anomalous steady longitudinal viscometric flows may exist due to frequency cancellation. The elastic and shear rate dependent viscosity characteristics of the fluid play important parts in setting up the oscillatory velocity field. In particular, shear-thinning in periodic shear is the dominant mechanism in smoothing out the effects of elasticity, and in increasing the velocities. A parametric study of the longitudinal oscillatory velocity field is presented for a range of liquids and driving conditions. The integral fluid shows drastic longitudinal steady velocity increases due to the interaction of the oscillatory, zero mean time average, transversal shear field with the longitudinal simple steady shear. A parametric study of the change in mass transport is also presented for a range of liquids to show that contrary to what is sometimes assumed, both elasticity and shear-thinning in oscillatory shear play important roles in defining the enhancement. In particular, nonlinear-elastic properties of the integral fluid of order three act to decrease the enhancement driven by orthogonal waves.
The longitudinal and orthogonal superposition of boundary driven, small strain, oscillatory shear flow and steady Poiseuille flow is investigated. Boundary oscillations are of different frequencies and amplitudes and are represented by sinusoidal waveforms. A regular perturbation in terms of the amplitude of the oscillations is used. The flow field is determined up to and including third order for a simple fluid of multiple integral type with fading memory. Flow enhancement effects dependent on material parameters, mean pressure gradient, and amplitude and frequency of the boundary waves are predicted and closed form formulas derived for the mass transport rate. Enhancement is determined both by the elastic and shear thinning or thickening properties of the liquid. Resonance effects are shown to take place and, in particular, mean secondary and longitudinal flows, independent of the mean pressure gradient, are shown to exist for certain frequency relationships.