Mathematical model of two-phase Taylor flow hydrodynamics for four combinations of non-Newtonian and Newtonian fluids in microchannels
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Pressure gradient
Generalized Newtonian fluid
Plug flow
Eccentricity (behavior)
Generalized Newtonian fluid
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Abstract The flow patterns obtained when viscous fluids are agitated inside baffled cylindrical tanks have been studied in both Newtonian and non‐Newtonian systems. The experimental technique consisted of observing the motions of small tracer particles in highly illuminated, narrow beams of light. The results may be broken down into two major categories. The first was a qualitative comparison between the flow patterns obtained in non‐Newtonian and Newtonian fluids of the same general viscosity levels. This part of the study included observation of changes in the flow fields as one moves from laminar into turbulent conditions for both fluid systems. The second portion of the paper deals with quantitative determinations of local flow velocities, shear rates, and power‐dissipation rates in various parts of the vessel. The following conclusions may be drawn from these measurements. 1. Local fluid shear rates were found to be directly proportional to impeller speed, in both Newtonian and non‐Newtonian systems. As would be expected, the shear rates decreased more rapidly with increasing distances from the impeller in pseudoplastic non‐Newtonian fluids than in Newtonian systems. 2. The rates of local power dissipation decreased rapidly with distance from the impeller. 3. The fluid velocities in the horizontal plane of the impeller varied almost linearly with rotational speed in the Newtonian systems, in accordance with prior observations. On the other hand, movement in pseudoplastic systems increased exponentially with impeller speed. This effect, like the dampening of shear rates, is caused by the cumulative effects of local velocity and viscosity changes in these systems. (Increases in velocity decrease the fluid viscosity, which in turn causes further increases in velocity, etc.) This work serves to define pertinent problems which are of importance in determining mixing rates, on a microscopic scale. Efforts may now perhaps be turned more profitably than before toward macroscopic fluid‐mixing studies.
Shear thinning
Generalized Newtonian fluid
Power-law fluid
Slip factor
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Pulsatile flow
Pressure gradient
Velocity gradient
Generalized Newtonian fluid
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Pressure gradient
Generalized Newtonian fluid
Plug flow
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The present analysis is motivated by the need to elucidate with more accuracy and sophistication the hydrodynamics of non-Newtonian flow via a channel containing a porous material under pulsating pressure gradient. A one-dimensional transient rheological model for pulsating flow through a Darcy-Forcheimmer porous channel is used. A modified Casson non-Newtonian constitutive model is employed for the transport fluid with a drag force formulation for the porous body force effects. The model is transformed and solved using a finite element numerical technique. Rheological effects are examined using a β parameter which vanishes in the limit (Newtonian flow). Velocity profiles are plotted for studying the influence of Reynolds number, Darcy number, Forchheimer number and the β (non-Newtonian) parameter. The channel considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. The model finds applications in industrial filtration systems, pumping of polymeric fluids etc.
Pulsatile flow
Pressure gradient
Darcy number
Darcy's law
Generalized Newtonian fluid
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The correct prediction of the pressure gradient is the fundamental parameter to establish an effective hydraulics program, which enables an optimised drilling process. In the present work, the effect of the orbital motion of the drill pipe on the pressure drop in an eccentric annulus flow with Newtonian and non-Newtonian fluids is studied numerically for both laminar and turbulent regimes using finite volume method (FVM). Furthermore, the effect of eccentricity when the inner pipe makes an orbital motion is evaluated. Different behaviours are observed in laminar and turbulent regimes. In the laminar regime, the simulation results showed that an increase of the orbital motion speed causes a considerable increment of the pressure gradient for the Newtonian fluid. For the power-law, non-Newtonian fluid in the laminar regime, on the contrary, a decrease of the pressure gradient is observed due to the shear-thinning effect. In the turbulent regime the mentioned trends are predicted to be much weaker. As eccentricity increases, the pressure drop of the non-Newtonian fluid decreases with a more pronounced diminish in pressure drop when the drill pipe is in orbital motion for both laminar and turbulent flow regimes.
Pressure gradient
Annulus (botany)
Generalized Newtonian fluid
Eccentricity (behavior)
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The correct prediction of the pressure gradient is the fundamental parameter to establish an effective hydraulics program, which enables an optimised drilling process. In the present work, the effect of the orbital motion of the drill pipe on the pressure drop in an eccentric annulus flow with Newtonian and non-Newtonian fluids is studied numerically for both laminar and turbulent regimes using finite volume method (FVM). Furthermore, the effect of eccentricity when the inner pipe makes an orbital motion is evaluated. Different behaviours are observed in laminar and turbulent regimes. In the laminar regime, the simulation results showed that an increase of the orbital motion speed causes a considerable increment of the pressure gradient for the Newtonian fluid. For the power-law, non-Newtonian fluid in the laminar regime, on the contrary, a decrease of the pressure gradient is observed due to the shear-thinning effect. In the turbulent regime the mentioned trends are predicted to be much weaker. As eccentricity increases, the pressure drop of the non-Newtonian fluid decreases with a more pronounced diminish in pressure drop when the drill pipe is in orbital motion for both laminar and turbulent flow regimes.
Pressure gradient
Annulus (botany)
Generalized Newtonian fluid
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Bingham plastic
Herschel–Bulkley fluid
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The laminar axial flow of non-Newtonian fluids obeying Robertson-Stiff model in concentric annuli is analyzed. Flow is caused simultaneously by the inner cylinder moving along its axis and by the pressure gradient imposed in the axial direction. Both cases - either pressure gradient assists to the moving cylinder or opposes - are considered. All possible cases with respect to the possible positions of the plug flow regions are uniquely diversified through the derived analytical criteria using the entry (geometrical, kinematical and rheological) parameters. For each possible case there is derived the explicit analytical expression for the volumetric flow rate.
Hagen–Poiseuille equation
Pressure gradient
Plug flow
Viscoplasticity
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Pressure gradient
Pipe flow
Herschel–Bulkley fluid
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