Power-law Liquids Research Articles

A simple mechanical spring-driven rheometer for measurement of Newtonian and non-Newtonian fluids—Design, validation, and input correction

This paper deals with the construction and validation of a new, very simple purely mechanical rheometer, which is assembled from a syringe and a steel spring. This rheometer does not require any expensive measuring equipment and yet can measure the viscosities of common Newtonian and non-Newtonian liquids with satisfactory results. By determining the temporary position of the piston, the force applied by the spring and the piston velocity can be ascertained and the viscosity of a given sample of Newtonian liquid can be calculated with repeatability of better than 2%. When measuring non-Newtonian and viscoelastic liquids, a camera is used to record the time course of the moving piston and the swelling ratio. Preliminary tests conducted on power-law liquids demonstrate reproducibility of rheological parameters even for very high viscosity liquids. A new correction to inlet effects is also derived as a function of Reynolds number.

Shape stability of a microbubble in a power–law liquid

The onset of non-spherical oscillations of a microbubble in an unbounded power–law liquid, important for biomedical ultrasound applications, is studied. Two sets of evolution equations are obtained from the equation of motion: a Rayleigh Plesset-type equation for the spherical oscillations and an equation for the non-spherical oscillations. The non-spherical oscillations are modeled using the perturbation method via the Legendre polynomials. Two kinds of instabilities, namely parametric and Rayleigh-Taylor instabilities, are investigated. A higher power–law index causes the damping of the oscillations for both spherical and non-spherical oscillations. The power–law index damping effect depends on the ultrasonic drive frequency. At natural frequency, the amplitude of the perturbations is high compared to the non-resonant cases. At a low consistency index, the damping effect of the power–law index decreases. Unlike Newtonian liquids, the viscosity of power–law liquids is affected by the frequency of the acoustic field, thereby affecting Rayleigh-Taylor instability.

Analysis of natural planar jump in power-law liquids—A generalized “shallow flow” approach

The study presents a generalized “shallow flow” analysis of natural planar hydraulic jump in power-law liquids. It is based on self-similar velocity profile defined as function of flow behavior index, n, and shows significant improvement over the previous analysis which assumed a quadratic velocity profile and failed for n < 0.5. Thus, the study enables a deeper understanding of the influence of n for shear thinning vis-a-vis shear thickening liquids and emphasizes that the power-law description is adequate for highly shear thinning liquids if the flow parameters are valid over the range of interest.

Close-contact melting of phase change materials with a non-Newtonian power-law fluid liquid phase—Modeling and analysis

Close-contact melting of phase change materials with a non-Newtonian power-law fluid liquid phase—Modeling and analysis

Second Law Investigation in a Non-Newtonian Liquid Flow in a Porous Channel with Circular Obstacle

The problem of non-Newtonian fluid flow has taken considerable interest and has been the subject of several work in latest years due to its various requests in different fields of engineering, in particular the interest in the problems of heat transfer in non-Newtonian liquids, such as lubrication, hot rolling, cooling problem and drag reduction. Here, mixed convection heat transport and its related entropy production in a porous channel with circular obstacle saturated via non-Newtonian power law liquid has been scrutinized. The influences on entropy production of the power law index, the Reynolds number, the Rayleigh number and the Darcy number are investigated. Being a novelty of this work, an optimization study of the thermodynamic irreversibility as a function of the channel inclination angle and the power law index is undertaken. The governing equations of the problem are solved employing the COMSOL software. Outcomes illustrate that the governing parameters strongly affect the entropy production. The thermal entropy generation is maximal at low value of power law index and high value of Reynolds number. The effect of Reynolds number become insignificant at relatively high power law index. At fixed Reynolds number value, a rise in the power index (n) leads to a reduce in the thermal entropy. This decrease is tiny, at low value of Reynolds number (Re) and turn into increasingly considerable as Re rises. The streamlines show the existence of two recirculation zones just after the circular obstacle, whose existence depends on both Re and power law index. Results show that the greatest variation relating to the inclination angle is for power law index equal to 0.4. Results indicate also that, at low Darcy number and relatively high power law index, the intrinsic effect of the modified Darcy number on Darcy viscous irreversibility become pronounced giving a sharp increase in the total entropy production.

Self-similarity formation of a pendant drop of power-law fluids

To fully explore the breakup behavior of gel propellant in both the macroscopical and microscopic scales, the present study started from the self-similarity analysis for a macroscopical power-law liquid thread, and a transition from viscocapillary to viscocapillary-inertia breakup regime was identified by the experimental verification, using high-speed photography technology and image processing. Furthermore, the dissipative particle dynamics method was employed to predict the profile of microscopic power-law liquid thread when the diameter of thinning liquid filament approaches the micro-/nanoscale. Three different breakup regimes, capillary-, viscocapillary-inertia-, and thermal-fluctuation-dominated modes, were carefully reproduced and validated. Results showed that the self-similarity breakup process can be retarded by the inertial and viscous effects. In addition, there are some similarities existing between the macroscopical and micro-/nanoscale thinning processes.

Power law liquid jets’ trajectories and instability during centrifugal spinning

Nanofibers are produced using a revolutionary technique called centrifugal jet spinning. This technique is known as an industrial prilling process, where small droplets are performed from breaking up of a thread liquid jet. Therefore, It has been used the curved jet to control the size of these small droplets and the break-up length. In this study, the linear instability of a power law liquid jet is investigated in the presence of centrifugal forces, gravity and surface tension. Furthermore, an asymptotic method has been applied to simplify the system of governing equations into a set of one-dimensional equations. Therefore, the trajectory of the power law liquid jet during the centrifugal spinning has been determined using the Roung-Kutta method. Further investigation has been done into wavenumber and the growth rate of the most unstable mode for various flow index numbers. From the linear instability results, it can be observed that when the rotation rate and gravitational force are high, shear thickening is more stable than shear thinning jets. We have also found that more viscous becomes longer jets and it produces larger droplet which is a crucial finding.

Laminar planar hydraulic jump in thin film flow of power-law liquids—Experimental, analytical and numerical study

This study explores the physics of laminar planar hydraulic jump of power-law liquids in a horizontal channel through shallow water analysis. The theory is supplemented and validated by numerical simulation performed by the phase-field method in COMSOL Multiphysics. The analysis is applicable for shear thinning as well as thickening liquids and reduces to Newtonian equations when the flow behavior index (n) is unity. The analytical and numerical results are further validated with experimental data of the present study. The steady state free surface profile in conjunction with a modified Bélanger type equation predicts jump location and strength (the ratio of film height just after and before the jump). The analysis provides a modified scaled relationship between the jump location and the liquid flow rate compared to that proposed for inviscid and viscous Newtonian liquids. An order of magnitude analysis expresses the scaled jump location and strength as a function of inlet Reynolds number (Rein), inlet Froude number (Frin), scaled channel length, and n. We find that an increase in the flow consistency index and/or n favors jump formation and the jump shifts toward the channel exit with increasing n for the same channel geometry, Rein and Frin. The influence of scaled channel length is more pronounced for n < 1 as compared to n > 1 while shear thickening liquids are more significantly influenced by Frin at fixed Rein and scaled channel length. The coupled effect of flow parameters on jump characteristics is depicted in the Rein–Frin plane, which denote the range of the existence of different jump types as the function of n.

Numerical study of enhancement of heat and mass transport in the flow of power-law hybrid nano liquid under chemical reaction

Ethylene glycol with nanoparticles behaves as a non-Newtonian fluid and its rheology can be best described by the power-law rheological model. Further, hybrid nanoparticles are responsible for anti-oxidation, anti-evaporation, and anti-aging. Therefore, their dispersion in ethylene glycol is considered as these properties make the nanofluid stable. This article examines the impact of hybrid nanoparticles on the thermal enhancement of ethylene glycol as it is a worldwide used coolant. Moreover, simultaneous effects of temperature and concentration gradients, Joule heating, viscous dissipation, thermal radiations, and Bouncy forces are modeled and models are solved numerically using the finite element method (FEM). An increase in temperature due to composition gradient and an increase in concentration due to temperature gradient are observed. A significant increase in the Ohmic phenomenon with an increase in the intensity of the magnetic field is observed. The thermal performance of ethylene glycol is much improved due to simultaneous dispersion of hybrid nanoparticles relative to the thermal performance of ethylene glycol with mono nanoparticles only. Highlights The simultaneous dispersion of and in ethylene glycol is recommended to improve and optimize its thermal conductivity. Hence, and -ethylene glycol is a better coolant. The use of the Newtonian rheological model for ethylene glycol (when nanoparticles are dispersed in it) is an appropriate model. Therefore, to capture accurate information from numerical/theoretical analysis, the power-law constitutive model is suggested as it is an appropriate model and that is why is used in this study. -ethylene glycol is more heat generative than -ethylene glycol. This is the draw back with –-ethylene glycol when it is used as an engine coolant. The property of ––ethylene glycol to generate heat may cause over heating in the engine en used as a coolant. Thus, it is recommended to use non-heat generating fluids as base fluids.

Using lattice Boltzmann method to control entropy generation during conjugate heat transfer of power-law liquids with magnetic field and heat absorption/production

Using lattice Boltzmann method to control entropy generation during conjugate heat transfer of power-law liquids with magnetic field and heat absorption/production

Detection of blood flow through artery in the presence of steno-occlusive disease post liver transplantation by modeling for theatrical and detrimental environmental changes

This research intends to expand a mathematical model for studying the non-Newtonian surge of blood through a hepatic artery in the presence of steno occlusive disease post-liver transplantation. Power law liquid demonstrates the non- Newtonian character of blood. The hemodynamic conduit of the fluid is altered by the occurrence of arterial stenosis. In our study, the difficulty is resolved by applying diagnostic methods with the assistance of marginal circumstances and consequences. The outcomes are explained graphically for unusual cases for such stenosis. The study design is based on a tensorial form and converts its solution using numerical and analytical techniques. Our study outcome suitably demonstrates that the mathematical model used corroborates with the clinical scenario of the patient with hepatic disease.

An investigation of a gas–liquid swirling flow with shear-thinning power-law liquids

A gas–liquid swirling flow with shear-thinning liquid rheology exhibits complex behavior. In order to investigate its flow characteristics, experiments and computational fluid dynamics (CFD) simulations are conducted based on dimensional analysis. A Malvern particle size analyzer and electrical resistance tomography are applied to obtain the bubble size distribution and section void fraction. A Coriolis mass flowmeter is applied to obtain the mixture flow rate and mixture density for an entrance gas volume fraction smaller than 7%. The CFD coupled mixture multiphase model and large eddy simulation model are applied, considering the liquid shear-thinning power-law rheology. The results show that the swirling flow can be divided into developing and decaying sections according to the swirl intensity evolution in the axial direction. A gas–liquid swirl flow with shear-thinning liquid prohibits a core-annulus flow structure. A smaller index n contributes to maintaining the development of the swirl flow field and its core-annulus flow structure so that the swirl flow can form over a shorter distance with a stronger intensity. For a more uniform distribution of the apparent viscosity, the gas column in the pipe center is thinner. On the other hand, a larger consistency k enlarges the stress tensor. The amplitude of the velocity and the pressure of the core-annulus flow structure are reduced. A weaker swirl intensity appears with a wider gas column appearing as a consequence. Furthermore, the swirl number decays with an exponential behavior with parameters sensitive to the consistency k and index n of the decaying section of the swirling flow field. These are beneficial to gas–liquid separator design and optimization when encountering the shear-thinning power-law liquid phase in the petroleum industry.

Numerical Study of Natural Convection of Power Law Fluid in a Square Cavity Fitted with a Uniformly Heated T-Fin

Flow of a liquid in an enclosure with heat transfer has drawn special focus of researchers due to the abundant thermal engineering applications. So, the aim of present communication is to explore thermal characteristics of natural convective power-law liquid flow in a square enclosure rooted with a T-shaped fin. The formulation of the problem is executed in the form of partial differential expressions by incorporating the rheological relation of the power-law fluid. The lower wall of the enclosure along with the fin is uniformly heated and vertical walls are prescribed with cold temperature. For effective heat transfer within the cavity the upper boundary is considered thermally insulated. A finite element based commercial software known as COMSOL is used for simulations and discretization of differential equations and is executed incorporating a weak formulation. Domain discretization is performed by dividing it into triangular and rectangular elements at different refinement levels. A grid independence test is accomplished for quantities of engineering interest like local and average Nusselt numbers to attain accuracy and validity in results. Variation in the momentum and thermal distributions against pertinent parameters is analyzed through stream lines and isothermal contour plots. Measurement of the heat flux coefficient along with the calculation of kinetic energy against involved parameters is displayed through graphs and tables. After the comprehensive overview of attained results it is deduced that kinetic energy elevates against the upsurging magnitude of the Rayleigh number, whereas contrary behavior is encapsulated versus power-law index n. Elevation in the Nusselt number for the shear thinning case i.e., n=0.5 adheres as compared to Newtonian i.e., n=1 and shear thickening cases i.e., n=1.5. It is perceived that by the upsurging power-law index viscosity augmentations and circulation zones increases. Heat is transferred quickly against Rayleigh number (Ra) due to production of temperature difference in flow domain.

Investigation on effect of drag models on flow behavior of power-law fluid–solid two-phase flow in fluidized bed

In this study, a Eulerian-Eulerian two-fluid model combined with the kinetic theory of granular flow is adopted to simulate power-law fluid–solid two-phase flow in the fluidized bed. Two new power-law liquid–solid drag models are proposed based on the rheological equation of power-law fluid and pressure drop. One called model A is a modified drag model considering tortuosity of flow channel and ratio of the throat to pore, and the other called model B is a blending drag model combining drag coefficients of high and low particle concentrations. Predictions are compared with experimental data measured by Lali et al., where the computed porosities from model B are closer to the measured data than other models. Furthermore, the predicted pressure drop rises as liquid velocity increases, while it decreases with the increase of particle size. Simulation results indicate that the increases of consistency coefficient and flow behavior index lead to the decrease of drag coefficient, and particle concentration, granular temperature, granular pressure, and granular viscosity go down accordingly.

The effect of the cavity formation on the energy consumption characteristics of the agitated gas–liquid bioreactor

Detailed power consumption characteristics from experiments and simulations of gas–liquid stirred tanks with shear-thinning power-law liquids are presented. The motion of bubbles was investigated based on the Euler–Euler approach with a bubble cluster concept. The drag coefficient of bubbles with a constant bubble diameter was modeled as the Schiller and Naumann function. The predicted power consumption of a gas–liquid mixture shows reasonable agreement with experimental data with a maximum deviation of 8.9%. For the studied aerated systems, a qualitatively new power reduction correction equation was derived and demonstrated a reasonable agreement with experimental results compared with the literature-reported equations. The effect of the concentrations and gas flow rates on power consumption was presented. It was found that the power consumption of different mixtures is related to the change in the critical generalized Reynolds number, which was Reg = 440, 230, 100, 30, and 25 for 0.2%, 0.4%, 0.62%, 0.85%, and 1.25%, respectively.

Rayleigh instability of power-law viscoelastic liquid with heat and mass transfer

The theoretical study of Rayleigh instability (also known as capillary instability) at the interface of power-law viscoelastic liquid and inviscid gas is conducted when the interface is transferring heat and mass from one phase to another. The viscoelastic liquid and gas are confined in an annular region enclosed by two concentric cylinders. The dispersion relation based on linear stability analysis is achieved and the outcome of flow parameters on the stability of interface explains through various plots. The results indicate that system gets towards stability when more heat is transporting at the interface. It is also found that the interface that contains power-law liquid is more unstable than the interface of a Newtonian fluid.

Numerical Analysis of Natural Convection Driven Flow of a Non-Newtonian Power-Law Fluid in a Trapezoidal Enclosure with a U-Shaped Constructal

Placement of fins in enclosures has promising utilization in advanced technological processes due to their role as heat reducing/generating elements such as in conventional furnaces, economizers, gas turbines, heat exchangers, superconductive heaters and so forth. The advancement in technologies in power engineering and microelectronics requires the development of effective cooling systems. This evolution involves the utilization of fins of significantly variable geometries enclosed in cavities to increase the heat elimination from heat-generating mechanisms. Since fins are considered to play an effective role in the escalation of heat transmission, the current study is conducted to examine the transfer of heat in cavities embedding fins, as well as the effect of a range of several parameters upon the transmission of energy. The following research is supplemented with the interpretation of the thermo-physical aspects of a power-law liquid enclosed in a trapezoidal cavity embedding a U-shaped fin. The Boussinesq approximation is utilized to generate the mathematical attributes of factors describing natural convection, which are then used in the momentum equation. Furthermore, the Fourier law is applied to formulate the streaming heat inside the fluid flow region. The formulated system describing the problem is non-dimensionalized using similarity transformations. The geometry of the problem comprises a trapezoidal cavity with a non-uniformly heated U-shaped fin introduced at the center of the base of the enclosure. The boundaries of the cavity are at no-slip conditions. Non-uniform heating is provided at the walls (l1 and l2), curves (c1,c2 and c3) and surfaces (s1 and s2) of the fin; the upper wall is insulated whereas the base and sidewalls of the enclosure are kept cold. The solution of the non-dimensionalized equations is procured by the Galerkin finite element procedure. To acquire information regarding the change in displacement w.r.t time and temperature, supplementary quadratic interpolating functions are also observed. An amalgam meshing is constructed to elaborate the triangular and quadrilateral elements of the trapezoidal domain. Observation of significant variation in the flow configurations for a specified range of parameters is taken into consideration i.e., 0.5≤n≤1.5 and 104≤Ra≤106. Furthermore, flow structures in the form of velocity profiles, streamlines, and temperature contours are interpreted for the parameters taken into account. It is deduced from the study that ascending magnitude of (Ra) elevates level of kinetic energy and magnitude of heat flux; however, a contrary configuration is encapsulated for the power-law index. Navier–Stokes equations constituting the phenomenon are written with the help of non-dimensionalized stream function, temperature profiles, and vortices, and the solutions are acquired using the finite element method. Furthermore, the attained outcomes are accessible through velocity and temperature profiles. It is worth highlighting the fact that the following analysis enumerates the pseudo-plastic, viscous and dilatant behavior of the fluid for different values of (n). This study highlights that the momentum profile and the heat transportation increase by increasing (Ra) and decline as the viscosity of the fluid increases. Overall, it can be seen from the current study that heat transportation increases with the insertion of a fin in the cavity. The current communication signifies the phenomenon of a power-law fluid flow filling a trapezoidal cavity enclosing a U-shaped fin. Previously, researchers have studied such phenomena mostly in Newtonian fluids, hence the present effort presents novelty regarding consideration of a power-law liquid in a trapezoidal enclosure by the placement of a U-shaped fin.

A deterministic model for bubble propagation through simple and cascaded loops of microchannels in power-law fluids

This paper investigates the path selection of bubbles suspended in different power-law carrier liquids in microfluidic channel networks. A finite volume-based numerical method is used to analyze the two-dimensional incompressible fluid flow in microchannels, while the volume of fluid method is used to capture the gas–liquid interface. To instill the influences of shear thinning, Newtonian, and shear-thickening fluids, the range of power-law indices (n) is varied from 0.3 to 1.5. We have validated our numerical model with the available literature data in good agreement. We have investigated the nonlinearity in the hydrodynamic resistance which arises due to single-phase non-Newtonian fluid flow. The path selection of a bubble in power-law fluids is examined from the perspective of velocity distribution and bubble deformation. We have found that the bubble indeed goes to the channel with a higher flow rate for all power-law fluids, but interestingly it did not always take the shorter route channel at a junction for n = 0.3. Our results suggest that long channels need not be more resistant for every fluid and that the longest arm becomes the least resistant resulting in the bubble leading into the long arm at a junction for shear-thinning fluid. We have proposed a deterministic model that enables predicting the second bubble path in a single bubble system for any location of the first bubble. We believe that the present study results will help design future generation microfluidic systems for efficient drug delivery and biomedical and biochemical applications.

Effect of surface contact angle on the wall impingement of a power-law liquid jet

This study theoretically investigated the impinging liquid sheet, formed by a power-law liquid jet obliquely encroaching on a wall surface. Based on the control volume method, the governing equations of the liquid sheet were established through force balance analysis at the curved edge. To solve the governing equations, energy conservation in the theoretical model was also considered throughout the impinging process. Typical working conditions were selected to validate the theoretical predictions. The results showed that the theoretical inner counter of liquid sheet agreed well with experimental data. Based on the theoretical model, influence of rheological parameters, surface contact angle, and surface tension coefficient are discussed, respectively. It is concluded that the surface contact angle could affect liquid sheet size by changing the total surface tension force at the rim, as well as the surface energy variation in the energy conservation equation.

CONVECTIVE HEAT TRANSFER AND FULLY DEVELOPED FLOW FOR CIRCULAR TUBE NEWTONIAN AND NON-NEWTONIAN FLUIDS CONDITION

We represent a conceptual scrutiny for completely organized convective heat transfer ring within the circular pipeline with power law liquids by means of realizing that the heat diffusivity has been a temperature gradient. The investigative resolution is availed and the behaviour of the heat transfer is inspected under a persistent thermic flux frontier condition. It has been demonstrated that the Nu stubbornly relies upon the power-law index n value. The Nu (Nusselt number) recognizably gets reduced in a range of n from 0 to 0.1. Nonetheless, for n greater than 0.5, there is a monotonic decrement in the Nu with the incremental n, and for n greater than 20, values of the Nu have approached a constant.