Fluid Behavior Index Research Articles

Performance Evaluation of Rankiya (Grewia venusta) as a Polymer for Enhanced Oil Recovery-Polymer Flooding

Polymer Flooding is an enhanced oil recovery method where high-molecular-weight polymers are added into the injected water, in order to increase the viscosity of injection fluid, improve volumetric sweep efficiency, and finally increase the oil recovery factor. Most research studies focused on the use of partially hydrolysed polyacrylamide (HPAM), xanthan gum, SPG, HEC as flooding fluid. This work focused on investigating the potential of natural polymer - Grewia venusta plant tree in formulating flooding fluid for polymer flooding operation. The polymer was prepared from the mucilage extracted from the inner stem bark of Grewia venusta. Rheological characterization shows that the formulated Grewia venusta mucilage (GVM)-based flooding fluid maintained high viscosity under very high salinity, also exhibits shear thinning behaviour which obeys power law model with fluid behaviour index n = 0.32 and consistency index K= 6.3 at highest GVM concentration of 3000 ppm, similarly revealed that GVM-based flooding fluid was stable when subjected to high salinity of 130,000 ppm and temperature, up to 90 oC an inconsequential decrease in viscosity was experienced. These indicate its potential in enhancing oil recovery process. Core flooding analysis was carried out on an outcrop core sample with porosity and permeability of 26.1% and 218 mD respectively. Core flooding analysis revealed that: with increase in GVM concentration of 500, 750, 1000 and 2000 ppm oil recovered against time were 55.1%, 62.6%, 69.2% and 72.9% respectively, beyond 2000 ppm GVM concentration (optimum concentration), increase in polymer concentration did not bring about an increase in oil recovery, this finally resulted to an incremental recovery of 29% original oil in place (OOIP).

Properties of Oxidized Potato Starch–Potassium Alum Mixtures, and Their Application in Starch Noodles

AbstractThis study explores the effects of potassium alum (PA) on oxidized potato starch (OS) with a carboxyl content of 0.0186%, in terms of their pasting and rheological properties. Furthermore, the application of oxidized starch in the manufacturing of starch noodles is investigated. The results indicate a positive correlation between pasting temperature and PA content (65.6–67.7 °C), while showing a negative correlation with peak viscosity (409–236 BU). The addition of PA leads to reduced dynamic moduli (G′' and G″), consistency coefficient (K), and hysteresis area, accompanied by an elevated fluid behavior index (n). Shear recovery assays demonstrate a positive correlation between PA content and shear resistance, with recovery rates escalating from 76% to 84%. The mouthfeel of starch noodles produced using oxidized starch exhibit comparable to commercial counterparts (PA content 0.35%), but with lower PA levels (at 0.2%). Additionally, these starch noodles have a higher whiteness compared to starch noodles made with potato starch.

On the analysis of time-dependent drainage of Sisko fluid film slowly down a vertical belt

Theoretical analysis of time-dependent drainage of Sisko fluid film slowly down a stationary vertical belt is presented in this paper. Employing [C. Gutfinger and J. A. Tallmadge, AIChE J. 10, 774 (1964)] approach the subsequent nonlinear partial differential equation is simplified. The Adomian decomposition method is then used to solve the simplified nonlinear partial differential equation to obtain the analytic expression for velocity. The analytic expressions for volume flow rate, shear stress, average film velocity, surface profile and film mean thickness are also derived. It is delineated that the velocity decreases by an increment in the Sisko fluid parameter and time while it increases by an increment in the fluid behavior index. The elevation of the Sisko surface profile decreases when the values of Sisko fluid parameter are increased, whereas it increases when the values of fluid behavior index and time are increased. The variable film thickness of four different lubricating greases is estimated by using experimental values of material constants and fluid behavior index [A. W. Sisko, Ind. Eng. Chem. Res. 50, 1789 (1958) and M. A. Delgado et al., Chem. Eng. Process. 44, 805 (2005)]. Furthermore, the flow variables studied for the Sisko fluid are also studied for the Newtonian fluid, and comparisons between both are provided.

Lifting and drainage of Sisko fluid film with surface tension: A theoretical study on stationary points and thickness of uniform film

This paper accords with the theoretical study of lifting and drainage of Sisko fluid film on a vertically upward moving cylinder with surface tension. The flow on cylinder is induced by the upward motion of the cylinder, gravity and surface tension gradient. The resulting nonlinear ordinary differential equation is solved for a series form solution by making use of the Adomian decomposition method (ADM). Expressions for the flow variables like velocity, volume flow rate, shear stress and surface tension are derived. Positions of stationary points and thickness of uniform film are computed numerically in MATHEMATICA. The inverse capillary number C, Stokes number [Formula: see text], Sisko fluid parameter [Formula: see text] and fluid behavior index n emerged as flow control parameters. The study showed that the positions of stationary points relocate towards the surface of the cylinder by the increase of C and [Formula: see text] while their positions relocate towards the fluid–air interface with increasing [Formula: see text] and n. Thickness of uniform film decreases when the values of C and [Formula: see text] are increased whilst it increases with the increase of [Formula: see text] and n. Analogy between the Newtonian fluid and the Sisko fluid’s shear thinning and shear thickening behaviors for positions of stationary points, thickness of uniform film and surface tension is also made.

Applications of Machine Learning Methods to Predict Hole Cleaning in Horizontal and Highly Deviated Wells

Summary Machine learning (ML) has become a robust method for modeling field operations based on measurements. For example, wellbore cleanout is a critical operation that needs to be optimized to enhance the removal of solids to reduce problems associated with poor hole cleaning. However, as wellbore geometry becomes more complicated, predicting the cleaning performance of fluids becomes more challenging. As a result, optimization is often difficult. Therefore, this research focuses on developing a data-driven model for predicting hole cleaning in deviated wells to optimize drilling performance. More than 500 flow loop measurements from eight studies are used to formulate a suitable ML model to forecast hole cleanout in directional wells. Measurements were obtained from hole-cleaning experiments that were conducted using different loop configurations. Experiments ranged in test-section length from 22 to 100 ft, in hole diameter from 4 to 8 in., and in pipe diameter from 2 to 4.5 in. The experiments provided measured equilibrium bed height at a specific flow rate for various fluids, including water-based and synthetic-based fluids and fluids containing fibers. Several relevant test parameters, including fluid and cutting properties, well inclination, and drillstring rotation speed (drillpipe rev/min), were also considered in the analysis. The collected data have been analyzed using the Cross-Industry Standard Process for Data Mining. This paper is unique because it systematically evaluates various ML models for their ability to describe hole cleanout processes. Six different ML techniques: boosted decision tree (BDT), random forest (RF), linear regression, multivariate adaptive regression spline (MARS), neural networks, and support vector machine (SVM) have been evaluated to select the most appropriate method for predicting bed thickness in a wellbore. Also, we compared the predictions of the selected ML method with those of a mechanistic model for cases without drillstring rotation. Finally, using the ML model, a parametric study has been conducted to examine the impact of various parameters on the cleanout performance of selected fluids. The results show the relative influence of different variables on the prediction of cuttings bed. Accordingly, flow rate, drillpipe rev/min, and fluid behavior index have a strong impact on dimensionless bed thickness, while other parameters such as fluid consistency index, solids density and diameter, fiber concentration, and well inclination angle have a moderate effect. The BDT algorithm has provided the most accurate prediction with an R2 of 92%, a root-mean-square error (RMSE) of 0.06, and a mean absolute error (MAE) of roughly 0.05. A comparison between a mechanistic model and the selected ML technique shows that the ML model provided better predictions.

Gravity currents of viscous fluids in a vertically widening and converging fracture

We are investigating flows in the viscous-buoyancy balance regime in a converging channel with an upward increase in the width, with the gap of the channel varying according to a xkzr power function, being x and z the horizontal and vertical coordinate, respectively, and with 0<k<1 and 0<r<1 in order to be consistent with the model. The fluid rheology is described according to the Ostwald–de Waele model, with a power-law relationship between shear stress and shear rate and with application for shear-thinning, shear-thickening and, as a special case, Newtonian fluids. While for the case of flow in the direction of widening of the horizontal channel, a self-similar solution of the first kind can be expected, for flow toward the origin, with channel narrowing horizontally, the solution is self-similar of the second kind, with the space and a reduced time coupled in a self-similar independent variable but with an unknown parameter of the transformation group that makes the differential problem invariant. The solution is found in the phase plane by numerical integration of the paths connecting pairs of singular points, separately for the pre-closure phase, in which the current front advances invading the channel, and for the post-closure or leveling phase, in which the fluid has reached the origin and the front no longer propagates, while the level progressively increases canceling the pressure gradient. Integration is performed with a trial and error procedure by modifying the unknown parameter, generally named eigenvalue and specifically critical eigenvalue when the path has been successfully integrated. The overall effect of an increasing permeability upward is that of an increase in the front speed, with the current profile also becoming locally steeper. The effect of an increase in the fluid-behavior index is mixed, as it reduces the speed of the front but still increases the steepness of the local current profile. In any case, the model implies that the eigenvalue tends to infinity for k→1 even in the presence of an increase in the vertical permeability (r > 0).

Experimental and modeling studies on dynamic barite sag and effects of particle size, shear rate, and fluid rheology

Barite is often utilized to control the weight of drilling muds. However, in inclined wellbores, barite particles settle out of the mud in a lateral direction and quickly reach the wellbore wall. Over time, deposited particles form unstable barite beds that slide intermittently downward, causing downhole pressure fluctuations. The observation is often referred to as barite sag, which occurs prominently when the system is in a dynamic state. Barite sag leads to density variation in the mud system, resulting in drilling issues such as stuck pipe, fluid loss and lost circulation, loss of well control, and wellbore instability. Various experimental studies have been conducted on barite sag, but limited mathematical modeling has been undertaken.This article presents the results of experimental and mathematical modeling studies on barite sag. First, particle size distribution tests were performed with API barite. Then, different oil-based muds (OBMs) were prepared using barite samples with various particle size distributions. Next, the apparent viscosities of the muds were measured with a rheometer. Then, the Viscometer Sag Shoe Test (VSST) method was used to study barite sag at 49 °C varying rotational speed and barite particle size distribution. Furthermore, the settling behavior of barite particles under dynamic conditions was simulated using a sedimentation-consolidation model. The model is solved numerically by applying a fully implicit finite difference method. The accuracy of the numerical solution is validated using simulation results presented in a previous study. The model has been improved to handle non-Newtonian fluids and simulate dynamic conditions.According to the apparent viscosity measurements, barite particle size has a minor effect on OBM rheology. The VSST results also show that barite sag increases with particle size and rotational speed. The improved model predicts VSST results fairly well. Additionally, a model-based parametric study indicates that barite sag decreases with increasing OBM rheological parameters (consistency index, yield stress, and fluid behavior index).

Oscillatory Marangoni flow in a deep layer of a Carreau fluid

We study the spreading dynamics of an insoluble and non-diffusive surfactant on the free surface of a deep layer of a Carreau fluid. When a non-uniform distribution of surfactant is imposed on the free surface of an initially motionless fluid, variations in surface tension are induced, causing the fluid motion from regions of lower surface tension to those of higher tension. Such movement redistributes the surfactant concentration until a uniform condition is reached. The two-dimensional momentum and convection–diffusion equations are employed to determine the hydrodynamics in the deep fluid layer and the evolution of the surfactant on the fluid surface. The modified vorticity-stream function formulation is used to solve numerically the hydrodynamic field, where the non-Newtonian dependent variables of the problem are decomposed into a Newtonian part and a non-Newtonian contribution. One of the most critical variables in practical applications regarding this phenomenon concerns the time required for the surfactant to reach a uniform distribution over the interface. The results show that the dimensionless parameters that control the decay of the variations in surfactant concentration in time are the Reynolds number Re, the fluid behavior index n, and ε, reflecting the influence of the inertia of the fluid. The results show that the temporal decay of the surfactant concentration on the fluid surface increases significantly for high values of the Reynolds number, it is more attenuated in pseudoplastic fluids than in Newtonian fluids, and the surfactant concentration decay exhibits asymmetric oscillations when inertial effects increase.

Heat Transfer Analysis on Peristaltic Transport of Sisko Fluid in an Inclined Uniform Channel

Peristaltic flow is a fundamental method of fluid conveyance in engineering, medicine, and the nuclear industry. The peristaltic mechanism is applied in designing blood pump machines, dialysis machines, and other medical devices. The current mathematical model is developed to investigate the peristaltic mechanism of Sisko fluid under the influence of heat transfer by considering variable viscosity, slip effects, variable thermal conductivity, and wall properties. Long wavelength and small Reynolds number approximations generate the nonlinear governing equations. The regular perturbation method is utilised to solve these equations. In contrast, the closed-form solution is obtained for the stream function for different values of the fluid behaviour index. The impact of several parameters on the relevant physiological factors is graphically represented using MATLAB. The results reveal that velocity and thermal slip parameters greatly impact heat transfer. The bolus volume grows as the velocity slip parameter increases. The coefficient of pseudo-plasticity plays a prominent role in the study for different values of fluid behaviour index.

3D printing surimi enhanced by surface crosslinking based on dry-spraying transglutaminase, and its application in dysphagia diets

Dry-spraying transglutaminase (TG) was explored as surface modification agent for enhancing the surimi structures and promoting its practical 3D printing application. Glycerol functionalization, 3D extruding critical parameters, TG based surface crosslinking, practical cooking loss, and innovative applications of 3D-printed surimi were investigated. Rheological performances (shear ramp, strain sweep and thixotropy tests) indicate that glycerol could enhance excellent pseudo plasticity (fluid behavior index n < 1), high mechanical strength & strain resistance (high G′, and wide linear viscoelastic region 2.51%), and outstanding thixotropy (high recovery rates, up to 61.47%) of surimi, owing to that glycerol could promote the hydration of surimi myosin and prevent protein aggregation by stabilizing aggregation-prone intermediates. The further optimization of the extruding parameters (nozzle diameter 1.00 mm and “Rectilinear” filling structure) would improve the surimi dimensional printing deviations, and increase surimi gel strength (up to 22.29 g mm) by regulating interlayer bonding zones. Compared with chemical crosslinking agents NaCl and CaCl2 for modifying surimi, surface crosslinking based on dry-spraying TG would better raise the printable height efficiency (97.50%), improve the surimi texture, and enhance suitable water distribution, resulting in fine and dense network by hydrophobic interactions, disulfide bonds and non-disulfide covalent bonds. Subsequently, the cooking loss tests and International Dysphagia Diet Standardization Initiative tests proved that 3D-printed surimi could be classified as a potential transitional food for dysphagia groups. Surface crosslinking based on dry-spraying TG suggests a bright promise in practical high-accuracy, sophisticated 3D printing of surimi and holds potential in dysphagia diets and innovating food products.

FRACTAL PERMEABILITY MODEL FOR POWER-LAW FLUIDS IN FRACTURED POROUS MEDIA WITH ROUGH SURFACES

A novel analytical model is derived based on fractal geometry theory to characterize the permeability of power-law fluids through fractured porous media with fractal asperities on surfaces. The proposed model is expressed as a function of structure parameters of fractured porous media, fractal dimensions for porous matrix and for fracture as well as the index [Formula: see text] of power-law fluid behavior. The influences of these parameters on the permeability are analyzed in detail. It is found that the relationship between permeability and roughness exhibits nonlinear characteristics. A higher power-law fluid behavior index significantly affects the reduction rate of permeability with relative roughness. Moreover, permeability is sensitive to the perturbation due to the rate of aperture to length. The proposed fractal model can clearly reveal more physical mechanisms for power-law fluid in fractured porous media than the existing models. Compared with the experimental data available in the literature, the validity of model predictions is verified.

A numerical study of two-dimensional laminar flow of power-law fluids around three circular cylinders in side-by-side arrangement

PurposeThis study aims at investigating two-dimensional laminar flow of power-law fluids around three unconfined side-by-side cylinders.Design/methodology/approachThe numerical study is performed by solving the governing (continuity and momentum) equations using a finite volume-based code ANSYS Fluent. The numerical results have been presented for different combinations of the governing dimensionless parameters (dimensionless spacing, 1.2 = L = 4; Reynolds number, 0.1 = Re = 100; power-law index, 0.2 = n = 1.8). The dependence of the kinematic and macroscopic characteristics of the flow such as streamline patterns, distribution of the surface pressure coefficient, total drag coefficient with its components (pressure and friction) and total lift coefficient on these dimensionless parameters has been discussed in detail.FindingsIt is found that the separation of the flow and the apparition of the wake region accelerate as the dimensionless spacing decreases, the number of the cylinder increases and/or the fluid behavior moves from shear-thinning to Newtonian then to shear-thickening behavior. In addition, the distribution of the pressure coefficient on the surface of the cylinders presents a complex dependence on the fluid behavior index and Reynolds number when the dimensionless spacing between two adjacent cylinders is varied. At low Reynolds numbers, the drag coefficient of shear-thinning fluids is stronger than that of Newtonian fluids; this tendency decreases progressively with increasing of Re until a critical value; beyond the critical Re, the opposite trend is observed. The lift coefficient of the middle cylinder is null, whereas, the exterior cylinders experience opposite lift coefficients, which show a complex dependence on the dimensionless spacing, the Reynolds number and the power-law index.Originality/valueThe flow over bluff bodies is a practical engineering problem. In the literature, it can be seen that the previous studies on non-Newtonian fluids are limited to the flow over one or two cylinders (effect of an odd number of cylinders on each other). Besides that, the available results concerning the flow of Newtonian fluids over three cylinders are limited to the high Reynolds numbers region only. However, this work treats the flow of non-Newtonian power-law fluids past three circular cylinders in side-by-side arrangements under a wide range of Re. The outcome of the present study demonstrates that the augmentation of the geometry complexity to three cylinders (effect of pair surrounding cylinders on the surrounded ones in what concerns Von Karman Street phenomenon) causes a drastic change in the flow patterns and in the macroscopic characteristics. The present results may be used to predict the flow behavior around multiple side-by-side cylinders.

Numerical study on the pipe flow characteristics of grouting repairing pastes used in slab track

In this study, the pipe flow characteristics of the grouting repairing pastes (GRPs) used in slab track were investigated based on three-dimensional flowing models taking into account the hydration effects. Firstly, the rheological properties of GRPs at different hydration times were measured and fitted to obtain key rheological parameters of GRPs. Then the flowing models of GRPs in pipes were established based on these rheological parameters and were verified by comparing with theoretical values. Finally, the effects of pressure gradients, pipe diameters and cement hydration on the flow characteristics of GRPs were systematically studied in terms of four indices including plug diameter, plug velocity, average velocity and the velocity ratio. Results show that the increases of pipe diameters and pressure gradients both lead to the growth of flow velocity, causing an inhomogeneity flow of GRPs in pipes. Yield stress of GRPs has the greatest influence on the flow indices. Consistency index contributes more to plug velocity and average velocity while fluid behavior index dominates the velocity ratio. To achieve a homogeneous flow at high flow rate, it is recommended to prepare a grouting repair material with moderate yield stress and low consistency index and fluid behavior index. Moreover, cement hydration causes noticeable decreases of plug velocity and average velocity under the coupling effects of rheological parameters, which may lead to the setting of GRPs near pipe wall and eventually to the occurrence of pipe blockage during transportation. In order to satisfy efficient repairing in short skylight period, it is suggested to adopt a special grouting repair material featured with slow hydration during grouting but rapid hardening after filling in the debonding area.

Physics-guided deep neural network to characterize non-Newtonian fluid flow for optimal use of energy resources

Numerical simulations of non-Newtonian fluids are indispensable for optimization and monitoring of several industrial processes such as crude oil transportation, nuclear cooling, geothermal and fossil fuel production. The governing equations derived for non-Newtonian fluid models result in nonlinear differential equations. Thus, increasing the complexity even for simple geometries. The cumbersome numerical computation and rudimentary empirical solutions hinder faster analysis over a wide range of parameters. However, machine and deep learning methods have higher accuracy but rely heavily on the quality and amount of training data, and the solution may become inconclusive if data is sparse. In this research, a novel algorithm (Herschel Bulkley Network) is introduced to simulate the non-Newtonian fluid flow in a pipe using data redundant deep neural network (DNN) for fully developed, laminar, and incompressible flow conditions. The objective of this investigation is to develop a physics dominated DNN solely driven by minimizing residuals from the Navier-Stokes based governing equations, establishing benchmark research. Herschel-Bulkley model is used to approximate the complex rheological behavior of a non-Newtonian fluid. The proposed DNN algorithm is structured to incorporate initial/boundary conditions in cylindrical coordinates and approximate the solution without the aid of any simulated or training data. The simulated results and analysis demonstrate an excellent agreement between the proposed algorithm and non-Newtonian fluids flow attributes. The detailed parametric analysis exhibits the competency of the proposed algorithm to explain the rheological features. Monte-Carlo simulation is performed by propagating uncertainty to investigate the dominant parameters affecting simulated results. The uncertainty in fluid consistency index is responsible for higher variance in the calculated flow rate, while the least variation is observed due to fluid behavior index uncertainty. The performance of the algorithm is validated with experimental datasets. The statistical error estimation exhibits a mean absolute error of 11.5%, and root mean squared error of 0.87. A comprehensive analysis on training unsupervised DNN and adjusted hyperparameters is also highlighted to achieve expedite convergence.

Explicit flow velocity modelling of yield power-law fluid in concentric annulus to predict surge and swab pressure gradient for petroleum drilling applications

Exact prediction and controlling of surge/swab pressure are required during drilling of hydrocarbon reservoirs and other geological formations that often leads to well control challenges. The existing methods to predict the surge/swab pressure gradient in the wellbore are much implicitly developed, which further reduces the model accuracy. Therefore, the present research aims to develop a novel analytical model by incorporating the explicit flow velocity equations to further improve the efficiency in predicting the surge pressure gradient. The governing flow velocity equations are developed for a concentric annulus exhibiting Couette–Poiseuille flow phenomenon that subsequently used in designing a new analytical model for yield power-law fluids to predict surge pressure gradient. Detailed analysis for the validation of a newly developed model is performed using existing predictive models and experimental data of surge pressure. The statistical analysis exhibits satisfactory outcomes with a maximum error of 5.61% and R2 of 0.988. A detailed analysis on the effect of relevant parameters on surge/swab pressure is also presented. The impact of fluid behaviour index and diameter ratio is found to be highly dependent on surge pressure under varying tripping speeds compared to other drilling parameters such as fluid yield point and consistency index.

Simplified Predictive Model for Downhole Pressure Surges During Tripping Operations Using Power Law Drilling Fluids

Abstract Surge/swab pressure is a crucial parameter that provokes well-control problems such as fluid loss, fractured formations, fluid influx, and kick. Thus, a precise estimation of differential pressure is required to evade any unforeseen drilling difficulties. The existing predictive models are based on narrow-slot approximation methods and consider the effect of drilling string axial movement on downhole pressure surges. However, it ignores the impact on the boundaries of the annular fluid velocity zone by the tripping velocity. In this research, a simplified model is developed using the flow velocity profile generated in the annulus by the tripping operation and the concentric annular Couette fluid flow phenomena for power-law fluid. A comparative study is performed with the existing analytical models and the experimental data to validate the developed model. The obtained results are convincingly in good agreement with the analytical and experimental data. A parametric study is performed to identify the effect of various parameters on surge/swab pressure. It is found that the diameter ratio has a significant impact on pressure differential with the increase in the tripping velocity. The fluid behavior index exhibits a considerable effect, and fluid consistency index shows a minor effect on the surge pressure gradient. The simplified developed model requires less numerical analysis to determine the outcomes for varying industrial applications, especially petroleum drilling operations.

Generalized models for predicting the drag coefficient and settling velocity of rigid spheres in viscoelastic and viscoinelastic power-law fluids

The design and optimization of several fluid-particle transport systems often require the determination of particle settling velocity in non-Newtonian fluids. These fluid-particle transport systems are encountered in a wide variety of industrial processes including drill cuttings transport in oil and gas well drilling operations and proppant transport in hydraulic fracturing operations. Current conventional approaches to estimate settling velocity in these non-Newtonian fluids often exclude the effect of elasticity on particle settling which can lead to erroneous estimation. It is therefore imperative to devise an accurate means to mathematically account for the fluid elasticity in particle settling in viscoelastic fluids. An experimental study was conducted to measure the settling velocity of spherical particles in viscoelastic and viscoinelastic power-law type fluids. Using a semi-mechanistic approach, explicit mathematical models were developed for estimating drag coefficient and particle settling velocity in viscoelastic fluids and viscoinelastic fluids. The main objectives of the study were: i.) To measure the terminal settling velocity of particles in various viscoelastic and viscoinelastic power-law type fluids intended at augmenting the present corpus of experimental data in literature. ii.) To develop new drag coefficient and particle Reynolds number correlations that are applicable to viscoelastic and viscoinelastic power-law type fluids and, iii.) To present a general explicit approach for predicting settling velocities of particles in viscoelastic and viscoinelastic fluids.Particle Image Shadowgraphy (PIS) was used to measure the settling velocities of the spherical particles (Specific gravity 2.5–7.7; Diameters: 0.71–4.00 mm) in Hydrolyzed Polyacrylamide and Tylose solutions of varying elastic properties. Rheological characterization of the fluids was carried out using the C-VOR Bohlin Rheometer. Experimental results from this study were combined with various data published in the literature to create an extensive database and widen the scope for empirical analysis. The database had a consistency index (k) range of 0.012–6.773 Pa.sn and a fluid behavior index (n) range of 0.370–0.940. New drag coefficient and Reynold number correlations for particles settling in viscoelastic and viscoinelastic power-law fluids were developed by using a semi-mechanistic approach, which also included the fluid elasticity effect quantified in terms of the longest relaxation time. The newly developed correlations and an advanced statistical modeling program (OriginPro 9.0) were used to mathematically create explicit models that can be used for predicting particle settling velocity in viscoelastic and viscoinelastic fluids.Comparative analysis showed that an increase in the fluid elasticity gave a corresponding decrease in the particle Reynolds number and dampened the particle settling velocity in viscoelastic fluids. This dampening effect can be attributed to the unique ability of elastic fluids to partially or fully regain their original structure after deformation. Furthermore, statistical analysis showed that the presented new models predict settling velocity accurately with a very low with a Percentage Mean Absolute Error of about 7.5% and 30% for viscoinelastic and viscoelastic fluids respectively. The proposed models also exhibited Root Mean Square Error (RMSE) values of 0.04 m/s and 0.009 m/s for viscoinelastic and viscoinelastic fluids respectively.

Hydrodynamic effects of mucus on swimming performance of an undulatory foil by using the DSD/SST method

This paper presents a DSD/SST study of the hydrodynamic effects of mucus on swimming performance of an undulatory foil in a non-Newtonian uniform flow. As the non-Newtonian effects are dominant in the boundary layer, this model can be taken as a simple strategy to study the hydrodynamic effects of fish mucus. Based on the simulations by varying the power-law fluid behavior index, some propulsive properties including the drag coefficients, the power coefficients, and the flow fields are analyzed in detail. It is found that in addition to other biological functions, the fish mucus serves to reduce the friction, enhance the thrust, save hydrodynamic power, reduce the force oscillations, and reduce the swimming sound. This work provides a better understanding of the fish mucus effects from the point of view of hydrodynamics.

Influence of convective conditions on the peristaltic mechanism of power-law fluid through a slippery elastic porous tube with different waveforms

PurposeThe purpose of this paper is to emphasize the peristaltic mechanism of power-law fluid in an elastic porous tube under the influence of slip and convective conditions. The effects of different waveforms on the peristaltic mechanism are taken into account.Design/methodology/approachThe governing equations are rendered dimensionless using the suitable similarity transformations. The analytical solutions are obtained by using the long wavelength and small Reynold’s number approximations. The expressions for velocity, flow rate, temperature and streamlines are obtained and analyzed graphically. Furthermore, an application to flow through an artery is determined by using a tensile expression given by Rubinow and Keller.FindingsThe principal findings from the present model are as follows. The axial velocity increases with an expansion in the estimation of velocity slip parameter and fluid behavior index, and it diminishes for a larger value of the porous parameter. The magnitude of temperature diminishes with an expansion in the Biot number. The flux is maximum for trapezoidal wave and minimum for the triangular wave when compared with other considered waveforms. The flow rate in an elastic tube increases with an expansion in the porous parameter, and it diminishes with an increment in the slip parameter. The volume of tapered bolus enhances with increasing values of the porous parameter.Originality/valueThe current study finds the application in designing the heart-lung machine and dialysis machine. The investigation further gives a superior comprehension of the peristaltic system associated with the gastrointestinal tract and the stream of blood in small or microvessels.

Bifurcation and stability analysis of critical/stagnation points for peristaltic transport of a power-law fluid in a tube

The stability of critical/stagnation points and streamline topologies along with their local and global bifurcations for peristaltic flow of an incompressible power-law model have been investigated. The flow is analyzed in an axisymmetric tube subject to the constraints of long wavelength and low Reynolds number, and an exact analytic solution is found in a moving frame of reference. Nonlinear autonomous differential equations are developed to unveil the particle paths and position of critical points in the flow. Stability of obtained critical points and streamline patterns along with their local bifurcations are inspected by using the theory of dynamical system. Three different flow distributions are found in the flow: backward flow, trapping and augmented flow. The transitions between these flow situations correspond to bifurcations in the flow field where non-hyperbolic degenerate points change their behavior to form heteroclinic connection between saddles. The nature and stability of these bifurcations and corresponding topological changes are explored graphically. A global bifurcation diagram is used to epitomize these bifurcations. The fluid behavior index has a significant impact on the stability of critical points and the ranges of flow regions. The backward flow region and trapping region are observed to shrink and expand, respectively, with an increase in the fluid behavior index. The findings of present article are verified by comparing them with the results already existing in the literature.