Viscoplastic Fluid Research Articles

Risk-based analysis of squeeze cementing operations

The success rate of a squeeze cementing operation is generally low due to complexities in the range of potential leakage pathways and enormous uncertainty in characterizing these pathways. This work aims first to develop a physically based numerical model of the key part of the squeeze cementing operation, i.e. invasion of cement slurry into a realistic microannuli geometry under operational conditions. Secondly, it aims to account for uncertainties by using statistical tools combined with the deterministic model to deliver probabilistic information regarding outcomes. This paper develops this novel risk-based approach. The first objective of this work is to build upon our previous model, which focused on a single-perforation injection scenario. We reconstruct a multi-perforation injection scenario by collocating radial (single-perforation) invasion flows. We use this model to investigate the invasion of a viscoplastic fluid, representing a cement slurry, into a randomized varying width microannulus channel. The second objective is to investigate the effect of relevant parameters on leakage reduction. This is broken into two parts. First, how effectively the squeeze operation fills the microannulus around a perforation, explored through metrics that quantify penetration/filling. Second, what effect the penetration/filling has on the leakage of the entire well, i.e. given that the squeeze operation is local. We compare the effect of different perforation patterns and rheological parameters on penetration/filling metrics and on the reduction of leakage. We generate a probability distribution of leakage rates before and after the operation. In this way can estimate both the mean reduction in leakage for different perforation patterns, and associated confidence intervals. Such predictions have not been made before. Our results demonstrate the inherent uncertainty of a squeeze operation, which arises from the geometrical complexity. Practically, this suggests that higher perforation density and lower yield stress slurry will lead to higher success rates, as is intuitive. However, the spread of uncertainty in outcomes is not reduced much by such practices, meaning that one can still be unlucky in perforating the wrong part of the annulus.

Elastoviscoplasticity intensifies the unstable flows through a micro-contraction geometry

This study focuses on the two-dimensional numerical investigation of complex fluid flows through a micro-contraction geometry in the creeping flow regime, specifically examining elastoviscoplastic (EVP) fluids. These fluids exhibit a combination of viscous, elastic, and plastic behaviors. The governing equations, including mass and momentum, are solved using a finite volume method-based discretization technique. Saramito’s constitutive model is utilized to accurately represent the viscous, elastic, and plastic responses of the EVP fluid. The present results demonstrate significant differences in flow dynamics, such as vortex dynamics and transitions between flow regimes (e.g., steady to unsteady), when compared to simple Newtonian and non-Newtonian viscoelastic (VE) or viscoplastic (VP) fluids. This study reveals that when the yield strain (ϵy) exceeds a critical value, approximately ranging from 0.79 to 0.89, the flow transits from a steady to an unsteady state for the EVP fluids. Importantly, the present study shows that EVP fluids exhibit intensified chaotic flow dynamics and increased instability compared to VE and VP fluids under similar flow conditions. However, the presence of shear-thinning behavior in EVP fluids suppresses this instability. The analysis of local velocity fields and flow deformation in this study highlights the impact on the stretching of fluid microstructure and elastic stresses, which ultimately contribute to the origin of this intensified unstable flow condition for EVP fluids. The finding from this study holds significant potential for enhancing heat or mass transfer rates and mixing efficiency in micro-scale systems, where the prevailing steady and laminar flow conditions often hinder these transport processes.

Implementing vorticity–velocity formulation in a finite difference lattice Boltzmann method for two-dimensional incompressible generalized Newtonian fluids

A finite difference lattice Boltzmann approach is introduced to address the two-dimensional macroscopic equations of velocity–vorticity for generalized Newtonian fluids (GNFs). The study involves equations governing macroscopic momentum, energy, and concentration, along with constitutive models applicable to Newtonian, power-law, and viscoplastic fluids. Subsequently, the lattice Boltzmann method, which recovers these macroscopic equations, is detailed, along with proof of its capability to reproduce the aforementioned equations. In order to evaluate the effectiveness and time efficiency of the method, it is validated against various benchmarks. The results demonstrate the efficacy of the proposed method in successfully solving isothermal, thermal, and solutal problems of GNFs, while significantly reducing computational time compared to our previously suggested approach in this domain.

Identification of rheological parameters for shallow water flows of viscoplastic fluids using elevation hydrographs

In this paper, rheological parameters, in particular yield stress and consistency index, for viscoplastic fluids are inferred from elevation hydrographs derived from experiments. The direct model consisting of shallow water equations with a Herschel–Bulkley rheology is used to simulate a fluid flowing down an inclined plane and past a cylindrical occlusion. Numerical simulations are validated with experimental and related results from the literature. The aim is to infer the unknown rheological parameters using hydrograph measurements in the contact line region between the fluid and the occlusion. The rheological identification problem is formulated to minimize an objective functional that measures the discrepancy between the elevation hydrographs from the model output and experimental data. The inverse solver is tested on both synthetic and laboratory data. The set of rheological parameters inferred is compared with the values measured on a rheometer for the fluid used in the experiments. Inference of the unknown flow quantities from the wetting free-surface data has direct applications not only in industrial settings, to predict the wetting dynamics, but also in geophysical ones for risk assessments and management plans.

Comparative predictions of turbulent non-isothermal flow of a viscoplastic fluid with yield stress

RANS simulation of turbulent non-isothermal flow in a pipe by transition of Newtonian fluid into a viscoplastic non-Newtonian fluid is carried out. Carrier phase turbulence was modeled using two-equation isotropic k‒ε˜ – model and Reynolds stress transport model. Results of calculations of Newtonian and non-Newtonian power-law fluids were compared with data of DNS calculations of other authors. Comparisons with data from other works for isothermal Schwedoff-Bingham fluid were performed in this work using k‒ε˜ – model. Satisfactory agreement was obtained with data from other studies for the axial averaged velocity and turbulent kinetic energy radial profiles (the difference is up to 15 %). Reynolds stress transport model showed significant anisotropy between streamwise and transverse velocity fluctuations (up to several times) and good agreement with DNS results of other authors. Averaged and pulsation profiles express the indicated transformation of the non-isothermal turbulent flow.

Buoyant miscible viscoplastic displacements in vertical pipes: Flow regimes and their characterizations

We experimentally study miscible displacement flows of a light Newtonian fluid by a heavy viscoplastic fluid, in a vertical pipe with a large aspect ratio (δ−1≫1). We use camera imaging, laser-induced fluorescence, and ultrasound Doppler velocimetry techniques, to capture and process data. Four dimensionless parameters, namely, the Reynolds (Re), Bingham (B), viscosity ratio (M), and densimetric Froude (Fr) numbers (or their combinations), mainly govern the flow dynamics. We identify and characterize three distinct flow regimes, including plug, separation, and mixing regimes, while we describe each regime's dynamics in detail, particularly in terms of the velocity and concentration fields as well as the displacement front velocity. In addition, we analyze the plug regime concerning the residual wall layers, the separation regime in terms of the separation dynamics, spatiotemporal separation zone, and viscoplastic layer thinning, and the mixing regime regarding the mixing index and macroscopic diffusion. Finally, we develop a simplified model to help delineate the flow regime classification, in the plane of Re/Fr2 and M.

Numerical Simulation of Thermally Radiative and EMHD Influenced Viscoplastic Fluid Flow: A Second Law Investigation

"This work rigorously presents the findings of entropy generation in Casson fluid flow on a Riga plate, exposed in a radiative environment. The conceptual basis for the investigation of fluid flow is the system of governing boundary layer equations. By means of implicit finite difference procedure the solutions of boundary layer equations are acquired. Primary goal of this study manifests the optimization of entropy generation in Casson fluid flow associated with EMHD (Electro Magneto Hydro Dynamics) Lorentz force and thermal radiation. Additionally, the contours of entropy generation and Bejan number are demonstrated. Validation of present results with previously obtained results from literature is accomplished conscientiously."

Numerical Investigation of a Viscoplastic Fluid Bubble Removal: a New Correlation to Find the Degassing Process Parameters

Numerical Investigation of a Viscoplastic Fluid Bubble Removal: a New Correlation to Find the Degassing Process Parameters

Flow and heat transfer analysis over a pair of heated bluff bodies in a channel: Characteristics of non-linear rheological models

In this computational study, the tribological characteristics of the flow of a visco-plastic fluid around a pair of cylinders in a channel are thoroughly analyzed. To numerically solve the governing equations, this investigation makes use of the Galerkin's Finite Element Method (FEM) in conjunction with Newton's and PARDISO solvers. The stable finite element pair (P2/P1) has been selected for the space discretization purpose. The impacts of several physically important parameters on the flow characteristics are investigated in depth, including the spacing ratio (GP), the power law index (n), the Bingham number (Bn), and the Reynolds number (Re). When using different gap spacing ratios (GP), the drag coefficient (CD) and lift coefficient CL were found to be strongly dependent on GP. The pressure, velocity, and viscosity profiles are plotted for varying n and Bn. In addition, the velocity behavior is observed along y-direction in a channel through line graphs. Code validation is done as special case when Bn=0andn=1. It has been observed that the gap between the obstacles can influence the overall flow pattern and subsequently the drag and lift forces.

Simulation of granular surface flows using incompressible non-Newtonian SPH (INNSPH) method

This study presents a comprehensive continuum approach to modeling granular surface flows using the Incompressible Non-Newtonian Smoothed Particle Hydrodynamics (INNSPH) method. The model integrates an incompressible SPH method, where pressure is computed by solving a pressure-Poisson equation with a non-Newtonian rheology. Projection-based SPH has a strong and rigorous theoretical basis can lead to stable and accurate simulations. This paper aims to develop a projection-based SPH method for modeling complex granular flows. INNSPH method combines incompressible SPH and μ(I) rheology models to simulate non-Newtonian viscoplastic fluid behavior in granular flows. Surface deposition, and velocity and pressure fields are estimated using a rheology model. Validation is performed by comparing simulation results, including surface profiles and run-out distances with experimental data, showing good agreement. INNSPH method is then employed to model a 2D column collapse and a dam-break scenario on horizontal and inclined planes for sands and glass beads. The method captures three distinct final deposition morphologies; truncated cone, conic, and Mexican hat shapes in collapsing columns. INNSPH computational efficiency enables simulations of large-scale granular flows, and its open-source nature facilitates collaboration and further modifications by researchers. The method provides a good understanding of granular flow dynamics in various industrial applications including powder technology.

Dynamics of displacement flows of viscoplastic fluids in obstructed eccentric annuli at moderate Reynolds numbers

As a sequel to Mitishita et al. [“Turbulent displacement flows of viscoplastic fluids in obstructed eccentric annuli: Experiments,” Phys. Fluids 34, 053114 (2022)], we present an experimental study of laminar displacement flows in obstructed eccentric annuli. Xanthan gum (XG) solutions (0.35%, 0.50%, or 0.75%) are used to displace a 0.15% viscoplastic Carbopol solution. The eccentricity of the annulus section is set to near 0.5. We study the effect of a solid obstruction in the narrow side of the annulus, similar to that provided by a consolidated residual cuttings bed, and compare the results to unobstructed displacement flows. While we predicted that all displacements would be in the laminar regime, we actually observe mixed regimes where the initial displacement of Carbopol can be transitional or turbulent. With the obstruction on the narrow side of the annulus, we observe the formation of cavities in the Carbopol layer, both upstream and downstream of the obstruction. We believe that the cavities are formed because the obstruction behaves like an abrupt contraction/expansion. This geometric irregularity affects the velocity profiles of the displacing fluid near the obstruction. Once the cavities reach the bottom of the pipe, we observe that the remaining Carbopol layer is more easily eroded. The dynamics of the Carbopol removal also share similarities to cleaning of soil layers in pipes, as described by Palabiyik et al. [“Flow regimes in the emptying of pipes filled with a Herschel–Bulkley fluid,” Chem. Eng. Res. Des. 92, 2201–2212 (2014)].

A method for determining the rheological properties of viscoplastic fluids using a rectangular die

This study introduces a method for determining the rheological parameters of viscoplastic fluids with the use of rectangular dies. The relationship between the wall shear rate and the wall shear stress is investigated for the Casson, Herschel-Bulkley, and Robertson-Stiff rheological models, using two geometric constants for non-circular dies with a regular cross-section. Then, the rheological behavior and parameters of a collagen material were examined by an analytical method and by the proposed approximate method, using experimental data obtained by a slit viscometer and a rectangular die. The yield stress value of the collagen was determined employing the pressure relaxation method. The values were 2940 (±209) Pa from the slit viscometer and 3100 Pa (± 200) Pa from the rectangular die. The rheological parameters of collagen were then obtained using the analytical method and the proposed approximate methods for Casson, Herschel-Bulkley, and Robertson-Stiff rheological models. It was shown that the wall shear rate and the wall shear stress values of the analytical method and the proposed method are in good agreement. It was found that the Herschel-Bulkley and Robertson-Stiff models successfully fitted the wall shear rate-wall shear stress curves with a coefficient of determination equal to or greater than 0.97, and the evaluated consistency values were 165 (±71) Pa.sn for the Herschel-Bulkley model and 947 (±225) Pa.sn for the Robertson-Stiff model, and the flow index values were found to be 0.50 (±0.06) for the Herschel-Bulkley model and 0.32 (±0.03) for the Robertson-Stiff model. However, it was shown that the Casson model is not suitable for describing the rheological characteristic of collagen material. Experimentally obtained parameters for the Herschel-Bulkley model were validated with the use of simulations, and it was found that the numerically and experimentally evaluated results showed good agreement. The maximum deviation was found to be less than 12%.

Wall slip effects in Rayleigh–Bénard convection of viscoplastic materials

PurposeAccording to the research, viscoplastic fluids are sensitive to slipping. The purpose of this study is to determine whether slip affects the Rayleigh–Bénard convection of viscoplastic fluids in cavities and, if so, under what conditions.Design/methodology/approachThe wall slip was evaluated using a model created for viscoplastic (Bingham) fluids. The coupled conservation equations were solved numerically using the finite element method. Simulations were performed for various parameters: the Rayleigh number, yield number, slip yield number and friction number.FindingsWall slip determines two essential yield stresses: a specific yield stress value beyond which wall slippage is impossible (S_Yc); and a maximum yield stress beyond which convective flow is impossible (Y_c). At low Rayleigh numbers, Y_c is smaller than S_Yc. Hence, the flow attained a stable (conduction) condition before achieving the no-slip condition. However, for more significant Rayleigh numbers Y_c exceeded S_Yc. Thus, the flow will slip at low yield numbers while remaining no-slip at high yield numbers. The possibility of slipping on the wall increases the buoyancy force, facilitating the onset of Rayleigh–Bénard convection.Originality/valueAn essential aspect of this study lies in its comprehensive examination of the effect of slippage on the natural convection flow of viscoplastic materials within a cavity, which has not been previously investigated. This research contributes to a new understanding of the viscoplastic fluid behavior resulting from slipping.

Agitation of Viscoplastic Fluid in a Rotating Vessel Using Close Clearance Agitators

Technological advancements have continued to progress in all fields, achieving remarkable feats. Additionally, productivity is increasing across the board as a result of strong economic expansion, which has encouraged changes in people’s way of life, such as the increasing use of pharmaceutical products, cosmetics, detergents, and food products. A hydrothermal study is required in these areas to optimize the design of the stirring system. The aim of the current work is to investigate the hydrodynamics and thermodynamics of a mechanical agitation system with a non-Newtonian fluid of the Bingham–Bercovier type in a cylindrical vessel with three blade configurations. Our research is specifically directed towards mechanically agitated systems utilizing close clearance stirrers, particularly focusing on the anchor, gate and two-bladed impellers, within cylindrical tanks that possess flat bottoms without baffles. The results show that the anchor impeller, with its broad blades and low-shear characteristics, is more suited for breaking down yield stress and inducing flow in these fluids, which creates a wide flow pattern that effectively overcomes yield stress. However, the addition of vertical arms to transform it into a gate impeller promotes mixing, heat transfer and thermal efficiency with a small energy cost compared to an anchor impeller against the two-bladed impeller.

Neutrally buoyant miscible jets into viscoplastic ambient fluids

Neutrally buoyant miscible jets into viscoplastic ambient fluids

The role of Cheeger sets in the steady flows of viscoplastic fluids in pipes: A survey

Given a convex or a Jordan domain Ω, let Ω′ be a subset of this domain, with P(Ω′) denoting its perimeter and A(Ω′) its area. If a subset Ωc exists such that h=P(Ωc)/A(Ωc) is a minimum, the subset Ωc is called the Cheeger set of Ω and h, the Cheeger constant of the given domain. If one considers the reciprocal of this minimum or the maximum ratio of the area of the subset to its perimeter, t∗=1/h. It follows from the work of Mosolov and Miasnikov that the minimum pressure gradient G to sustain the steady flow of a viscoplastic fluid in a pipe, with a cross section defined by Ω, is given by G>τy/t∗, where τy is the constant yield stress of the fluid. In this survey, we summarize several results to determine the constant h when the given domain is self-Cheeger or a Cheeger-regular set that touches each boundary of a convex polygon and when the Cheeger-irregular set does not do so. The determination of the constant h for an arbitrary ellipse, a strip, and a region with no necks is also mentioned.

A CFD examination of free convective flow of a non-Newtonian viscoplastic fluid using ANSYS Fluent

In this work, a laminar steady-state investigation of free convection in a square cavity with differential heated side walls is examined. The cavity is immersed with a viscoplastic liquid the Bingham prototype. The horizontal walls are assumed as adiabatic and the vertical wall has two spatial differing sinusoidal temperature profiles with diverse phases and amplitudes. The hydro-thermal features are systematically analyzed via a broad choice of Rayleigh numbers Ra (103-106), Bingham numbers Bn, Prandtl numbers Pr (0.1, 1, 10), amplitude ratio ε (0–––1), phase difference ϕ (0-π) and flow index n (0.3–2). The governing equations are treated computationally utilizing a commercial computational simulation code CFD: FLUENT. It has been observed that average Nusselt numbers grow with growing Rayleigh numbers and drop with increasing Bingham quantity Bn, since heat transition occurs primarily due to thermic conductivity. In general, a higher Rayleigh number promotes convection and increases heat transfer efficiency, leading toa higher Nusselt number, whereas a higher Bingham number, indicating a higher degree of viscous or yield-stress behavior, may inhibit convection and decrease heat transfer efficiency, which ended in a lower Nusselt number. These connections frequently appear in heat transport and fluid dynamics simulations. The rise in the phase difference suggests an upsurge in heat transference, as the impact of the phase shift on the Nusselt is perpetually enhanced due to the amount of Rayleigh boosts for all phase differences. Heat transition rate forϕ=πis boosted because of the values. Moreover, when the amplitude ratio goes up, so does heat transfer. The gap between average Nusselt and Rayleigh amounts rose as the Rayleigh rose. The thermal flow rate is bigger in ε=1 than in the other cases. The rise in phase difference suggests a rise in heat transference, as this effect of phase shift on Nusselt continues to be enhanced due to the amount of Rayleigh boosts for all phase differences. Heat transition rate is enhanced forϕ=πbased on the values. Plus, when the amplitude ratio grows, so does heat transmission. The rate of heat transport for ε=1 is larger than in the other cases.

Lattice Boltzmann simulation of cavity flows driven by shear and internal heat generation for both Newtonian and viscoplastic fluids

Following our recent investigation [G. Kefayati, “Internally heated convection of viscoplastic fluids in enclosures using a lattice Boltzmann method,” Phys. Fluids 35, 013108 (2023)], this paper centers on exploring the influence of shear on internally heated convection and its flow within a square cavity. The study delves into the behavior of both Newtonian and viscoplastic fluids within this setup. The cavity features two vertical side walls that consistently maintain low temperatures, serving as isotherms. Meanwhile, the horizontal walls are adiabatic and provide thermal insulation. In this work, we present dimensional macroscopic equations and introduce innovative non-dimensional macroscopic equations. To generate shear, the top lid is continuously translated, and we quantify its intensity using the corresponding Richardson number. For investigating the viscoplastic behavior and defining the yielded (fluid) and unyielded (solid) zones, we employ an exact Bingham model, which relies on a unique tensor. To tackle the problem effectively, we develop a dimensionless lattice Boltzmann method to derive the specified macroscopic non-dimensional equations and subsequently solve the fluid motion scenario. Throughout the study, we introduce modified non-dimensional parameters, including the introduced yield number (Y), Reynolds number (R) ranging from 0 to 400, Prandtl number (Pr) ranging from 0 to 100, and the modified Grashof number (G) within the range of 104–106. By varying these parameters, we analyze their influence on streamlines, isotherms, and the regions of yield and unyielded zones. The obtained results revealed that shear plays a significant role in influencing fluid flow, heat transfer, and the behavior of the unyielded section within the enclosure.

A review on rheological models and mathematical problem formulations for blood flows

A review on constitutive equations proposed for mathematical modeling of laminar and turbulent flows of blood as a concentrated suspension of soft particles is given. The rheological models of blood as a uniform Newtonian fluid, non-Newtonian shear-thinning, viscoplastic, viscoelastic, tixotropic and micromorphic fluids are discussed. According to the experimental data presented, the adequate rheological model must describe shear-thinning tixotropic behavior with concentration-dependent viscoelastic properties which are proper to healthy human blood. Those properties can be studied on the corresponding mathematical problem formulations for the blood flows through the tudes or ducts. The corresponding systems of equations and boundary conditions for each of the proposed rheological models are discussed. Exact solutions for steady laminar flows between the parallel plates and through the circular tubes have been obtained and analyzed for the Ostwald, Hershel-Bulkley, and Bingham shear-thinning fluids. The influence of the model parameters on the velocity profiles has been studied for each model. It is shown, certain sets of fluid parameters lead to flattening of the velocity profile while others produce its sharpening around the axis of the channel. It is shown, the second-order terms in the viscoelastic models give the partial derivative differential equations with high orders in time and mixed space-time derivatives. The corresponding problem formulations for the generalized rhelogical laws are derived. Their analytical solutions in the form of a normal mode are obtained. It is shown, the dispersion equations produce an additional set for the speed of sound (so called second sound) in the fluid. It is concluded, the most general rheological model must include shear-thinning, concentration and second sound phenomena

Modeling of Viscoplastic Fluids Separation in a Cylindroconical Hydrocyclone by Pressure Flotation

Modeling of Viscoplastic Fluids Separation in a Cylindroconical Hydrocyclone by Pressure Flotation