Dimensionless Yield Stress Research Articles

Laminar planar jets of elastoviscoplastic fluids

We perform numerical simulations of planar jets of elastoviscoplastic (EVP) fluid (Saramito (2007) model) at low Reynolds number. Three different configurations are considered: (i) EVP jet in EVP ambient fluid, (ii) EVP jet in Newtonian ambient fluid (miscible), and (iii) EVP jet in Newtonian ambient fluid (immiscible). We investigate the effect of the Bingham number, i.e. of the dimensionless yield stress of the EVP fluid, on the jet dynamics, and find a good agreement with the scaling for laminar, Newtonian jets for the centerline velocity uc/u0∝(x/h)−1/3 and for the jet thickness δmom/h∝(x/h)2/3 at small Bingham number. This is lost once substantial regions of the fluid become unyielded, where we find that the spreading rate of the jet and the decay rate of the centerline velocity increase with the Bingham number, due to the regions of unyielded fluid inducing a blockage effect on the jet. The most striking difference among the three configurations we considered is the extent and position of the regions of unyielded fluid: large portions of ambient and jet fluids (in particular, away from the inlet) are unyielded for the EVP jet in EVP ambient fluid, whereas for the other two configurations, the regions of unyielded fluid are limited to the jet, as expected. We derive a power law scaling for the centerline yield variable and confirm it with the results from our numerical simulations. The yield variable determines the transition from the viscoelastic Oldroyd-B fluid (yielded) to the viscoelastic Kelvin–Voigt material (unyielded).

Design of equi-strength annular disks made of functionally graded materials

This research proposes a robust method for designing functionally graded disks subject to internal and external pressures. The design objective is to find the profile of equi-strength disks. The von Mises yield criterion controls the initiation of plastic yielding. The yield stress and Young’s modulus are entirely arbitrary functions of the polar radius. Poisson’s ratio is constant. The solution is facilitated using the dimensionless yield stress as an independent variable instead of the polar radius. In particular, a numerical technique is only required to solve two ordinary differential equations. Moreover, one of these equations is independent of the other. Therefore, the equations can be solved individually, simplifying the solution method. The limitation imposed by the thickness gradient on the acceptability of plane stress conditions is considered. Particular designs are proposed assuming that the power function describes the radial distribution of material properties. A critical condition that allows for deriving relatively simple design solutions is emphasized. It is shown that this condition is satisfied for many specific material property distributions used in the literature.

Obstructed free-surface viscoplastic flow on an inclined plane

The interaction of steady free-surface flows of viscoplastic material with a surface-piercing obstruction of square cross-section on an inclined plane is investigated theoretically. The flow thickness increases upstream of the obstruction and decreases in its lee. The flow depends on two dimensionless parameters: an aspect ratio that relates the flow thickness, the obstruction width and the plane inclination; and a Bingham number that quantifies the magnitude of the yield stress relative to the gravitationally induced stresses. Flows with a non-vanishing yield stress always form a static ‘dead’ zone in a neighbourhood of the upstream and downstream stagnation points. For relatively wide obstructions, a deep ‘ponded’ region develops upstream with a small dead zone, while the deflected flow reconnects over relatively long distances downstream. The depth of the upstream pond increases with both the dimensionless yield stress and width of the obstruction, while the unyielded dead zone varies primarily with the yield stress. Both are predicted asymptotically by balancing the volume flux of fluid into and out of the ponded region. When the obstruction is narrow, the perturbation to the depth of the oncoming flow is reduced. It exhibits fore–aft antisymmetry, while the dead zone is symmetric to leading order. Increasing the yield stress leads to larger dead zones that eventually encompass all of the upstream- and downstream-facing boundaries of the obstruction and fully divert the flow. Results for obstructions with circular and rhomboidal cross-sections are also presented and illustrate the effects of boundary shape on the properties of the steady flow.

Viscoplastic flow between hinged plates

The incompressible motion of viscoplastic fluid between two semi-infinite rigid plates, hinged at their ends and rotating towards one another at constant angular velocity, generates self-similar flow fields because there is no externally imposed length scale in the absence of inertia. The magnitude of the strain rate scales with the angular velocity of the plates and the dimensionless deviatoric stresses are functions only of the polar angle and a dimensionless measure of the yield stress; they are independent of the radial distance from the corner. These flows feature unyielded regions adjacent to the boundaries for sufficiently large angles between the plates. Moreover, when the dimensionless yield stress is large, there are viscoplastic boundary layers that are attached to the boundary or the plug, the asymptotic structures of which are constructed.

Effects of debris flow rheology on overflow and impact dynamics against dual-rigid barriers

It is well recognised that the rheology of an interstitial fluid has profound effects on debris flow dynamics. Existing design guidelines for multiple resisting barriers, however, do not consider the rheological behaviour of debris flows explicitly while estimating barrier spacing. A modified overflow equation is proposed, considering an improved overflow trajectory and a new yield stress-based velocity attenuation model, to estimate the overflow distance in two-phase flows. This study experimentally investigates the effects of yield stress of an interstitial fluid on the impact behaviour of two-phase flows with similar Froude numbers against dual-rigid barriers. The flow composition is varied to model a wide range of natural flows based on dimensionless yield stress. The results reveal that the hydrodynamic impact coefficient increases with increasing dimensionless yield stress and exceeds the existing international design guidelines by more than 13%. The existing guidelines underestimate the overflow distance by up to 115%. The modified formulation is verified and conservatively predicts overflow distance for water floods to debris flows. It is recommended that the dimensionless yield stress of interstitial fluid together with Froude number should be used to characterise the impact and overflow dynamics of two-phase flow for a conservative design of dual barriers.

Research on the Relation between Slump Flow and Yield Stress of Ultra-High Performance Concrete Mixtures.

The relation between slump flow and yield stress of ultra-high performance concrete (UHPC) mixtures was studied with theoretical analysis and experimentation. The relational expression between slump flow and yield stress of UHPC mixtures was built and then verified with a rheological test. The results showed that the prediction model, as a function of cone geometry of dimensionless slump flow and dimensionless yield stress of the UHPC mixtures, was constructed based on Tresca criteria, considering the geometric relation of morphological characterization parameters before and after slump of the UHPC mixtures. The rationality and applicability of the dimensionless prediction model was verified with a rheological test and a slump test of UHPC mixtures with different dosages of polycarboxylate superplasticizer. With increase in polycarboxylate superplasticizer dosage, yield stress of the two series of UHPC mixtures (large/small binding material consumption) gradually decreased, leading to a gradual increase in slump flow. Based on the prediction model of dimensionless slump flow and dimensionless yield stress, the relational expression between slump flow and yield stress of the UHPC mixtures was built. The comparison result showed that the calculated data was consistent with the experimental data, which provided a new method for predicting yield stress of UHPC mixtures with a slump test.

Generalized models of slump and spread in combination for higher precision in yield stress determination

The cone slump test is a simple alternative for on-site measure of yield stress, and on this principle, cylinder mold is employed owing to its easy accessibility. As an extension of the previous investigation which has validated the cone's cylinder-like behavior in the slump geometry, this work adopted an equivalent cylinder to facilitate comparison in the spread geometry, together with cylinders of various dimensions to explore dimensionless spread to yield stress relation. Good consistency was observed in both slump profiles and spread contours between the mini cone and its equivalent cylinder. The spread diameters after normalization displayed a definite common correlation with dimensionless yield stress. After integrating the corrective coefficient β, the models of slump and spread were generalized to both cylinder and cone molds with desired accuracy, alleviating the overall deviation of 14.88 % by individual slump height to 10.25 % combining with spread and enhancing the robustness of predicted values.

Viscoplastic corner eddies

When viscous fluid in a corner is disturbed, eddies can form in the absence of inertia. Examples of flow configurations in which this motion occurs include flow through an abrupt contraction and over a cavity. Six decades ago, Moffatt (J. Fluid Mech., vol. 18, 1964, pp. 1–18) calculated the slow viscous flow of Newtonian fluids in sharp corners, detailing his eponymous ‘Moffatt eddies’. In this study we examine corner flows of viscoplastic materials, a class of non-Newtonian fluids which exhibit solid-like behaviour for stresses below a yield stress. Specifically, we consider a Bingham fluid, for which the material is perfectly rigid at stresses below the yield stress. While a static unyielded plug forms at the tip of the corner, eddies analogous to those found by Moffatt can also form. We examine these viscoplastic eddies numerically, by computing finite element solutions using the augmented-Lagrangian method, and analytically, by employing a viscoplastic boundary layer formulation and scaling arguments. We measure the depth of the static plug as a function of the Bingham number (dimensionless yield stress), show that the process of a new eddy forming as the Bingham number is decreased is driven by the pressure in the yielded fluid adjacent to the static plug, and provide a heuristic argument for the critical Bingham number at which this occurs.

Hazards in mining: A novel model for the prediction of run-out distances in tailings dams using CFD

Tailings dams are potential facilities capable of failure, with the potential to generate high-impact environmental, economic, and social catastrophes given that they do collapse. In this study, numerical simulations of tailings as non-Newtonian fluids based on the Herschel–Bulkley model have been carried out to characterize the runout distances under different physical conditions. Using scaling arguments, a mathematical expression formed by three dimensionless groups including dimensionless yield stress, a modified Reynolds number , and the angle of the inclination of the system is proposed to explain the runout distance in tailings dams. The subsequent results show a good correlation between the variables, allowing us to deduce a high influence of the yield stress and the slope, albeit reflected both in the modified Reynolds number and the yield coefficient. Finally, a simple mathematical model is obtained from multidimensional analysis and the possibility of an abacus for regular intervals is proposed, which in turn supports an additional complement to the existing models for estimating the runout distances. • Prediction of dam breaking in mining. • Runout distances using CFD. • Dense suspensions in mining.

Experimental study on the critical condition of river blockage by a viscous debris flow

A debris flow flowing into a river may cause river blockage and form a dam. When the dam breaks, large floods can occur in the areas downstream, which can lead to fatalities and property damage. In this study, the parameters of river blockage were classified as three types of factors: morphological factors, dynamic factors, and characteristics factors of debris flows. The confluent angle, the dimensionless volume, the unit discharge ratio, and the dimensionless yield stress are important parameters for river blockage. They are all independent and dimensionless parameters. The degree of river blockage was divided into 4 stages: minor blockage, partial blockage, major blockage, and complete blockage. A classification based on the blockage coefficient is proposed to assess the degree of blockage. An experimental study was conducted with a total of 61 experimental runs. Based on the blockage coefficient of each run of the tests, the relationships between the degree of blockage and the key parameters (i.e., the confluent angle, the dimensionless volume, the unit discharge ratio, and the dimensionless yield stress) were obtained. A prediction model of the degree of river blockage is proposed based on these relationships. The area total of 21 debris flow tributaries and their corresponding rivers in China were selected to validate the prediction model. In these 21 tributaries, 24 events involving a debris flow flowing into a river resulted in partial blockage, major blockage, and completely blockage of the rivers. The prediction model was successful validated using the 22 events in China involving partial blockage, major blockage, and complete blockage.

Effect of frequency of minute-amplitude oscillatory shear loadings on ultimate yield stress of cohesive sediments

The ultimate yield stress of cohesive sediments changes with oscillatory loading or vibration. Given a strong enough vibration, the sediment may be fluidized. In this study, the effect of the frequency of minute-amplitude oscillatory shear loadings on the ultimate yield stress of cohesive sediments was experimentally and analytically investigated in a laboratory. The test samples were prepared with cohesive sediments with a median particle size of 31 μm and at four water content (31.8% to 37.03%). The sediments were subjected to continuous oscillatory shear loadings with a constant frequency (0–131.6 Hz). The findings of the study indicated that the ultimate yield stress of cohesive sediments under minute-amplitude oscillatory shear loadings was dependent on the oscillatory shear frequency, water content, and the ultimate yield stress of the sediments prior to the application of the oscillatory shear loading. This study revealed that there exists a critical shear loading frequency fcr. When the oscillatory shear frequency (f) was less than the critical shear frequency (fcr), the ultimate yield stress decreased as f increased. However, when f was greater than fcr, the ultimate yield stress was constant, irrespective of further increase of the oscillatory shear frequency. The former condition is identified as the non-equilibrium fluidization stage and the latter, the equilibrium fluidization stage. The fcr value decreased as the water content increased. In the equilibrium fluidization stage, the dimensionless yield stress Su/Su0 did not vary with the water content or oscillatory shear frequency. Two discrete formulae were proposed to estimate the ultimate yield stress of cohesive sediments subjected to minute-amplitude oscillatory shear loadings for the non-equilibrium and equilibrium fluidization stages. To explore the engineering applications of the formula for the equilibrium fluidization stage, a series of vertical pull out tests were performed using a dynamic torpedo anchor. This study provides an important method for distinguishing the degree of fluidization and sheds lights on potential applications in coastal and marine engineering, such as pile or anchor installation and extraction and scour protection in cohesive bed.

A New Approach to the Modeling of Magnetorheological Dampers and Application to Resonance Control

Abstract A predetermined flow pattern in a magnetorheological damper providing continuously variable resistance to flow is required for efficient damping of a given load. The required predetermined flow pattern rests on the a priori determination of the constitutive properties of the magnetorheological (MR) fluid determined to generate variable resistance to flow. The inverse problem of constructing the predetermined response of the damper with a specific displacement pattern of the piston in the damper for efficient damping of a given load is solved. The MR fluid in the damper is modeled as a Bingham phase change material with time-dependent yield stress offering continuously variable resistance to the flow in the piston to achieve the required specific displacement pattern. The governing equations are solved for any time history of the dimensionless yield stress of the fluid which in turn is determined from the imposed response of the damper. Analytical tools developed can be used in optimizing damper performance. The application of the method to resonance mitigation is illustrated.

Dispersion induced by non-Newtonian gravity flow in a layered fracture or formation

Abstract

A Classification of Clay‐Rich Subaqueous Density Flow Structures

This study presents a classification for subaqueous clay‐laden sediment gravity flows. A series of laboratory flume experiments were performed using 9%, 15%, and 21% sediment mixture concentrations composed of sand, silt, clay, and tap water, on varying bed slopes of 6°, 8°, and 9.5°, and with discharge rates of 10 and 15 m3/hr. In addition to the characteristics of the boundary and plug layers, which have been previously used for the classification of open‐channel clay‐laden flows, the newly presented classification also incorporates the treatment of the free shear layer. The flow states within the boundary and free shear layers were established using calculation of the inner variable, self‐similarity considerations, and the magnitude of the apparent viscosity. Based on the experimental observations four flow types were recognized: (1) a clay‐rich plug flow with a laminar free shear layer, a plug layer, and a laminar boundary layer, (2) a top transitional plug flow containing a turbulent free shear layer, a plug layer, and a laminar boundary layer, (3) a transitional turbidity current with a turbulent free shear layer, no plug layer, and a laminar boundary layer, and (4) a fully turbulent turbidity current. A connection between the emplaced deposits and the relevant flow types is drawn and it is shown that a Froude number, two Reynolds numbers, and a dimensionless yield stress parameter are sufficient to associate an experimental flow type with a natural large‐scale density flow.

Rayleigh-Bénard convection of Casson fluids

This study aims at investigating numerically the Rayleigh-Bénard Convection (RBC) in viscoplastic fluids. A Casson fluid is considered in a bidimensional square cavity heated from below. The effects of the dimensionless yield stress, the Bingham number Bn, on the heat transfer and motion is investigated in the range 5.103<Ra<105 for the Rayleigh number and Pr=10,100,1000 for the Prandtl number. One shows that the yield stress has a stabilizing effect, reducing the convection intensity. Above a certain value of Bnmax, the convection does not occur and the heat transfer is only due to conduction. For moderate Bn values, truly unyielded regions are located in the center of the cavity; their areas grow with increasing Bingham number and invade the whole cavity at the threshold value Bnmax.

Laboratory study on submarine debris flow

ABSTRACTSubmarine debris flows were studied through a set of laboratory tests to investigate the flow characteristics and the effects of varying the water content. These tests used the Kaolin clay with water content from 125 to 185% as an artificial marine clay. The observed flow behavior confirmed that submarine debris flows can be divided into strongly coherent flows and weakly coherent flows dependent on the shear strength of sliding material. A deeper understanding of the flow behavior of submarine debris flows has been established through the particle image velocimetry technique. The direction of a strongly coherent flow is parallel to the slope with steady flow velocity. In contrast, the velocity distribution of a weakly coherent flow is in disorder, due to ambient water penetrating the flow head. In this study, a densimetric Froude number Frd is presented as the indicator for the threshold of hydroplaning, which occurs if Frd is greater than 0.3. In addition, the dimensionless yield stress , is introduced to determine the onset of weakly coherent flow. The threshold value of between strongly and weakly coherent flows is around 0.25.

The “avalanche effect” of an elasto-viscoplastic thixotropic material on an inclined plane

The so-called avalanche effect is one of the fingerprints of thixotropic materials. This self-reinforcing process where the decrease in viscosity, due to a rejuvenation process triggered by a stress field, induces a motion which in turn contributes to decrease the viscosity again, is well exemplified by the inclined plane problem. In this situation, the material in its fully-structured state is placed on an inclined plane with respect to the gravity force which is responsible for the beginning of the breakdown process. These thixotropic systems generally have a yield stress, a strength that must be overcome in order to induce rejuvenation. In addition, they exhibit elastic features, especially in the pre-yield state. In the present work we numerically solve the transient evolution of an elasto-viscoplastic thixotropic material subjected to the action of gravity on an inclined plane. In order to handle with the moving free-surface boundary condition encountered in the avalanche effect, we have used a combination of the Marker-And-Cell (MAC) method with the front-tracking scheme. This formulation was successfully employed for this kind of material in the recent paper of Oishi et al. (2016) [28]. In the present work, we have adapted our finite difference formulation to analyze the effects associated with an extended Herschel–Bulkley model in the simulation of a transient complex free surface flow. Concerning the parameters of the flow curve, it is shown that the dimensionless yield stress (plastic number) is the most significant one. However, for a fixed plastic number, different combinations of dimensionless consistency index and dimensionless Newtonian viscosity plateau can lead to a diversity of responses. The thixotropic equilibrium time had a significant impact on shifting the instant when the flow regime changes from an accelerating (when the front part of the material accelerates) to a retardation one (when this front part decelerates). Higher elasticity, as captured by the Weissenberg number, led to longer distances covered by the material.

Friction Coefficients for Bingham and Power-Law Fluids in Abrupt Contractions and Expansions

Industrial processes with non-Newtonian fluids are common in many segments such as petroleum, cosmetic, and food industries. Slurries, emulsions, and gas–liquid dispersions are some examples with industrial relevance. When a fluid flows in a pipe system, pressure losses are always present. For Newtonian fluids, a quite reasonable understanding of this phenomenon was already achieved and is available in the literature. The same cannot be stated for non-Newtonian fluids owing to their complex characteristics, such as pseudoplasticity, viscoplasticity, elasticity, and thixotropy. The understanding of the influence of these characteristics on flow behavior is very important in order to design efficient pipeline systems. The design of such systems requires the estimation of the pressure drop due to friction effects. However, there are few works regarding friction losses for non-Newtonian fluids in pipeline systems, making this task a difficult one. In this study, two classes of fluids are investigated and compared with the Newtonian results. The first category of fluids are the ones that exhibits pseudoplastic behavior and can be modeled as a power-law fluid, and the second category are the ones that possesses a yield stress and can be modeled as a Bingham fluid. Polyflow was used to compute the friction losses in both abrupt contractions and expansions laminar flow conditions. It shows that for the expansion cases, the aspect ratio affects more the local friction coefficients than for the contraction cases. The influence of the power index n on local friction losses is similar for both cases, abrupt contractions and abrupt expansions. At low Reynolds numbers, dilatant fluids present the lowest values of the friction coefficient, K, independent of geometry. At high Reynolds numbers, a reversal of the curves occurs, and the dilatant fluid presents larger values of K coefficient. For the cases investigated, there is also a Reynolds number in which all the curves exhibit the same value of K for any value of the power-law index. The effect of τy′ shows a different behavior between contractions and expansions. In the case of contractions, the material with the highest dimensionless yield stress has the highest K value. In the case of the expansions, the behavior is the opposite, i.e., the higher the yield stress, the lower is the values of the K coefficient. Equations for each accessory as a function of the rheological parameters of the fluid and the Reynolds number of the flow are also proposed. The data were adjusted according to two main equations: the two Ks method proposed by Hooper (1981, “The Two-K Method Predicts Head Losses in Pipe Fittings,” Chem. Eng., 81, pp. 96–100.) is used for all the contractions cases, and the equation proposed by Oliveira et al. (1997, “A General Correlation for the Local Coefficient in Newtonian Axisymmetric Sudden Expansions,” Int. J. Heat Fluid Flow, 19(6), pp. 655–660.) is used for all the expansions cases. The equations found were compared with the numerical results and showed satisfactory precision and thus can be used for engineering applications.

Role of interactions between cationic polymers and surfactants for foam properties

Abstract We study the effect of two classes of cationic polymers, Lupasols (based on polyethylenimine, PEI) and Merquats (based on diallyldimethyl ammonium chloride, DADMAC), on the surface and rheological properties of foams, stabilized with the mixture of anionic (SLES) and zwiterionic (CAPB) surfactants, with and without myristic acid (MAc) present as a cosurfactant. The effects of several polymers from each class, with different molecular mass and charge density, are compared. Polymers from Lupasol series were found to suppress the cosurfactant effect of MAc on all surface and foam properties studied—surface rheological properties, inside foam friction, foam-wall friction, and mean bubble size. The obtained results show that Lupasol polymers bind strongly the MAc molecules in the bulk solution, thus reducing MAc surface activity and adsorption. The cosurfactant effect of MAc could be restored at neutral pH, after increasing MAc concentration to reach a certain weight ratio of MAc/Lupasol. Merquat 740, which is a co-polymer of DADMAC and acrylamide with low charge density, affects strongly the dimensionless foam yield stress, foam-wall friction, and thinning behavior of BS + MAc films. This effect is explained with the strong interactions between polymer molecules and MAc in the mixed adsorption layer at the air–water interface—a relatively thick polymer adsorption layer is formed, able to bridge neighbouring surfaces. In contrast, Merquat 100 with very high charge density (homopolymer of DADMAC) has week effect on foam properties, due to the formation of relatively thin adsorption layers. Thus we observe a variety of possible scenario, depending on (1) the competition between the binding of surfactant/cosurfactant to the polymer molecules in the bulk solution with the polymer adsorption on the bubble surface, and (2) on the ability of the polymer to form thick adsorption layers, bridging the surfaces of neighbouring bubbles.

Control of instabilities in non-Newtonian free surface fluid flows

Free surface flows in inclined channels can develop periodic instabilities that are propagated downstream as shock waves with well-defined wavelengths and amplitudes. Such disturbances are called “roll waves” and are common in channels, torrential lava, landslides, and avalanches. The prediction and detection of such waves over certain types of structures and environments are useful for the prevention of natural risks. In this work, a mathematical model is established using a theoretical approach based on Cauchy’s equations with the Herschel–Bulkley rheological model inserted into the viscous part of the stress tensor. This arrangement can adequately represent the behavior of muddy fluids, such as water–clay mixture. Then, taking into account the shallow water and the Rankine–Hugoniot’s (shock wave) conditions, the equation of the roll wave and its properties, profile, and propagation velocity are determined. A linear stability analysis is performed with an emphasis on determining the condition that allows the generation of such instabilities, which depends on the minimum Froude number. A sensitivity analysis on the numerical parameters is performed, and numerical results including the influence of the Froude number, the index flow and dimensionless yield stress on the amplitude, the wavelength of roll waves and the propagation velocity of roll waves are shown. We show that our numerical results were in agreement with Coussot’s experimental results (1994).