Bingham Liquid Research Articles

The influence of grout and bentonite slurry on the process of TBM tunnelling

AbstractThe bentonite and grout flow around a TBM is elaborated, as well as grout flow along the lining. The calculated grout flow along the lining is compared with the results of measurements. Measurement data for the flow around the TBM are not available. Both the bentonite and the grout are modelled as a Bingham liquid and it will be shown that, due to the relatively low flow velocities, the yield stress is the governing parameter. The results of the calculations show that both the flow around the TBM and the flow around the lining may significantly influence loading on the TBM, the soil, and the lining. The bentonite and grout flow around the TBM may result in a lower volume loss than calculated when assuming that the soil follows the tapered TBM. The grout flow and especially grout consolidation lead to lower pressures around the lining if the tunnel is constructed in sandy soil.

Solid Particle Mobility in Agitated Bingham Liquids

Motivated by applications in oil sands processing, numerical simulations of the combined flow of yield-stress (Bingham) liquids and solid particles in a mixing tank have been performed. The conditions were such that, generally, the flow systems were in a transitional regime, between laminar and developed turbulence. The fluid flow was simulated according to a lattice-Boltzmann scheme, with the yield stress being mimicked as a highly viscous fluid for low deformation rates. Particles were assumed to move under the influence of drag, gravity, and particle−wall and particle−particle collisions. Agitation formed a cavity (active volume) around the impeller, with the rest of the tank being virtually inactive. This mobilized the particles in the cavity. In their ability to suspend and mobilize particles, agitated Bingham liquids behave markedly different from Newtonian liquids.

Survey of Russian Federation patents on refractories

The method of making a ceramic filter with fibrous structure includes dispersing the ceramic fibers to a given L d, preparing a suspension of the ceramic fibers, polymer binder, and ceramic bonding agent, deposition, drying, and firing. The method differs in that the dispersal is performed in the presence of a surface-active substance; to prepare the suspension, one makes a mixture of Bingham liquids containing the polymer binder of film type and the ceramic bonding agent; to that liquid mixture one adds the fibers; homogenization with shearing stresses is used, and then the suspension is deposited by filtering it under vacuum through a hollow water-permeable mold, in shape and size corresponding to the hollow internal volume of the ceramic filtering element, with a given angle for the vector for the motion of the suspension relative to the filtration surface; the blank is dried to remove the residual liquid; and the firing is done at the temperature of formation for the crystalline phases of a given chemical composition in the ceramic binding agent, but below the recrystallization temperature for the fiber material. The fibers can be provided by technological wastes from the manufacture of basalt, quartz, and kaolin fibers, and also acicular single crystals of zirconium dioxide, aluminum oxide, or mixtures of them. The surfactant may consist of fatty acids from the following series: oleic, stearic, linolenic, linoleic, palmitic, arachidonic, or mixtures of them with contents from 0.5 to 1.5 wt.% of the fiber mass. A polymer bonding agent of film type may be provided by polyvinyl alcohol or polyvinylbutyral in amounts from 1.5 to 6 wt.% of the fiber mass. As the ceramic binding agent, one can use orthophosphoric acid, aluminum phosphate, magnesium phosphate, aluminum-magnesium phosphate, aluminum-boron phosphate, or mixtures of them in amounts from 3 to 8 wt.% of the fiber mass. The Bingham liquids have dynamic viscosity 35 – 50 Pa·sec. The deposition is performed with an angle for the motion vector of the suspension flow relative to the surface of the filtration varying from 0 to 90°. The blank is dried to remove the residual liquid in the mold by blowing with air at 60 – 100°C.

Finite-amplitude long-wave instability of Bingham liquid films

The long-wave perturbation method is employed to investigate the weakly nonlinear hydrodynamic stability of a thin Bingham liquid film flowing down a vertical wall. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. It is shown that the necessary condition for the existence of such a solution is governed by the Ginzburg–Landau equation. The modeling results indicate that both the subcritical instability and supercritical stability conditions can possibly occur in a Bingham liquid film flow system. For the film flow in stable states, the larger the value of the yield stress, the higher the stability of the liquid film. However, the flow becomes somewhat unstable in unstable states as the value of the yield stress increases.

Lattice-Boltzmann method for yield-stress liquids

In the present study we propose a new version of the lattice-Boltzmann (LB) method for the simulation of flow of yield-stress liquids. Unlike traditional LB methods, collisions are treated implicitly, i.e., the collision term is chosen in such a way that the stress and strain rate tensors satisfy the constitutive equation after the collision. This approach requires the solution of a (one-dimensional) non-linear algebraic equation at each point and at each time step. In the practically important cases of a Bingham liquid this equation can be solved analytically. We calculated the flow of Bingham fluid through a channel and periodic mesh of cylinders.

Zastosowanie epoksydowanego oleju sojowego do regulowania lepkosci kompozycji epoksydowych

The results of research concerning the possibility of application of epoxidized soybean oil (EOS) as a reactive diluent to reduce the viscosity of low-molecular-weight epoxy resins were presented. Fluxing curve of the composition of the resin "Rütapox 0162" with EOS as a function of EOS content has been determined (Fig. 1). On the base of the courses of flow curves registered at various temperatures, 25-65 oC, (Fig. 2, Table 2) and calculated on this basis the values of flow index (n), consistence coefficient (k) and flow activation energy (Ea), the rheological characters of the compositions were determined. They were classified as non-Newtonian liquids showing the features like of viscoplastic Bingham's liquids. It was found that the curing of EOS containing compositions with isophorone diamine run with decrease in heat release (even to 50 %) and lower peak temperature (Table 5) what significantly facilitated these materials' processing. EOS incorporated into the structure of cured epoxy resin causes decrease in its tensile strength (Fig. 3), flexural strength, compression strength and hardness (Fig. 4) but simultaneously causes increase in impact strength (Fig. 4) and relative elongation at break (Table 6). Significant decrease in Tg value was also observed. As a result of EOS content choice the various EP/EOS compositions can be obtained - showing the features characteristic for the constructional plastic up to elastomers. Decrease in crosslinking density of EP resin, being a result of EOS fragments' incorporation, causes the lowering of thermal stability of the composition (Fig. 5, Table 7) and its chemical resistance (Table 8) as well as higher water absorption.

Application of Modified Natural Oils as Reactive Diluents for Epoxy Resins

AbstractBisphenol A based low‐molecular‐weight epoxy resin was modified with epoxidized soybean oil, which exhibit viscosity reducing ability comparable to commercial grade active diluents. The studied compositions showed a non‐Newtonian rheological behavior, typical for Bingham liquids. The values of the flow index (n) and the consistency index (k) for the compositions tested in the temperature range 25–65 °C were calculated from the Ostwald‐de Waele rheological model and were used to calculate the flow‐activation energy (Ea) using the Arhenius equation. Studies of co‐crosslinking of mixed oil‐resin compositions using isophorone diamine showed essential decrease of the reaction heat and peak maximum temperature. Mechanical properties, thermal stability, water absorption and chemical resistance of the epoxy resin modified with natural oil, were also investigated. Compositions of epoxy resin Ruetapox 0162, modified with the oil diluent, preserved very good mechanical properties of the epoxy resins and demonstrated relatively low water absorption as well as high chemical resistance. The compositions displayed even higher impact strength than pure epoxy resin due to plasticizing effect of the built‐in oil. Compositions with the high contents (up to 60 weight %) of the oil were flexible materials with fast elastic recovery.

Flows of Bingham Materials Through Ideal Porous Media: an Experimental and Theoretical Study

The flow of Bingham liquids through porous media has been studied. Experiments have been performed to determine the flow rate / pressure drop relationship for the flow of a grease of Binghamian rheological behavior through an array of rods of circular cross section. The yield stress and plastic viscosity of the grease have been determined with the aid of a controlled stress rotational rheometer. To investigate a wider range of the flow parameters, the mass and momentum conservation equations have been solved numerically, in conjunction with the generalized Newtonian constitutive law and the bi-viscosity model. The finite volume method has been employed to obtain the numerical solution. These numerical results also yielded a flow rate / pressure drop relationship, which is in very good agreement with the experimental results. A capillaric theory has been developed to determine an analytical relationship between the flow rate and pressure drop for flows of Bingham liquids through porous media. It is shown that the predictions of this theory are in good agreement with the experimental and numerical results.

Tectonics and Evolution of Novae and Coronae on Venus: Tectonophysical Modeling Based on Gravitational Models

This paper describes the results of tectonophysical modeling of the formation and evolution of novae and coronae—radial/concentric volcanotectonic structures typical of the surface of Venus. The formation of these structures is usually associated with the effect of the rising and subsequently relaxing mantle diapirs on the surface layers of the lithosphere. Two series of experiments with gravitational models reproduce the topographic changes and the evolution of structural patterns in the course of the formation of novae and coronae on Venus. For model materials, we chose (1) rubber (a Bingham liquid) to reproduce the behavior of the elastoviscous diapir material in one series of experiments and the lower part of the lithosphere in the other series and (2) flour to model tectonic structures in the upper, brittle part of the lithosphere. Regularities in the formation of the topographic and structural characteristics of novae and coronae have been demonstrated on models of different geometry. The process of formation of the dense radial fracturing in novae due to the mechanical elevation caused by the formation of a rising dome, which was suggested by many authors, is not corroborated by our models. In the course of modeling, we studied the influence of the relative dimensions of the diapir and the thickness of the overlying structures, or the relative depth of the neutral buoyancy surface of the diapir, on the topographic, morphological, and structural features of novae and coronae and on the possible paths of their evolution. Regularities are also revealed in the formation of tectonic structures in relation to the environment in which the diapir evolution occurs—in the brittle upper part of the lithosphere or in its lower, viscoplastic part.

Shear-induced rupturing of a viscous drop in a Bingham liquid

Deformation and breakup of a viscous drop in a Bingham liquid is investigated numerically with a volume-of-fluid scheme. Initially, a spherical drop is placed between two moving parallel plates. For our parameters, the matrix liquid has yielded. The competing effects driving the motion are the shear and interfacial tension. When interfacial tension effects dominate, the drop evolves to a steady shape which is elongated compared with the case when the outer liquid is Newtonian. Prior to breakup, stress levels are highest at the ends of the elongated drop. When shearing effects dominate, the drop breaks up, again with features that are elongated compared with the Newtonian counterpart. After the initial breakup, the daughter drops assume steady shapes.

A three‐dimensional Bingham model for channeled lava flows

We propose a three‐dimensional (3‐D) Bingham model for channeled lava flow. Unlike from the 3‐D Newtonian models, this model can be applied also far from the vent where the Bingham rheology cannot be neglected as a consequence of the lava cooling. We assume the lava to be an isothermal Bingham liquid flowing in a rectangular channel down a constant slope. The flow velocity is calculated by solving semianalytically the steady state Navier‐Stokes equation together with the 3‐D Bingham constitutive equation. The flow vorticity is evaluated and used to define the plug shape and position for different flows: a completely filled conduit, a partially filled conduit, and an open channel. Each component of the flow vorticity vector satisfies the Laplace equation and has been evaluated by using the relaxation method. The mass flow rate is evaluated for different values of the yield stress; it appears that the Bingham rheology causes a significant reduction in flow rate as the yield stress increases. For the highest yield stress values the plug in the center of the flow welds with the plugs in the flow corners, suggesting a possible rheological mechanism for the lava tube formation.

Phase Behavior, Transport Properties, and Thermodynamics of Water/AOT/Alkanol Microemulsion Systems

The phase diagrams of ternary systems of water/Aerosol-OT/alkanol (having carbon numbers 5, 6, 7, 8, and 10) are presented. Appreciable single-phase zones with viscous regions at higher proportions of AerosoI-OT (AOT) have been witnessed for all the alkanols. The ternary systems have also shown water-induced percolation of conductance with multistep phenomena in some cases. The viscous preparations have behaved like Bingham liquids (the viscosity has increased with the rate of shear). The enthalpy of the solubilization of water in alkanol/AOT medium has been calorimetrically determined to be positive; the free energy has been evaluated from the knowledge of maximum water intake until phase separation. The free energy and entropy of water solubilization (derived from Gibbs' equation) have been found to be positive and negative, respectively, and they follow a regular trend with the [alkanol]/[AOT] mole ratio ( R) as well as with the alkanol carbon number. On the other hand, the enthalpy values, although they increased with R , increase with alkanol chainlength to a maximum for heptanol and then decrease for both octanol and decanol. It is considered that the heptanol acts as an efficient cosurfactant with AOT and helps to produce microdroplets with increased endothermicity.

Spherical particle terminal settling velocity and drag in Bingham liquids

Graphical relations have been developed from data on the fall of spherical particles in Bingham fluids available in literature for predicting terminal settling velocity and drag coefficient. It has been found that the relations fit the data extremely well.

Laminar jets of Bingham‐plastic liquids

The steady and transient behavior of jets generated by circular and slit nozzles are analyzed by the Galerkin finite‐element method with free‐surface parametrization and Newton iteration. A novel constitutive equation is used to approximate Bingham liquids that is valid uniformly in yielded and unyielded domains and which approximates the ideal Bingham model and the Newtonian liquid in its two limiting behaviors. At steady state the influence of yield stress on the die swell is equivalent to that of surface tension; that is, suppression of jet diameter at low Reynolds numbers and necking at high Reynolds number. The predictions at high Reynolds numbers agree with the asymptotic behavior at infinite Reynolds number of the jet far downstream. In the transient analysis, surface tension destabilizes round jets and increases the size of satellite drops. Yield stress was found to retard jet breakup times in addition to producing smaller satellites. Shear thinning was found to result in shorter collapse times than those for Newtonian fluid; furthermore, the satellite drop size increased with increasing shear thinning. The nonlinear analysis predicts that, although round jet breakup may occur spontaneously by surface tension, an external factor, commonly air shear, must be applied to break a planar jet at Reynolds numbers below its transition to a turbulent jet.

Concentration inhomogeneity in a practical agitated test vessel with aeration and double impellers.

The concentration inhomogeneity and mixing rate of tracer gas absorbed by a Bingham liquid in a practical agitated test vessel with aeration and double impellers was compared with those when a simple impeller or a Newtonian liquid is used. The concentration inhomogeneity in the case of double impellers was clearly different from that of a simple impeller. The mixing processes were classified into three stages, and the mixing rate was found not to be affected by the number of impellers regardless of the mixing stage. Additionally, the concentration inhomogeneity was larger and the mixing rate in the first mixing stage was lower than when water was used.

Downslope flow models of a Bingham liquid: Implications for lava flows

It is widely recognized that lavas behave as Bingham liquids, which are characterized by a yield stress σϒ and a plastic viscosity η. We consider two models describing downslope flows of a Bingham liquid with different aspect ratios A (= flow height/flow width): model 1 with A ⪡ 1 and model 2 with A ≈ 1. Sufficiently uphill with respect to the front, such flows can be considered as laminar and locally isothermal. For both models, we obtain analytically the steady-state solution of the Navier-Stokes equations and the constitutive equation for a Bingham liquid. We study the flow height and velocity as functions of flow rate, rheological parameters and ground slope. It is found that such flows remain in the Newtonian regime at low yield stresses ( σϒ ⪅ 10 3 dyne/ cm 2), but the transition to the Bingham regime also depends on flow rate and occurs at higher values of σϒ for higher flow rates: for instance, a high aspect ratio flow (model 2) is still very close to the Newtonian regime at σϒ = 10 4 dyne/cm 2, if the flow rate is greater than 10 5 g/s. In the Bingham regime, flow heights are generally greater and flow velocities are smaller than in the Newtonian regime; moreover, flow heights are independent of flow rate, so that a change in flow rate results exclusively in a velocity change. After assuming a specific temperature dependence of σϒ and η between the solidus and the liquidus temperatures of an ideal Bingham liquid (1000°C and 1200 °C respectively), flow heights and velocities are examined as functions of temperature along the flow. Several effects observed in lava flows are predicted by these models and allow a more quantitative insight into the behaviour of lava flows.

On the shearing zone around rotating vanes in plastic liquids: theory and experiment

The fracture zone (or shearing surface) around a four-bladed vane rotating in a Bingham liquid has a diameter D c which is significantly larger than the vane diameter. In typical plastic liquids D c/ D ≈ 1.00–1.05. We have measured D c and the rheology of some automotive greases. We have also photographed the fractural surface in a transparent Bingham liquid and have found it to be approximately cylindrical. Computer simulations of a four-bladed vane rotating in a Bingham liquid have produced a value of D c/ D = 1.025 which agrees well with experimental data on two viscoelastic automotive greases. We have not been able to obtain agreement between experiment and theory on the dependence of D c/ D on τ y/η p. The experimental and theoretical data presented here support the use of the vane for yield stress measurements if the diameter correction is applied. The present experimental data suggests the vane diameter has little or no effect on D c/ D.

Film thickness of a Bingham liquid on a rotating disk

Film thickness of a Bingham liquid on a rotating disk

Drop-Size Distributions of Newtonian and Bingham Liquid Sprays Produced by Fan-Jet Pressure Nozzles With and Without the Preorifice

Measurements were made of the drop-size distributions of water and of paint sprays produced by fan-jet pressure nozzles, operating in the pressure range 900 to nearly 3000 psi (6200–20,680 kPa). A collection device was constructed and droplets were captured on soot-coated and on plain microscope slides. Subsequent sizing of the impacted particles with a microscope yielded drop-size distribution data of accumulated volume percent versus diameter. Data were gathered of water and of paint sprays produced by a fan-jet pressure nozzle-preorifice combination. The effect of the preorifice on drop-size distribution was evaluated.

Drop-Size Distributions of Bingham Liquid (PAINT) Sprays Produced by Fan-Jet Pressure Nozzles

The drop-size distribution of Bingham liquid sprays was determined by experimentation. Three different highly viscous paints were sprayed with fan-jet airless spray nozzles at pressure ranging from 5 170 to 18 200 kPa. A collection device was constructed to capture a spray sample on microscope slides. Measurement of flattened droplet diameters with a microscope yielded drop-size distribution curves of accumulated volume per cent versus volume median diameter. It was postulated that the wall shear stress existing at the exit plane of the nozzle initiated liquid atomization. A logarithmic correlation was found between shear stress and volume median diameter.