N. G. Domostroeva, N. N. Trunov
We inroduce a new model for Bingham fluids with a complicated dependence of the deformation velocity on the shear stress. Specific features of the flow rate for such fluid are studied. This model embraces many special and limiting cases, for many of them analytic calculations become possible
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In this paper, we seek an adequate macroscopic model for a hydraulic jump in Bingham fluid. The formulas for conjugate depths, sequent bottom shear stress and critical depth are established. Since no exact analytical solution in closed form is available for conjugate depths, an approximate formula is developed. This formula can provide good results with an error less than 4%. The analytical results have revealed that the critical depth and the ratio of conjugate depths increase until bottom shear stress exceeds a certain value and then decrease afterwards. The bottom shear stress downstream of…
We derive an expression for the velocity profile of a pressure-driven yield-stress fluid flow-ing around a two-dimensional concentric annulus. This result allows the prediction of the effects of channel curvature on the pressure gradient required to initiate flow for given yield stress, and for the width of the plug region and the flux through the channel at different curvatures. We use it to validate numerical simulations of the flow from a straight channel into a curved channel which show how the fluid first yields everywhere before reaching the predicted velocity profile.
Vortex shedding and heat transfer from a heated circular cylinder in Bingham plastic fluids
本文数值研究了Bingham塑性流体中受热圆柱体的涡脱落与传热特性，系统分析了Re、Pr和Bn的影响，揭示了亚临界分岔导致的阻力与传热突跳，并建立了平均Nusselt数与Bingham数之间的类Carreau-Yasuda黏度模型关系。
We derive an expression for the velocity profile of a pressure-driven yield-stress Bingham fluid flowing around a 2D concentric annulus. The formula requires the numerical solution of a nonlinear equation for the positions of the yield surfaces. The results allow the prediction of the effects of channel curvature on the pressure gradient required to initiate flow for given yield stress, and for the width of the plug region and the flux through the channel at different curvatures.
The settling efficiency, and stability with respect to settling, of a dilute suspension of infinite circular cylinders in a quiescent viscoplastic fluid is examined by means of direct numerical simulations with varying solid volume fraction, $ϕ$, and yield number, $Y$ . For $Y$ sufficiently large we find higher settling efficiency for increasing $ϕ$, similar to what is found in shear-thinning fluids and opposite to what is found in Newtonian fluids. The critical yield number at which the suspension is held stationary in the carrier fluid is found to increase monotonically with $ϕ$, while the t…
We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier-Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increas…
A parametric study of the pipeline hammer phenomenon in plastic Bingham slurry flows using the finite element method
本文用最低阶 FEM 与自适应摩擦模型参数化分析 Bingham 浆体管道水锤，揭示屈服应力增强阻力并加速压力峰值衰减。
This paper presents a method for the simulation of scour around arbitrary offshore structures. It is based on the solution of the Reynolds-Averaged-Navier-Stokes equations implemented in the OpenFOAM framework. The sediment is simulated with the help of a Bingham model, which basically models a solid sediment behavior by introducing a very high viscosity. The relative pressure used by the Bingham model is estimated with a new approach based on the solution of a Poisson equation. The position of the sediment surface is calculated with the Volume-of-Fluid approach using a high-resolution scheme.…
General hydrodynamic features of elastoviscoplastic fluid flows through randomised porous media
本文数值研究了随机多孔介质中弹黏塑性流体的流动，发现弹性效应在低Bingham数下增大压降、在高Bingham数下减阻，并促进屈服，最终可能导致流动失稳。
A comprehensive Darcy-type law for viscoplastic fluids: II. Rheology & topology
扩展框架推导粘塑性流体渗流达西型定律，考虑更现实流变模型与多孔介质拓扑，改进原工作，给出统一理论基础以预测复杂多孔介质中屈服应力流体输运。
Magnetorheological fluids (MR) are stable suspensions of magnetizable microparticles, characterized by the property to change the rheological characteristics when subjected to the action of magnetic field. Together with another class of materials that change their rheological characteristics in the presence of an electric field, called electrorheological materials are known in the literature as the smart materials or controlled materials. In the absence of a magnetic field the particles in MR fluid are dispersed in the base fluid and its flow through the apertures is behaves as a Newtonian flu…
The flow of non-Newtonian fluids is ubiquitous in many applications in the geological and industrial context. We focus here on yield stress fluids (YSF), i.e. a material that requires minimal stress to flow. We study numerically the flow of yield stress fluids in 2D porous media on a macroscopic scale in the presence of local heterogeneities. As with the microscopic problem, heterogeneities are of crucial importance because some regions will flow more easily than others. As a result, the flow is characterized by preferential flow paths with fractal features. These fractal properties are charac…
We consider the fluid mechanical problem of identifying the critical yield number $Y_c$ of a dense solid inclusion (particle) settling under gravity within a bounded domain of Bingham fluid, i.e. the critical ratio of yield stress to buoyancy stress that is sufficient to prevent motion. We restrict ourselves to a two-dimensional planar configuration with a single anti-plane component of velocity. Thus, both particle and fluid domains are infinite cylinders of fixed cross-section. We show that such yield numbers arise from an eigenvalue problem for a constrained total variation. We construct pa…
Slip flows of a Bingham fluid in curved channels
研究了在弯曲通道中压力驱动的Bingham流体的流速分布和屈服表面位置，结合Navier壁滑动理论，分析了滑流对流体屈服区域的影响，发现滑流长度增加会推动未屈服区域向通道内侧移动并略微减小其宽度。
Curvature-driven transport of thin Bingham fluid layers in airway bifurcations
本文通过润滑理论和三维模拟研究气道分叉中薄宾汉流体层在表面张力作用下的位移行为，揭示曲率驱动输运可能扰乱黏液清除并增加感染风险。
The numerical approach has been performed to study the Bingham fluid flow through an oscillatory porous plate with Ion-Slip and Hall current. Initially, at time; t = 0 both the fluid and the upper plate are at rest. At time; t > 0 the upper plate begins to oscillate in its own plane while the lower plate is stationary. The lower plate temperature is constant while the upper plate temperature has oscillated. A uniform magnetic field is applied perpendicular to the plates. To obtain the dimensionless equations from the governing non-linear partial differential equations, the usual transformation…
Influence of the imposed flow rate boundary condition on the flow of Bingham fluid in porous media
本文研究施加流速边界条件下宾汉流体在多孔介质中的流动，发现流动路径边界层尺度随流速呈幂律变化，并通过有向聚合物映射揭示了其粗糙度指数及非流动表面的雪崩统计特性。
A comprehensive Darcy-type law for viscoplastic fluids: I. Framework
本文提出一种适用于粘塑性流体整个Bingham数范围的综合Darcy型定律，通过结合屈服/塑性极限与牛顿极限的理论模型，并利用增广拉格朗日方法及各向异性自适应网格的计算数据验证了其有效性。
We extend our recent work on the creeping flow of a Bingham fluid in a lid-driven cavity, to the study of inertial effects, using a finite volume method and the Papanastasiou regularisation of the Bingham constitutive model [J. Rheology 31 (1987) 385-404]. The finite volume method used belongs to a very popular class of methods for solving Newtonian flow problems, which use the SIMPLE algorithm to solve the discretised set of equations, and have matured over the years. By regularising the Bingham constitutive equation it is easy to extend such a solver to Bingham flows since all that this requ…
We reconsider the radial Saffman-Taylor instability, when a fluid injected from a point source displaces another fluid with a higher viscosity in a Hele-Shaw cell, where the fluids are confined between two neighboring flat plates. The advancing fluid front is unstable and forms fingers along the circumference. The so-called Brinkman equations is used to describe the flow field, which also takes into account viscous stresses in the plane and not only viscous stresses due to the confining plates like the Darcy equation. The dispersion relation agrees better with the experimental results than the…
Yield-Stress Fluid Mixing: Localization Mechanisms and Regime Transitions
本研究通过模拟二维Bingham流体的搅拌过程，揭示了屈服应力流体混合的三种局域化机制，划分出三类混合流态并明确其临界参数，为搅拌釜应用中的混合行为预测提供了机制框架。
Atypical plug formation in internal elastoviscoplastic fluid flows over a non-smooth topology
本文结合 OCT/共聚焦实验与自适应有限元模拟，研究 Carbopol 凝胶越过空腔的弹黏塑性流动，发现非典型不对称塞状流，并揭示其可由 Weissenberg 数与 Bingham 数乘积统一表征。
In the present work we formulated the boundary-value-problem, comprising partial differential equations (PDEs) of steady flow for laminar/turbulent circular jet of a micropolar fluid. A new boundary layer-similarity transformation/solution was derived which is valid not only for the Newtonian fluids but also for the micropolar fluids. Through this transformation PDEs are transformed into the ordinary differential equations (ODEs). These ODEs were solved numerically by the finite-difference method. The obtained results were compared with existing results [9] for the Newtonian fluids. The compar…
The combined effect of fluid elasticity and yield-stress on the flow past a circular cylinder is studied by two-dimensional direct numerical simulation. We analyze the effects of yield-stress, elasticity, shear-thinning, and shear-thickening on the wake characteristics using the Saramito constitutive model. The elastoviscoplastic (EVP) wake flow is studied at a moderate Reynolds number (Re = 100) where two-dimensional vortex shedding occurs in the Newtonian case. We find that in the shear-thinning elastoviscoplastic flow, when yield stress increases, the drag coefficient and root mean square o…
A planar two-dimensional computational analysis is presented to qualify traditional and fractal vane-in-cup geometries for accurate rheometry of simple viscoplastic fluids with and without slip. Numerical simulations based on an adaptive augmented Lagrangian scheme are used to study the two-dimensional flow field of yield-stress fluids within and around vane tools with N=3 to 24 arms for a wide range of Bingham numbers, B (i.e. the ratio of the yield stress over the characteristic viscous stress). This allows for accurate calculations of the velocity and stress fields around vanes with various…
Weakly-compressible particle-based discretization methods, utilized for the solution of the subsonic Navier-Stokes equation, are gaining increasing popularity in the fluid dynamics community. One of the most popular among these methods is the weakly-compressible smoothed particle hydrodynamics (WCSPH). Since the dynamics of a single numerical particle is determined by fluid dynamic transport equations, the particle per definition should represent a homogeneous fluid element. However, it can be easily argued that a single particle behaves only pseudo-Lagrangian as it is affected by volume parti…
There are more than 300,000 heart valves implanted annually worldwide with about 50% of them being mechanical valves. The heart valve replacement is often a common treatment for severe valvular disease. However, valves may dysfunction leading to adverse hemodynamic conditions. The current computational study investigated the flow around a bileaflet mechanical heart valve at different leaflet dysfunction levels of 0%, 50%, and 100%, and documented the relevant flow characteristics such as vortical structures and turbulent shear stresses. Studying the flow characteristics through these valves du…
We showed that various expressions of stress in different models of fluids and in different forms of applying Newton's Second Law can be chosen, however there is always one Newton's Second Law which restricts and provides flexibility in these expressions. When fluids are regarded as being made of cells from a microscopic point of view, temperature force (gradient of internal kinetic energy) can also drive them flow.
The dynamics of thin films on a horizontal solid substrate is investigated in the case of non-Newtonian fluids exhibiting normal stress differences, the rheology of which is strongly non-linear. Two coupled equations of evolution for the thickness of the film and the shear rate are proposed within the lubrication approximation. This framework is applied to the motion of an advancing contact line. The apparent dynamic contact angle is found to depend logarithmically on a lengthscale determined solely by the rheological properties of the fluid and the velocity of the contact line.
Direct numerical simulations of closely interacting infinite circular cylinders in a Bingham fluid are presented, and results compared to asymptotic solutions based on lubrication theory in the gap. Unlike for a Newtonian fluid, the macroscopic flow outside of the gap between the cylinders is shown to have a large effect on the pressure profile within the gap and the resulting lubrication force on the cylinders. The presented results indicate that the asymptotic lubrication solution can be used to predict the lubrication pressure only if the surrounding viscoplastic matrix is yielded by a macr…
Newtonian fluid invasion into a Yield-Stress Fluid-Saturated Medium
本研究通过孔隙网络模型，发现牛顿流体驱替宾汉屈服应力流体时，除经典Lenormand模式外，还存在低粘度比下的树状和高粘度比下的柱状两种新侵入模式，并建立了突破条件。
We study the flow of a thixotropic fluid around a cylinder. The rheology of the fluid is described by means of a structural viscoplastic model based on the Bingham constitutive equation, regularised using the Papanastasiou regularisation. The yield stress is assumed to vary linearly with the structural parameter, which varies from zero (completely broken structure) to one (fully developed skeleton structure), following a first-order rate equation which accounts for material structure break-down and build-up. The results were obtained numerically using the Finite Element Method. Simulations wer…
Active stresses, which are collectively generated by the motion of energy-consuming rod-like constituents, generate chaotic autonomous flows. Controlling active stresses in space and time is an essential prerequisite for controlling the intrinsically chaotic dynamics of extensile active fluids. We design single-headed kinesin molecular motors that exhibit optically enhanced clustering, and thus enable precise and repeatable spatial and temporal control of extensile active stresses. Such motors enable rapid, reversible switching between flowing and quiescent states. In turn, spatio-temporal pat…
Viscoelastic flow of an Oldroyd-B fluid through a slowly varying contraction-expansion channel: pressure drop and elastic stress relaxation
本研究通过润滑理论分析Oldroyd-B流体在收缩-扩张通道中的流动，推导出弹性应力与压降的闭式解，发现高Deborah数下压降趋于平台，且收缩段松弛长度更短。
An axisymmetric squirmer in a Bingham viscoplastic fluid is studied numerically to determine the effect of a yield stress environment on locomotion. The nonlinearity of the governing equations necessitates numerical methods, which is accomplished by solving a variable-viscosity Stokes equation with a Finite Element approach. The effects of stroke modes, both pure and combined, are investigated and it is found that for the treadmill or "neutral" mode, the swimmer in a yield stress fluid has a lower swimming velocity and uses more power. However, the efficiency of swimming reaches its maximum at…
Surfactant-induced Marangoni stresses and surface viscosity in Faraday instability
该研究扩展双流体弗洛凯公式，探究不溶性表面活性剂弹性与Boussinesq-Scriven表面粘度对法拉第不稳定性的影响，发现二者均增大onset加速度且趋近切向固定条件。
Observations of transient wave-induced mean drift profiles caused by virtual wave stresses in a two-layer system
本研究通过实验首次验证了虚拟波应力在两层流体界面附近产生瞬态波致平均漂移的重要作用，采用PTV技术测量了不同振幅和频率的界面波引起的拉格朗日漂移。
A four component decomposition of the local instantaneous velocity is proposed. It brings out more readily the terms in the Navier-Stokes equations associated with different events and fluid structures of turbulent flows than the classic two component decomposition of Reynolds. In particular the new composition highlights the existence of two types of Reynolds stresses: fast and slow. The fast Reynolds stresses can be linked to a streaming process that describes the ejection of wall fluid in the bursting process. It also provides a simple method for modelling the wall layer. The four component…
The motion of incompressible fractional Oldroyd-B fluids between two parallel walls perpendicular to a plate that applies time-dependent shear stresses to the fluid is studied by means of integral transforms. In the special cases of Newtonian and second grade fluids, these shear stresses reduces to fH(t)sin(wt) or fH(t)cos(wt). General solutions for velocity are presented as a sum of Newtonian solutions and the corresponding non-Newtonian contributions. They reduce to the similar solutions corresponding to the motion over an infinite plate if the distance between walls tend to infinity and can…
The paper contains an extension of the Khristianovich-Geertsma-de Klerk (KGD) model to the case when the confining rock pressure, which closes a hydraulic fracture, varies in the direction of its propagation. The extension is impelled by the need to simulate fracture hampering (acceleration) when it penetrates into a layer with increased (decreased) rock pressure. The paper presents the problem formulation, an efficient numerical method for its solving, examples of fractures propagating through layers with various stresses and general conclusions. It is established that when the fracture enter…
Two converging and superimposing shock and Rayleigh waves are generated on a glass substrate by focusing laser pulses on two concentric rings in a bullseye configuration (67\mm~and 96\mm~radii). We study experimentally the threshold for substrate damage as a function of the number of repetitions and the delay (0-20\,ns). The bullseye focusing experiments are compared to a single focusing ring. Additionally, fluid-structure interaction simulations using a Volume-of-Fluid framework are utilized to estimate the stresses. The lowest number of repetitions to attain surface damage is found for const…
Flow of yield stress fluid in a percolating network
研究了在孔隙网络模型中，具有均匀分布半径孔隙的Bingham yield-stress流体流动，发现当阻塞最大半径分数超过临界阈值时，流体仅通过渗流簇流动，存在两种不同的流动模式。
In this paper we demonstrate the influence of the pore pressure to the development of a hydraulically-driven fracture in a poroelastic medium. We present a novel numerical model for propagation of a planar hydraulic fracture and prove its correctness by demonstration of the numerical convergence and by comparison with known solutions. The advantage of the algorithm is that it does not require the distinguishing of the fracture's tips and reconstruction of the numerical mesh according to the fracture propagation. Next, we perform a thorough analysis of the interplay of fluid filtration and redi…
We present an experimental and numerical study of immiscible two-phase flow in 3-dimensional (3D) porous media to find the relationship between the volumetric flow rate ($Q$) and the total pressure difference ($ΔP$) in the steady state. We show that in the regime where capillary forces compete with the viscous forces, the distribution of capillary barriers at the interfaces effectively creates a yield threshold, making the fluids reminiscent of a Bingham viscoplastic fluid in the porous medium, introducing a threshold pressure $P_t$. In this regime, $Q$ depends quadratically on an excess press…
In this study, it was formulated the boundary-value-problem (BVP), comprising partial differential equations (PDEs), of steady flow for plane, laminar jet of a micropolar fluid. A new similarity transformation/solution was derived which is valid not only for the Newtonian fluids but also for the micropolar fluids. Obviously, this transformation will be transformed the PDEs into the ordinary differential equations (ODEs). These ODEs were solved numerically by the finite difference method. The obtained results were compared with existing results [1, 12] for the Newtonian fluids. The comparison w…
Viscous fingering (VF) is an interfacial instability that occurs in a narrow confinement or porous medium when a less-viscous fluid pushes a more viscous one, producing finger-like patterns. Controlling the VF instability is essential to enhance the efficiency of various technological applications. However, the control of VF instability has been challenging and so far focused on simple Newtonian fluids of constant viscosity. Here, we extend to complex yield-stress fluids and examine the controlling feasibility by carrying out a linear stability analysis using a radial cell with a converging ga…
A comprehensive scheme for the spatial discretisation of continuity equation, momentum advection and normal and shear stresses at the fluid interfaces is presented for numerically simulating the incompressible two phase flows based on the finite volume and volume of fluid methods. The scheme uses the mass conservation for the advection of the interface between the two fluids, physical considerations in determining the momentum flux at the surfaces of the finite volume so that it is consistent with that for the advection of the interfaces, and correctly accounts for the contributions to the nor…
In the present work, we study the flow of thixotropic yield stress fluids between two concentric cylinders. In order to take into account the thixotropy, the constitutive relation uses a structural parameter which is driven by a kinetic equation. Here, the Houska's model is considered. Depending on the breakdown rate of the structural parameter, localization or shear-banding are observed. We show that for fragile structures, a shear-banding flow may be observed although for stronger structures, only localisation of the flow is observed such as in Bingham fluids. Physical explanations of the sh…
We develop a framework for analyzing the momentum balance of laminar particle-laden flows based on immersed boundary methods, which solve the Navier-Stokes equations and resolve the particle surfaces. This framework differs from previous studies by explicitly accounting for the fluid inside the particles, which is a by-product of the immersed boundary method, allowing us to close the momentum balance for the flow around a single rolling sphere. We then compute a momentum balance of a laminar Poiseuille flow over a dense bed of particles, finding that the stresses remain in equilibrium even dur…
The present experimental study addresses the flow of a Yield Stress Fluid with some elasticity (Carbopol gel) in a square duct. The behaviour of two fluids with lower and higher yield stress is investigated at multiple Reynolds numbers $Re^* \in$ (1, 200) and Bingham numbers $Bi \in$ (0.01, 0.35). A secondary flow consisting of eight vortices is observed to recirculate the fluid from the corners to the core. Their extent and intensity grows with increasing $Re^*$. The second objective of this study is to explore the change in flow in the presence of particles. Almost neutrally-buoyant finite-s…
In this paper, the performance of two lattice Boltzmann method formulations for yield-stress (i.e. viscoplastic) fluids has been investigated. The first approach is based on the popular Papanastasiou regularisation of the fluid rheology in conjunction with explicit modification of the lattice Boltzmann relaxation rate. The second approach uses a locally-implicit formulation to simultaneously solve for the fluid stress and the underlying particle distribution functions. After investigating issues related to the lattice symmetry and non-hydrodynamic Burnett stresses, the two models were compared…
Many fascinating phenomena such as large-scale collective flows, enhanced fluid mixing and pattern formation have been observed in so-called active fluids, which are composed of particles that can absorb energy and dissipate it into the fluid medium. For active particles immersed in liquids, fluid-mediated viscous stresses can play an important role on the emergence of collective behavior. Here, we experimentally investigate their role in the dynamics of self-assembling magnetically-driven colloidal particles which can rapidly form organized hexagonal structures. We find that viscous stresses …
Topology optimization offers optimal material layouts, enabling automation in the design of devices. Given the recent advances in computer technology and additive manufacturing, topology optimization is increasingly being used to design complex porous structures, for example, microfluidic devices. For the flow of fluids in such miniature-sized porous structures, viscous shearing stress will be significant. But the Darcy model -- the most popular mathematical model describing the flow of a single-phase incompressible fluid in rigid porous media -- neglects the internal friction arising from vis…
On buoyancy in disperse two-phase flow and its impact on the well-posedness of two-fluid models
本文探讨了分散两相流中浮力的分解及其对两流体模型正则性的影响，推导了新的闭合关系，表明除雷诺应力外，所有应力和伪应力均贡献于浮力背景流，并具有低通滤波特性，防止哈达玛不稳定性。
We study hydrodynamic fluctuations in a compressible and viscous fluid film confined between two rigid, no-slip, parallel plates, where one of the plates is kept fixed, while the other one is driven in small-amplitude, translational, displacements around its reference position. This jiggling motion is assumed to be driven by a stochastic, external, surface forcing of zero mean and finite variance. Thus, while the transverse (shear) and longitudinal (compressional) hydrodynamic stresses produced in the film vanish on average on either of the plates, these stresses exhibit fluctuations that can …
Active nematic response to a deformable body or boundary: elastic deformations and anchoring-induced flow
本文用复变量方法解析二维活性向列相中线弹性物体的流动、指向矢、牵引力与形变，揭示活性应力和锚定条件诱导的效应及应力测量新思路。
Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical surface stresses on the body. Moreover, these inaccurate stresses often lead to unphysical oscillations in the history of integrated surface forces such as the coefficient of lift. While the errors in the surface stresses and forces do not necessarily affect the convergence of the velocity field, it is desirable, especially in fluid-structure interaction proble…
A two-phase Volume of Fluid approach to model rigid-perfectly plastic granular materials
针对颗粒流大变形问题，提出结合Drucker-Prager准则、Bingham流体与VoF法的刚理想塑性两相模型，经不同休止角材料验证，预测结果与实验和数值数据吻合良好，可用于大规模颗粒介质模拟。
A new pressure sensor array for local normal stress measurement in complex fluids
本文提出一种置于扭转流变仪底板的5×5压电电容式聚合物泡沫压力传感器阵列，可局部映射复杂流体法向应力，并在聚合物溶液、负应力检测和玉米淀粉剪切增稠悬浮液中验证其高精度与表征能力。
We develop a coarse-grained description of the point-vortex model, finding that a large number of planar vortices and antivortices behave as an inviscid non-Eulerian fluid at large scales. The emergent binary vortex fluid is subject to anomalous stresses absent from Euler's equation, caused by the singular nature of quantum vortices. The binary vortex fluid is compressible, and has an asymmetric Cauchy stress tensor allowing orbital angular momentum exchange with the vorticity and vortex density. An analytic solution for vortex shear flow driven by anomalous stresses is in excellent agreement …
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