Yannis Dimakopoulos

Bio: Yannis Dimakopoulos is an academic researcher from University of Patras. The author has contributed to research in topics: Newtonian fluid & Viscoelasticity. The author has an hindex of 22, co-authored 70 publications receiving 1474 citations. Previous affiliations of Yannis Dimakopoulos include Eindhoven University of Technology & University of Cyprus.

Steady bubble rise and deformation in Newtonian and viscoplastic fluids and conditions for bubble entrapment

Abstract: We examine the buoyancy-driven rise of a bubble in a Newtonian or a viscoplastic fluid assuming axial symmetry and steady flow. Bubble pressure and rise velocity are determined, respectively, by requiring that its volume remains constant and its centre of mass remains fixed at the centre of the coordinate system. The continuous constitutive model suggested by Papanastasiou is used to describe the viscoplastic behaviour of the material. The flow equations are solved numerically using the mixed finite-element/Galerkin method. The nodal points of the computational mesh are determined by solving a set of elliptic differential equations to follow the often large deformations of the bubble surface. The accuracy of solutions is ascertained by mesh refinement and predictions are in very good agreement with previous experimental and theoretical results for Newtonian fluids. We determine the bubble shape and velocity and the shape of the yield surfaces for a wide range of material properties, expressed in terms of the Bingham Bn=τy*ρ*g*R b Bond B o = ρ*g*R* 2 b /γ* and Archimedes A r =ρ *2 g*R *3 b /μ * o 2 numbers, where ρ* is the density, μ * o the viscosity, γ* the surface tension and τ * y the yield stress of the material, g* the gravitational acceleration and R * b the radius of a spherical bubble of the same volume. If the fluid is viscoplastic, the material will not be deforming outside a finite region around the bubble and, under certain conditions, it will not be deforming either behind it or around its equatorial plane in contact with the bubble. As Bn increases, the yield surfaces at the bubble equatorial plane and away from the bubble merge and the bubble becomes entrapped. When Bo is small and the bubble cannot deform from the spherical shape the critical Bn is 0.143, i.e. it is a factor of 3/2 higher than the critical Bn for the entrapment of a solid sphere in a Bingham fluid, in direct correspondence with the 3/2 higher terminal velocity of a bubble over that of a sphere under the same buoyancy force in Stokes flow. As Bo increases allowing the bubble to squeeze through the material more easily, the critical Bingham number increases as well, but eventually it reaches an asymptotic value. Ar affects the critical Bn value much less.

Steady bubble rise in Herschel–Bulkley fluids and comparison of predictions via the Augmented Lagrangian Method with those via the Papanastasiou model

Abstract: The steady, buoyancy-driven rise of a bubble in a Herschel–Bulkley fluid is examined assuming axial symmetry. The variation of the rate-of-strain tensor around a rising bubble necessitates the coexistence of fluid and solid regions in this fluid. In general, a viscoplastic fluid will not be deforming beyond a finite region around the bubble and, under certain conditions, it will not be deforming either just behind it or around its equatorial plane. The accurate determination of these regions is achieved by introducing a Lagrange multiplier and a quadratic term in the corresponding variational inequality, resulting in the so-called Augmented Lagrangian Method (ALM). Additionally here, the augmentation parameters are determined following a non-linear conjugate gradient procedure. The new predictions are compared against those obtained by the much simpler Papanastasiou model, which uses a continuous constitutive equation throughout the material, irrespective of its state, but does not determine the boundary between solid and liquid along with the flow field. The flow equations are solved numerically using the mixed finite-element/Galerkin method on a mesh generated by solving a set of quasi-elliptic differential equations. The accuracy of solutions is ascertained by mesh refinement and comparison with our earlier and new predictions for a bubble rising in a Newtonian and a Bingham fluid. We determine the bubble shape and velocity and the shape of the yield surfaces for a wide range of material properties, expressed in terms of the Bingham, Bn, Bond, and Archimedes numbers. As Bn increases, the bubble decelerates, the yield surfaces at its equatorial plane and away from it approach each other and eventually merge immobilizing the bubble. For small and moderate Bingham numbers, the predictions using the Papanastasiou model satisfactorily approximate those of the discontinuous Herschel–Bulkley model for sufficiently large values of the normalization exponent (⩾104). On the contrary, as Bn increases and the rate-of-strain approaches zero almost throughout the fluid-like region, much larger values of the exponent are required to accurately compute the yield surfaces. Bubble entrapment does not depend on the power law index, i.e. a bubble in a Herschel–Bulkley fluid is entrapped under the same conditions as in a Bingham fluid.

Yielding the yield-stress analysis: a study focused on the effects of elasticity on the settling of a single spherical particle in simple yield-stress fluids

Abstract: The sedimentation of a single particle in materials that exhibit simultaneously elastic, viscous and plastic behavior is examined in an effort to explain phenomena that contradict the nature of purely yield-stress materials. Such phenomena include the loss of the fore-and-aft symmetry with respect to an isolated settling particle under creeping flow conditions and the appearance of the “negative wake” behind it. Despite the fact that similar observations have been reported in studies involving viscoelastic fluids, researchers conjectured that thixotropy is responsible for these phenomena, as the aging of yield-stress materials is another common feature. By means of transient calculations, we study the effect of elasticity on both the fluidized and the solid phase. The latter is considered to behave as an ideal Hookean solid. The material properties of the model are determined under the isotropic kinematic hardening framework via Large Amplitude Oscillatory Shear (LAOS) measurements. In this way, we are able to predict accurately the unusual phenomena observed in experiments with simple yield-stress materials, irrespective of the appearance of slip on the particle surface. Viscoelasticity favors the formation of intense shear and extensional stresses downstream of the particle, significantly changing the entrapment mechanism in comparison to that observed in viscoplastic fluids. Therefore, the critical conditions under which the entrapment of the particle occurs deviate from the well-known criterion established theoretically by Beris et al. (1985) and verified experimentally by Tabuteau et al. (2007) for similar materials under conditions that elastic effects are negligible. Our predictions are in quantitative agreement with published experimental results by Holenberg et al. (2012) on the loss of the fore–aft symmetry and the formation of the negative wake in Carbopol with well-characterized rheology. Additionally, we propose simple expressions for the Stokes drag coefficient, as a function of the gravity number, Yg (related to the Bingham number), for different levels of elasticity and for its critical value, under which entrapment of particles occurs. These criteria are in agreement with the results found in the recent work by Ahonguio et al. (2014). Finally, we propose a method to quantify experimentally the elastic effects in viscoplastic particulate systems.

Transient displacement of a viscoplastic material by air in straight and suddenly constricted tubes

Abstract: We examine the transient displacement of a viscoplastic material from straight or suddenly constricted cylindrical tubes of finite length. Our general goal is to develop accurate and efficient numerical methods for the fundamental study of processes in which a gas is displacing a liquid from prototype geometries under various operating conditions. Such processes can be part of the Gas Assisted Injection Molding (GAIM) or enhanced oil recovery. To this end, we use the mixed finite element method coupled with a quasi-elliptic mesh generation scheme in order to follow the very large deformations of the fluid volume. The displacing fluid is gas at high pressure, which forms a bubble of increasing length and a shape that depends on the fluid properties, the flow conditions, and the tube geometry. The cross-section of the bubble is always smaller than that of the tube due to adherence of fluid on the tube walls. The thickness of the remaining film depends on the same parameters and for most of its length it behaves as unyielded material. Unyielded material also arises in front of the bubble, around the axis of symmetry of the tube(s) and in the case of a constricted tube near the recirculation corner, but not around the entrance of the secondary tube. The rate of growth of the ‘tip splitting’ instability, that arises at relatively large values of the Reynolds number for Newtonian fluids in straight tubes, decreases as the Bingham number increases and, eventually, the instability disappears. The resistance provided by the constricted tube downstream makes the bubble move at a nearly constant velocity only when the Bingham number is not large. When the bubble approaches the constriction it becomes more pointed, but after entering it, the bubble reassumes its well-developed profile. Depending on parameter values, the bubble in the secondary tube may periodically split, thus forming a train of smaller bubbles directed towards the exit of the tube, a phenomenon for which experimental evidence exists.

Fracture and adhesion of soft materials: a review.

Abstract: Soft materials are materials with a low shear modulus relative to their bulk modulus and where elastic restoring forces are mainly of entropic origin. A sparse population of strong bonds connects molecules together and prevents macroscopic flow. In this review we discuss the current state of the art on how these soft materials break and detach from solid surfaces. We focus on how stresses and strains are localized near the fracture plane and how elastic energy can flow from the bulk of the material to the crack tip. Adhesion of pressure-sensitive-adhesives, fracture of gels and rubbers are specifically addressed and the key concepts are pointed out. We define the important length scales in the problem and in particular the elasto-adhesive length Γ/E where Γ is the fracture energy and E is the elastic modulus, and how the ratio between sample size and Γ/E controls the fracture mechanisms. Theoretical concepts bridging solid mechanics and polymer physics are rationalized and illustrated by micromechanical experiments and mechanisms of fracture are described in detail. Open questions and emerging concepts are discussed at the end of the review.

Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics

Abstract: The archetypal feature of a viscoplastic fluid is its yield stress: If the material is not sufficiently stressed, it behaves like a solid, but once the yield stress is exceeded, the material flows like a fluid. Such behavior characterizes materials common in industries such as petroleum and chemical processing, cosmetics, and food processing and in geophysical fluid dynamics. The most common idealization of a viscoplastic fluid is the Bingham model, which has been widely used to rationalize experimental data, even though it is a crude oversimplification of true rheological behavior. The popularity of the model is in its apparent simplicity. Despite this, the sudden transition between solid-like behavior and flow introduces significant complications into the dynamics, which, as a result, has resisted much analysis. Over recent decades, theoretical developments, both analytical and computational, have provided a better understanding of the effect of the yield stress. Simultaneously, greater insight into the material behavior of real fluids has been afforded by advances in rheometry. These developments have primed us for a better understanding of the various applications in the natural and engineering sciences.

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

Abstract: This article presents a comprehensive review of numerical methods and models for interface resolving simulations of multiphase flows in microfluidics and micro process engineering. The focus of the paper is on continuum methods where it covers the three common approaches in the sharp interface limit, namely the volume-of-fluid method with interface reconstruction, the level set method and the front tracking method, as well as methods with finite interface thickness such as color-function based methods and the phase-field method. Variants of the mesoscopic lattice Boltzmann method for two-fluid flows are also discussed, as well as various hybrid approaches. The mathematical foundation of each method is given and its specific advantages and limitations are highlighted. For continuum methods, the coupling of the interface evolution equation with the single-field Navier–Stokes equations and related issues are discussed. Methods and models for surface tension forces, contact lines, heat and mass transfer and phase change are presented. In the second part of this article applications of the methods in microfluidics and micro process engineering are reviewed, including flow hydrodynamics (separated and segmented flow, bubble and drop formation, breakup and coalescence), heat and mass transfer (with and without chemical reactions), mixing and dispersion, Marangoni flows and surfactants, and boiling.

Yield stress fluid flows: A review of experimental data

Abstract: Yield stress fluids are encountered in a wide range of applications: toothpastes, cements, mortars, foams, muds, mayonnaise, etc. The fundamental character of these fluids is that they are able to flow (i.e., deform indefinitely) only if they are submitted to a stress above some critical value. Otherwise they deform in a finite way like solids. The flow characteristics of such materials are difficult to predict as they involve permanent or transient solid and liquid regions that are generally hard to locate a priori. Here we review the present state of the art as it appears from experimental data for flows of simple (non-thixotropic) yield stress fluids under various conditions, viz., uniform flows in straight channels or rheometrical geometries, complex stationary flows in channels of varying cross-section such as extrusion, expansion, flow through a porous medium, transient flows such as flows around obstacles, spreading, spin-coating, squeeze flow, and elongation. The effects of surface tension, confinement, and secondary flows are also reviewed. We focus especially on experimental work identifying internal flow characteristics that can be compared with numerical predictions. It is shown in particular that: (i) deformations in the solid regime can play a critical role in transient flows; (ii) the yield character is not apparent in the flow field when the boundary conditions impose large deformations; (iii) the yield character is lost in secondary flows.

On the usage of viscosity regularisation methods for visco-plastic fluid flow computation

Abstract: Viscosity regularisation methods are probably the most popular current method for computing visco-plastic fluid flows. They are however generally used in an ad hoc manner. Here we examine convergence of regularised solutions to those of the corresponding exact models, in both mathematical and physical senses. Mathematically, the aim is to give practical guidance as to the order of error that one might expect for different regularisations and for different types of flow. Our theoretical results are illustrated with a number of computed example flows showing the orders of error predicted. Physically, the question is whether or not the regularised solutions behave in the same way as the exact solutions, qualitatively as well as quantitatively. We show that there are flows for which regularisation methods will generate their maximum errors, e.g. lubrication-type flows. In this context, we also consider the effects of regularisation on problems of hydrodynamic stability. For broad classes of problems, stability characteristics of the flow are incorrectly predicted by the use of viscosity regularisation methods.