Particles In Viscoelastic Fluids Research Articles

Locomotion in complex fluids: Integral theorems

The biological fluids encountered by self-propelled cells display complex microstructures and rheology. We consider here the general problem of low-Reynolds number locomotion in a complex fluid. Building on classical work on the transport of particles in viscoelastic fluids, we demonstrate how to mathematically derive three integral theorems relating the arbitrary motion of an isolated organism to its swimming kinematics in a non-Newtonian fluid. These theorems correspond to three situations of interest, namely, (1) squirming motion in a linear viscoelastic fluid, (2) arbitrary surface deformation in a weakly non-Newtonian fluid, and (3) small-amplitude deformation in an arbitrarily non-Newtonian fluid. Our final results, valid for a wide-class of swimmer geometry, surface kinematics, and constitutive models, at most require mathematical knowledge of a series of Newtonian flow problems, and will be useful to quantity the locomotion of biological and synthetic swimmers in complex environments.

Statistical challenges in microrheology

Microrheology is the study of the properties of a complex fluid through the diffusion dynamics of small particles, typically latex beads, moving through that material. Currently, it is the dominant technique in the study of the physical properties of biological fluids, of the material properties of membranes or the cytoplasm of cells, or of the entire cell. The theoretical underpinning of microrheology was given in Mason and Weitz (Physical Review Letters; 1995), who introduced a framework for the use of path data of diffusing particles to infer viscoelastic properties of its fluid environment. The multi‐particle tracking techniques that were subsequently developed have presented numerous challenges for experimentalists and theoreticians. This study describes some specific challenges that await the attention of statisticians and applied probabilists. We describe relevant aspects of the physical theory, current inferential efforts and simulation aspects of a central model for the dynamics of nano‐scale particles in viscoelastic fluids, the generalized Langevin equation.

Structure Formation of Non‐Colloidal Particles in Viscoelastic Fluids Subjected to Simple Shear Flow

AbstractThe alignment and the aggregation of particles in a viscoelastic fluid in simple shear flow are qualitatively analyzed using a two‐dimensional direct numerical simulation. Depending on the shear thinning, solvent viscosity, and Weissenburg number, a typical sequence in structural transitions from random particle configuration to string formation is found with clustering and clustered string formation in between. The solvent viscosity and the Weissenburg number, the ratio of normal stress to shear stress, are found to be the most influential parameters for the onset of string formation. The influence of shear thinning is less clear. More shear thinning seems to promote string formation if the stress ratio is constant. The angular velocity of the particles is reduced by approximately 60% when particles form a string, independent of the parameters used. magnified image

Flow-induced orientation of non-spherical particles: Effect of aspect ratio and medium rheology

The flow-induced orientation of spheroidal particles in viscoelastic fluids is studied by means of rheo-optical methods and flow microscopy. Using suitable model systems a wide range of rotational Péclet and Weissenberg numbers have been covered, providing a systematic and global picture of the various orientational transitions. The effects of particle size and aspect ratio have been considered separately. Increasing the shear rate gradually causes first the well-known change from a random orientation to spinning in Jeffery orbits. Upon further increasing both the Péclet and Weissenberg numbers, the period of rotation becomes larger. At this stage the orbits start to drift slowly toward a ‘log-rolling’ state, which leads to an orientation distribution function that is narrowly peaked around the vorticity axis. For the fluids tested here, the orbit drift rates are proportional to the shear rate. At still higher elasticities, the particles are observed to reorient again in the flow direction, with the notable exception of suspensions in Boger fluids. Some of the experimentally observed features are qualitatively in line with the results of a theory for slender bodies in second order fluids, despite both relatively small aspect ratios and a more complex rheological behavior of the suspending media. An effect of absolute particle size is also noted which might indicate interference from Brownian motion, as suggested earlier. With suitable flow histories bimodal flow-vorticity orientation distributions can be generated. Finally, specific flow-induced alignment and aggregation are observed, they are more difficult to generate than in suspensions with spheres.

Experimental Study and Modeling of Flow Behavior and Orientation Kinetics of Layered Silicate/Polypropylene Nanocomposites in Start-up of Shear Flows

Abstract Effects of organoclay contents on the startup flow properties of layered nano-scale particles in the simple shear mode are investigated. The addition of small amounts of nanoclays to polypropylene melts was found to dramatically change the flow characteristics and creates stress overshoots at large shear rates. A rheological model, initially developed for studying the motion of a group of symmetric ellipsoid particles in viscoelastic fluids was used to describe the orientation state of the uniformly dispersed suspensions of layered silicate in polypropylene melts. The effects of shear, particle loadings, particle interactions, flow reversal and rest time after cession of shear are studied and discussed according to our experimental observations and model predictions. It is shown that another diffusion term in the governing equation for the particles can be used to predict the properties by applying the rest time which was found to change the orientation of particles and shifts it to more isotropic microstructures. The experimental results of the startup viscosity are reasonably well predicted by the model at the three shear rates tested.

Alignment and aggregation of spherical particles in viscoelastic fluid under shear flow

In this study, we performed experiments on the alignment and chaining of non-colloidal, spherical particles suspended in viscoelastic liquid under simple shear flow as a model problem for investigating the microstructure formation in viscoelastic suspensions. Monolayer experiments show that both the chain-like structure and uniformly distributed structure can be observed after the dynamic steady state has been reached depending upon fluid rheology. Even though the driving force for the migration is the first normal stress difference of viscoelastic liquid, shear thinning is responsible for the formation of string-like structure.

Particle Motion and Segregation in Piston Driven Free Surface Flows of Viscoelastic Fluids

We have investigated the motion, redistribution and segregation of solid particles dispersed in a viscoelastic fluid during piston-driven free surface flows. This phenomenon and its effect on suspension microstructure is of significant importance in a number of processes used to form composite materials, notably injection and compression moulding. In the experimental part of this study we used a 5% w/w suspension of PMMA particles dispersed in a hydrated hydroxypropyl guar gel. A reversible motor with variable speed and minimal vibration was used to move a tube up and down on a stationary piston, creating a piston-driven flow with a free surface. We observed that the particles move away from the piston and towards the free surface where they slowly accumulate. This observation confirms theoretical predictions that in the presence of a normal stress gradient perpendicular to the direction of bulk flow, as would be observed with viscoelastic fluids, suspended particles tend to gravitate towards and then remain near the free surface. Simulations show that the speed of this segregation increases with fluid elasticity, shear rate and particle size, in agreement with literature models for the lateral migration velocity of particles in viscoelastic fluids.

Rheology of a suspension of particles in viscoelastic fluids

In this paper we study the bulk stress of a suspension of rigid particles in viscoelastic fluids. We first apply the theoretical framework provided by Batchelor [J. Fluid Mech. 41 (1970) 545] to derive an analytical expression for the bulk stress of a suspension of rigid particles in a second-order fluid under the limit of dilute and creeping flow conditions. The application of the suspension balance model using this analytical expression leads to the prediction of the migration of particles towards the centerline of the channel in pressure-driven flows. This is in agreement with experimental observations. We next examine the effects of inertia (or flow Reynolds number) on the rheology of dilute suspensions in Oldroyd-B fluids by two-dimensional direct numerical simulations. Simulation results are verified by comparing them with the analytical expression in the creeping flow limit. It is seen that the particle contribution to the first normal stress difference is positive and increases with the elasticity of the fluid and the Reynolds number. The ratio of the first normal stress coefficient of the suspension and the suspending fluid decreases as the Reynolds number is increased. The effective viscosity of the suspension shows a shear-thinning behavior (in spite of a non-shear-thinning suspending fluid) which becomes more pronounced as the fluid elasticity increases.

Effects of fluid elasticity on the static and dynamic settling of a spherical particle

The results of an experimental investigation of the settling velocity of spherical particles in viscoelastic fluids are presented. As well as being fundamentally interesting, this problem is also of relevance to the under- standing of particle transport by well-technology fluids used in the oil industry. It is shown that the settling velocity is reduced by elastic effects in the fluid (e.g., presence of normal stress differences and high elongational viscosity), and that this effect becomes significantly higher with increasing shear rates experienced by the falling sphere, i.e. the ratio of settling velocity to sphere diameter. Imposing an orthogonal shear-flow field on the settling particle causes a further dramatic reduction of the settling velocity in viscoelastic fluids.