Flexible scraping of viscous fluids

International audienceWe study the thickness h(d) of the liquid film left on a wet surface after scraping it with an elastic wiper (length L, rigidity B) moved at a velocity V. The scraper is clamped vertically at a given distance above the substrate, and h(d) is maximal when the tip of the scraper is just tangent to the surface. We show experimentally and theoretically that this maximum thickness is hmax similar or equal to 0.33L (eta VL2/B)(3/4) where eta is the liquid viscosity. The deposition law is found to be sensitive to the shape of the wiper: the film thickness can also be tuned by using wipers with a permanent curvature, and varying this curvature

Viscoplastic plates

An asymptotic model is constructed to describe the bending of thin sheets, or plates, of viscoplastic fluid described by the Herschel–Bulkley constitutive law, which incorporates the von Mises yield condition and a nonlinear viscous stress. The model reduces to a number of previous ones from plasticity theory and viscous fluid mechanics in various limits. It is characterized by a yield criterion proposed by Ilyushin which compactly combines the effect of the bending moment and in-plane stress tensors through three particular invariants. The model is used to explore the bending of loaded flat plates, the deflection of impulsively driven circular plates, and the tension-controlled deflection of loaded beams

Mathematics of crimping

The aim of this thesis is to investigate the mathematics and modelling of the industrial crimper, perhaps one of the least well understood processes that occurs in the manufacture of artificial fibre. We begin by modelling the process by which the fibre is deformed as it is forced into the industrial crimper. This we investigate by presuming the fibre to behave as an ideal elastica confined in a two dimensional channel. We consider how the arrangement of the fibre changes as more fibre is introduced, and the forces that are required to confine it. Later, we apply the same methods to a fibre confined to a three dimensional channel. After the fibre has under gone a preliminary deformation, a second process known as secondary crimp can occur. This involves the `zig-zagged' material folding over. We model this process in two ways. First as a series of rigid rods joined by elastic hinges, and then as an elastic with a highly oscillatory natural configuration compressed by thrusts at each end. We observe that both models can be expressed in a very similar manner, and both predict that a buckle can occur from a nearly straight initial condition to an arched formation. We also compare the results to experiments performed on the crimped fibre. Throughout much of the process, the configuration of the fibre does not alter. This part of the process we call the block, and model the material in this region in two ways: as a series of springs; and as an isotropic elastic material. We discuss the coupling between the different regions and the process that occurs in the block, and consider both the steady state and stability of the system

Curved jets of viscous fluid : interactions with a moving wall

The processes where a jet of viscous fluid hits a moving surface arise in various industrial and everyday-life applications. A simple example is pouring honey onto a pancake. Similar processes are used in the production of glass wool, thermal isolation, three-dimensional polymeric mats, and para-aramid fibers. In all these processes a liquid jet emerges from a nozzle and is driven by gravity and possibly centrifugal and Coriolis forces towards a moving surface. The performance of the processes depends strongly on the properties of the jet between the nozzle and the moving surface. Very often experimental study of the jet is very difficult or sometimes even impossible. Therefore, modeling can give some insight into the process and describe the influence of the parameters on the performance. The parameters one can think of are: flow velocity at the nozzle, surface velocity, distance between the nozzle and the moving surface, and fluid properties such as viscosity. One of the simplest examples one can look at is the viscous jet falling under gravity from an oriented nozzle onto a moving belt. There is a vast amount of literature on jets hitting a stationary surface, but only very few publications involving a moving one. In our experiments we identify three stationary regimes: i) a concave shape aligned with the nozzle orientation (comparable to a ballistic trajectory), ii) a vertical shape, or iii) a convex shape aligned with the belt. The convexity or concaveness of the shape characterizes the three flow regimes. In addition to this overall structure, stationary or instationary boundary effects can be observed at the nozzle and near the belt. Moreover, when the nozzle does not point vertically down the whole jet can be instationary. To describe the jet we use a model which takes into account the effects of inertia, viscosity, and gravity, and disregards bending. This allows us to focus on the large-scale jet shape while avoiding the modeling of bending and buckling regions at the jet ends. Also, we neglect surface tension and assume the fluid to be isothermal and Newtonian. The key issue for this model are boundary conditions for the jet shape. They follow from the conservation of momentum equation which is a hyperbolic equation for the shape. The correct boundary conditions follow from consideration of the characteristic directions of that equation at each end. This also provides a criterion for partitioning the parameter space into the three regimes. The physical quantity which characterizes the three flow regimes is the momentum transfer through a jet cross-section, which has contributions from both inertia and viscosity. In a concave jet the momentum transfer due to inertia dominates the viscous one everywhere in the jet, and therefore the nozzle orientation is relevant. In the vertical jet the momentum transfer due to viscosity dominates at the nozzle and due to inertia at the belt, and in the point where they are equal the stationary jet should be aligned with the direction of gravity. From this the vertical shape follows. In the convex jet the viscous momentum transfer dominates in the jet and the tangency with the belt becomes important. This gives an alternative characterization of the three flow regimes in which the jet can be inertial, viscous-inertial, and viscous respectively. Moreover, for this model we prove existence and investigate uniqueness. When we have non-uniqueness, up to three stationary solutions are possible, which explains the instationary behaviour observed experimentally. The comparison between our theory and experiments shows a qualitative agreement. A similar process of rotatory fiber spinning is modeled using the same approach. In this process the jet is driven out from a rotating rotor by centrifugal and Coriolis forces towards a cylindrical surface (the ‘coagulator’). The parameter space contains four possible situations. Two correspond to the inertial and the viscous-inertial jets discussed before. The two others correspond to different types of non-existence of stationary jets, one because no stationary jet can reach the coagulator (causing real-world jets to wind around the rotor), and one because a stationary jet can not match velocities at the coagulator. An interesting fact is that the viscous jet situation is not possible; this would require the coagulator to rotate in the same direction as the rotor with at least half of its angular velocity

Elastogranular mechanics: far-from-equilibrium behaviors of thin elastic structures deforming in granular matter

Confined thin elastic objects are abundant in nature. With spatial constraints typically arising from a combination of different loading profiles, confining media, or coupling effects, the unique deformation strategies of slender structures, with their propensity to buckle, bend, fold, & wrinkle, is observed across a range of different length scales, from the nano-scale folding of graphene and the microscopic wrinkling of cellular membranes, to the macroscopic development of plant root networks. Much previous work has focused on growing or deforming thin structures confined by rigid, fixed boundaries. Comparatively, much less is known about the behavior of thin structures interacting with compliant or transitional boundaries, such as those formed by granular materials. By varying the geometries of slender elastic structures embedded within a granular medium and studying the resulting buckling behaviors under area or displacement control, we have established an experimental framework allowing us to apply the results of classical elastic stability theory to deformations occurring within complex & fragile media. These elastogranular systems couple the finite deformations of slender, flexible bodies with the qualitative phase changes observed in granular materials, which may transition between being gas, fluid, or solid-like states of matter. The elongation of a slender elastica in a 2D monodisperse medium leads to two length scales {∆c,λc} encoding system behavior before and after a critical jamming point φj, while introducing bidispersity into the same experiments changes the underlying structural composition/order in the grains, allowing bending energy in the elastica to relax as the medium transitions from crystalline solid to a more fluid-like amorphous state. The planar injection of a pinched elastic loop shows the intricate coupling between large elastic deformations and developing boundaries, while the buckling morphologies of a slender elastic ring compressed in a granular gas shows promise as a device-free probe of mechanical packing properties. These results will bring new insight into the behavior of deformable structures within granular media, colloidal systems, and soft gels, and will be relevant in the study of plant root morphogenesis, the modeling of animal movements, the design of soft robots, and in developing smart, steerable optical & surgical tools

Instabilities of jets of non-Newtonian fluids impacting a plate

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2008.Includes bibliographical references (p. 106-111).The problem of buckling and coiling of jets of viscous, Newtonian liquids impacting a plate has received a substantial level of attention over the past two decades, both from experimental and theoretical points of view. Nevertheless, most industrial and everyday life fluids are non-newtonian, and their rheological properties affects their behavior in this problem. The present work aims at studying the instabilities of jets of such fluids falling on a plate, via both phenomenological descriptions and theoretical analysis of jet motion and shape. Several fluids with different rheological properties, including viscous Newtonian oil, model non-Newtonian fluids, and commercial shampoos, are used and different dynamical regimes are documented. A special focus is placed on viscoelastic, shear-thinning cetylpyridinium (CPyC1) solutions. In concentrated solutions, CPyCl surfactant molecules have been shown to assemble in long wormlike micellar structures, which gives the fluid its non-Newtonian properties. Jets of CPyCl solution show several novel shapes and dynamical regimes not observed in the case of Newtonian fluids. The present study provides quantitative experimental measurements and mechanisms for these novel features.by Matthieu Varagnat.S.M

Puncture resistance of turf reinforcement mat

Turf Reinforcement Mats are used as a non-degradable erosion control material to provide long-term slope or channel protection before and during vegetation establishment. While most manufacturers are interested in emphasizing the service life of their products, the question of mechanical damage during and after installation is always a key issue that has rarely been addressed in previous studies. Puncturing is one of the main mechanical damage issues that happens quite often during the lifetime of turf reinforcement mats. The thesis focuses on the analysis of puncture resistance as well as other physical and mechanical properties of turf reinforcement mats. This work seeks to identify the correlation between index properties and their mechanical properties, which can help engineers identify suitable materials during product selection. The experimental results show that the static puncture resistance and extensibility of woven turf reinforcement mats increase as mass per unit area increases. This study also investigates the puncture resistance of soil-turf reinforcement mat systems by performing California Bearing Ratio based puncture tests. Experimental results show that turf reinforcement mat can remarkably improve the penetration value of soil-turf reinforcement mat system by up to almost 60% compared to the soil-only system. It is also observed that soil benefits more in penetration tests with higher puncture resistance and mass per unit area of the turf reinforcement mat. The numerical simulation of the puncture test of turf reinforcement mats illustrates their damage characteristics with the change of projectile shape, material density, and material geometry. The results indicate that turf reinforcement with greater density has a higher puncture resistance which reflects a similar trend seen in experimental tests. Also, the modeling results show that a turf reinforcement mat impacted by a projectile with a flat tip presents the greatest puncture resistance compared with those punctured by the projectiles of conical and hemispherical tips. The simulation of the soil-turf reinforcement mat system shows higher soil reinforcement at shallow soil depths. In engineering practice, turf reinforcement mats are usually applied for soil erosion control together with vegetation reinforcement. A series of experiments were also performed to explore the reinforcement of the plant roots-turf reinforcement mat system, especially for young plants. In this study, Dandelion and Ryegrass were selected as representative of vegetation with taproots and fibrous roots. The experimental results suggest that the pullout resistance of fibrous roots is greater than that of taproots. Although the application of turf reinforcement mat does not have a clear effect on the pullout resistance of plant roots, it improves their initial pullout modulus. In addition, turf reinforcement mat coverage over soil can reduce water evaporation up to 78% thereby retaining soil moisture during seed germination.Ph.D