195 research outputs found

    Fully coupled simulations of non-colloidal monodisperse sheared suspensions

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    In this work we investigate numerically the dynamics of sheared suspensions in the limit of vanishingly small fluid and particle inertia. The numerical model we used is able to handle the multi-body hydrodynamic interactions between thousands of particles embedded in a linear shear flow. The presence of the particles is modeled by momentum source terms spread out on a spherical envelop forcing the Stokes equations of the creeping flow. Therefore all the velocity perturbations induced by the moving particles are simultaneously accounted for. The statistical properties of the sheared suspensions are related to the velocity fluctuation of the particles. We formed averages for the resulting velocity fluctuation and rotation rate tensors. We found that the latter are highly anisotropic and that all the velocity fluctuation terms grow linearly with particle volume fraction. Only one off-diagonal term is found to be non zero (clearly related to trajectory symmetry breaking induced by the non-hydrodynamic repulsion force). We also found a strong correlation of positive/negative velocities in the shear plane, on a time scale controlled by the shear rate (direct interaction of two particles). The time scale required to restore uncorrelated velocity fluctuations decreases continuously as the concentration increases. We calculated the shear induced self-diffusion coefficients using two different methods and the resulting diffusion tensor appears to be anisotropic too. The microstructure of the suspension is found to be drastically modified by particle interactions. First the probability density function of velocity fluctuations showed a transition from exponential to Gaussian behavior as particle concentration varies. Second the probability of finding close pairs while the particles move under shear flow is strongly enhanced by hydrodynamic interactions when the concentration increases

    Dynamic structure factor study of diffusion in strongly sheared suspensions

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    Diffusion of neutrally buoyant spherical particles in concentrated monodisperse suspensions under simple shear flow is investigated. We consider the case of non-Brownian particles in Stokes flow, which corresponds to the limits of infinite PĂŠclet number and zero Reynolds number. Using an approach based upon ideas of dynamic light scattering we compute self- and gradient diffusion coefficients in the principal directions normal to the flow numerically from Accelerated Stokesian Dynamics simulations for large systems (up to 2000 particles). For the self-diffusivity, the present approach produces results identical to those reported earlier, obtained by probing the particles' mean-square displacements (Sierou & Brady, J. Fluid Mech. vol. 506, 2004 p. 285). For the gradient diffusivity, the computed coefficients are in good agreement with the available experimental results. The similarity between diffusion mechanisms in equilibrium suspensions of Brownian particles and in non-equilibrium non-colloidal sheared suspensions suggests an approximate model for the gradient diffusivity: {\textsfbi D}^\triangledown\,{\approx}\,{\textsfbi D}^s/S^{eq}(0), where {\textsfbi D}^s is the shear-induced self-diffusivity and Seq(0)S^{eq}(0) is the static structure factor corresponding to the hard-sphere suspension at thermodynamic equilibrium

    The mechanics of suspensions

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    Suspension mechanics—the flow of a fluid with small fragments of solid material suspended in it—is an area of wide applicability in both industry and nature. Examples include the transport of silt in rivers, the manufacture of toothpaste, and inkjet printing where pigments remain solid within the ink. One widespread method to simulate these flows is Stokesian Dynamics, a truncated multipole expansion of the Stokes equations. It is computationally efficient while making a reasonable approximation to the hydrodynamic interactions between particles; however, all particles are identical spheres and the background matrix must be Newtonian. This project extends Stokesian Dynamics to include differently-sized spheres. This allows us to study a variety of previously inaccessible suspension problems. In many suspensions, e.g. toothpaste, the suspending fluid itself is non-Newtonian and exhibits viscoelastic properties. We have extended Stokesian Dynamics to incorporate a simple model of viscoelasticity by using the small spheres as 'beads' in bead--spring dumbbells. Different spring laws are then tested in shear, and their rheological behaviour is compared to continuum constitutive models. Next, we replicate experiments in which a large sphere is dropped through a suspension of neutrally buoyant smaller spheres undergoing oscillatory shear flow. We qualitatively replicate the principal experimental observation—that at the moment of shear reversal, the suspension microstructure hinders the falling; while at the instant of fastest shear, it enhances the falling. We propose a physical mechanism explaining the observations. Finally, we extend Stokesian Dynamics to properly implement interparticle frictional contact. Contact forces are a critical component of shear thickening in suspensions such as cornflour, yet are usually implemented in an ad hoc way, resulting in inaccurate predictions or high computational cost. The new method allows us to investigate contact models quickly and efficiently, and suggests an important factor in models of strongly shear-thickening fluids

    Methods for suspensions of passive and active filaments

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    Flexible filaments and fibres are essential components of important complex fluids that appear in many biological and industrial settings. Direct simulations of these systems that capture the motion and deformation of many immersed filaments in suspension remain a formidable computational challenge due to the complex, coupled fluid--structure interactions of all filaments, the numerical stiffness associated with filament bending, and the various constraints that must be maintained as the filaments deform. In this paper, we address these challenges by describing filament kinematics using quaternions to resolve both bending and twisting, applying implicit time-integration to alleviate numerical stiffness, and using quasi-Newton methods to obtain solutions to the resulting system of nonlinear equations. In particular, we employ geometric time integration to ensure that the quaternions remain unit as the filaments move. We also show that our framework can be used with a variety of models and methods, including matrix-free fast methods, that resolve low Reynolds number hydrodynamic interactions. We provide a series of tests and example simulations to demonstrate the performance and possible applications of our method. Finally, we provide a link to a MATLAB/Octave implementation of our framework that can be used to learn more about our approach and as a tool for filament simulation

    Coalescence of Liquid Drops: Different Models Versus\ud Experiment

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    The process of coalescence of two identical liquid drops is simulated numerically in the framework of two essentially different mathematical models, and the results are compared with experimental data on the very early stages of the coalescence process reported recently. The first model tested is the ‘conventional’ one, where it is assumed that coalescence as the formation of a single body of fluid occurs by an instant appearance of a liquid bridge smoothly connecting the two drops, and the subsequent process is the evolution of this single body of fluid driven by capillary forces. The second model under investigation considers coalescence as a process where a section of the free surface becomes trapped between the bulk phases as the drops are pressed against each other, and it is the gradual disappearance of this ‘internal interface’ that leads to the formation of a single body of fluid and the conventional model taking over. Using the full numerical solution of the problem in the framework of each of the two models, we show that the recently reported electrical measurements probing the very early stages of the process are better described by the interface formation/disappearance model. New theory-guided experiments are suggested that would help to further elucidate the details of the coalescence phenomenon. As a by-product of our research, the range of validity of different ‘scaling laws’ advanced as approximate solutions to the problem formulated using the conventional model is\ud established

    Numerical analysis of sprays with an advanced collision model

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    [EN] Modelling of collisions between liquid droplets in the frame of a Lagrangian spray simulation has still many open issues, especially when considering higher viscous droplets and if colliding droplets have a large size difference. A generalisation of the collision maps is attempted based on the behaviour of characteristic points, namely the triple point where bouncing, coalescence and stretching separation coincide and the critical Weber-number where reflexive separation first occurs in head-on collisions. This is done by correlating experimental data with respect to the Capillary number with the Ohnesorge-number for the triple point and the critical Weber-number is also well described by a correlation the Ohnesorge-number. Based on these results the boundary line between stretching separation and coalescence is found by adapting the Jiang et al. (1992) correlation. For the upper boundary of reflexive separation the shifted Ashgriz and Poo (1990) correlation is used. It was however so far not possible to predict the lower bouncing boundary through the Estrade et al. (1999) boundary line correctly. The proposed boundary-line models were validated for various liquid, however still considering only a size ratio of one. With the developed three-line boundary model Euler/Lagrange numerical calculations for a simple spray system were conducted and the droplet collisions were analysed with respect to their occurrence. Droplet collision modelling is performed on the basis of the stochastic droplet collision model, also considering the influence of impact efficiency, which so far was neglected for most spray simulations. The comparison with measurements showed reasonable good agreement for all properties.The authors acknowledge the financial support of this research project by the Deutsche Forschungsgemeinschaft (DFG) under contract SO 204/35-1 to 3.Sommerfeld, M.; Lain, S. (2017). Numerical analysis of sprays with an advanced collision model. En Ilass Europe. 28th european conference on Liquid Atomization and Spray Systems. Editorial Universitat Politècnica de València. 418-431. https://doi.org/10.4995/ILASS2017.2017.4785OCS41843
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