Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session D04: Focus Session: The Physics of Microscale Fluid Structure Interactions: Fully Coupled Flow and Deformation Mechanics II |
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Chair: Federico Municchi, Purdue University Room: Georgia World Congress Center B206 |
Sunday, November 18, 2018 2:30PM - 2:43PM |
D04.00001: Evaporation of gelled sessile drops Matthew Hennessy, Arandeep Uppal, Richard V Craster, Omar K Matar Gelation occurs during the evaporation of many complex biological fluids. Further evaporation of solvent from the gel leads to a variety of patterning behaviours. During evaporation, flow drives solid particles to the contact line, where compaction leads to the formation of a gel front, which propagates into the bulk. An assortment of complex phenomena is involved in the formation and fracture of the gel front, however, the dynamics of fully-gelled droplets is not understood. Hence, we consider the problem of a drop with an already present solid network undergoing evaporation. A model is derived for the drying of a fully-gelled drop from the governing equations of nonlinear poroelasticity alongside the lubrication approximation. Poroelastic free surface profiles show good agreement with experiments. The evolution of the mechanical properties of the gel obtained from the fluid/solid dynamics can be fed into a fracture model to simulate a variety of crack morphologies also seen in experiments. |
Sunday, November 18, 2018 2:43PM - 2:56PM |
D04.00002: Fully-coupled model of a solid-liquid composite beam Yoav Matia, Amir Daniel Gat Elastic structures containing embedded fluid-filled cavities have been receiving considerable attention in recent years in various fields such as smart materials, sensors, actuators and soft-robotics. Such structures can be viewed as meta materials, or solid-liquid composites. Deformation of solid-liquid composites both creates, and is induced by, a fluidic pressure gradient and viscous flow which deforms the cavities and thus the surrounding solid. We examine a beam-like appendage embedded with a set of a fluid-filled bladders, interconnected via elastic slender channels; a common arrangement of the abovementioned fields. Utilizing homogenization and Cosserat models, we model two-way transient interaction, enabling the analysis of highly coupled nonlinear problems with large deformations, extending the scope of existing research. We then show how the obtained coupled equation system enables exploration of new ideas involving soft smart-materials for control of structural response to external excitations as well as energy harvesting applications. |
Sunday, November 18, 2018 2:56PM - 3:09PM |
D04.00003: Static response of a soft microtube due to low Reynolds number non-Newtonian flow Vishal Anand, Ivan C. Christov Microfluidic devices are often made of polymeric materials, while biological tissue is soft. Both can deform significantly due to flow, even at vanishing Reynolds number. Due to deformation, the pressure gradient in the flow-wise direction is not constant. Deformation leads to significant enhancement of flow due to the change in cross-sectional area; hence, a nonlinear flow rate--pressure drop relation (unlike the Hagen--Poiseuille law for a rigid tube). We study steady flow in a thin, slender deformable microtube. To capture non-Newtonian effects of biofluids, we employ the power-law model. The structural problem is reduced to transverse loading of linearly-elastic cylindrical shells. A perturbative approach (in the slenderness parameter) yields analytical solutions for the flow and deformation. Then, we obtain a ``generalized Hagen--Poiseuille law'' for soft microtubes. We benchmark the analytical results against fully-3D two-way coupled numerical simulations of flow and deformation performed using the commercial CAE software ANSYS. The simulations establish the range of validity of the theory, showing excellent agreement. |
Sunday, November 18, 2018 3:09PM - 3:22PM |
D04.00004: Viscous flow in bistable elastic channels - analogy to Stefan's solidification problem Ofek Peretz, Amir Gat The presented work examines the effect of cross-section bi-stability on the dynamics of viscous flow propagating into slender elastic channels. In the examined configuration, the channel boundaries include a compressed and curved elastic sheet which is stable in two different deformation patterns for a given pressure. The state of the elastic arc is determined by the history of the pressure changes and the initial conditions of the system. The viscous flow is analyzed via applying the lubrication approximation and examining self-similarity. For the case of constant inlet pressure, the propagation rate of the location in which snap between the two states occurs, is presented for various physical limits. An analogy between the examined bi-stable configuration and Stefan's solidification problem is presented. |
Sunday, November 18, 2018 3:22PM - 3:35PM |
D04.00005: A non-iterative, second-order in time approximation of fluid-structure interaction problem Martina Bukac, Catalin Trenchea We present a novel, partitioned method for the interaction between a viscous, incompressible fluid and a thin structure. The method is similar to the sequential Backward Euler - Forward Euler implementation of the Crank-Nicolson discretization scheme. The structure and fluid sub-problems are first solved using a Backward Euler scheme, and them solved using a Forward Euler scheme. The stability analysis based on energy estimates shows that the scheme is unconditionally stable. Error analysis of the semi-discrete problem yields second-order convergence in time. We will present numerical examples showing an excellent comparison of the proposed scheme to the monolithic scheme using the same time step for both methods. |
Sunday, November 18, 2018 3:35PM - 3:48PM |
D04.00006: Modelling bubble propagation in elasto-rigid Hele-Shaw channels Joao Fontana, Anne Juel, Andrew Hazel We study a model of pulmonary airway reopening where air is driven at constant volume flux into a liquid-filled Hele-Shaw channel, with an upper compliant boundary. An equivalent rigid channel supports a stable, steadily propagating air finger and a variety of unstable solutions. In the compliant channel, however, initial collapse of the channel introduces additional cross-sectional depth gradients. The induced normal and transverse depth variations alter the finger morphology and promote a variety of instabilities from tip-splitting to small-scale fingering on the curved front. A depth-averaged model for the system is simulated numerically using the open-source, finite-element library, oomph-lib, in order to explore underlying mechanisms and the relative importance of the elastic, capillary and viscous effects. The model exhibits a complex solution structure and qualitatively similar instabilities to those observed experimentally. The solution structure is related to that found in a rigid Hele-Shaw channel but here the solutions interact due to the fluid-structure interaction introduced by the compliant boundary. |
Sunday, November 18, 2018 3:48PM - 4:01PM |
D04.00007: Simulation of deformation-dispersion of a blood clot using immersed boundary method Somnath Roy, Piru Mohan Khan To study the dynamics of blood clot in artery, we have chosen a simplified case of deformation of an initially spherical shaped object during its motion in fluid medium. The mass diffusion from this body is also considered in this model. Forces acting on this moving body by the nearby fluid and deformation due to these applied forces are calculated here by using immersed boundary method (IBM). Spurious fluctuation of pressure and mass conservation in the intercepted cells (both fluid and solid are present) is a serious issue in IBM. To eliminate these issues we have used Marker-and-Cell Method (MAC) in the fluid cells and SOLA method in the intercepted cell for the pressure-velocity correction and these methods are repeated until a divergence free velocity field is obtained. Viscoelastic constitutive properties are considered for the blood clot. An unstructured triangular surface mesh is deployed the define the clot surface which is deformed due to the mass and momentum transport from the fluid. A loosely coupled fluid-structure interaction strategy has been used. |
Sunday, November 18, 2018 4:01PM - 4:14PM |
D04.00008: Computer simulations of drug release from a liposome into the bloodstream Badr Kaoui I propose two-dimensional simulations of drug release from a liposome into the bloodstream. I perform the fluid-structure coupling, between the particles deformation (the liposome and the red blood cells) and the plasma flow, using the immersed boundary method. I compute both the flow and the drug mass transport using the lattice Boltzmann method. The simulations allow computing the instantaneous amount of the released drug, its distribution and its accumulation in the blood vessel wall. These quantities are sensitive to multiple factors and parameters. Here, I briefly explore the impact of having surrounding red blood cells, which are found to enhance slightly the drug release at large Schmidt numbers. In the limit of extremely large permeability of the particles, the drug transport is mainly affected by the complex flow induced by the interplay between the applied flow and the collective motion of the particles [B. Kaoui, European Physical Journal E - Soft Matter and Biological Physics 41 (2), 20 (2018)]. |
Sunday, November 18, 2018 4:14PM - 4:27PM |
D04.00009: A 1D model for unsteady fluid--structure interactions in a soft-walled microchannel Tanmay C. Inamdar, Ivan C. Christov A one-dimensional model for the transient fluid--structure interaction (FSI) between a soft-walled microchannel and viscous fluid flow within it is developed. An Euler--Bernoulli beam, with transverse bending rigidity and nonlinear axial tension, is coupled to a 1D fluid model obtained by depth-averaging 2D incompressible Navier--Stokes equations in the lubrication scaling. The resulting set of coupled nonlinear PDEs are solved numerically through a segregated approach employing fully-implicit time stepping and second-order finite-difference discretizations. The Strouhal number is fixed at unity, while the Reynolds number $Re$ and a dimensionless Young's modulus $\Sigma$ are varied independently to explore the parameter space. A critical $Re$ is defined by determining when the maximum steady-state deformation exceeds a certain threshold. It is shown that the critical $Re\propto\Sigma^{3/4}$, a scaling that indicates ``wall modes'' play a role in the evolution of the system away from an initially flat state. The maximum wall displacement at steady state correlates with a single dimensionless group, namely $Re/\Sigma^{0.9}$ for both pure bending and bending with tension. |
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