Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session G23: General Fluid Dynamics: Viscous Flows |
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Chair: Neil Balmforth, University of British Columbia Room: 605 |
Sunday, November 24, 2019 3:48PM - 4:01PM |
G23.00001: Experiments and analysis of viscous flows in bistable elastic channels Ofek Peretz, Anand Mishra, Robert Shepherd, Amir D. Gat We present experimental results of viscous fluid propagating into a slender channel with bi-stable cross-section shape, emanating from an upper surface which is a compressed curved elastic sheet. During the propagation of the liquid into the channel, the surface snaps from one stable shape to the other, and a moving front is observed. This front includes wrinkling of the elastic surface, and is shown to provide a stable transition between the two stable shapes of the channel. 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 transition region is presented for various physical limits. Good agreement is obtained between the experiments and analysis. [Preview Abstract] |
Sunday, November 24, 2019 4:01PM - 4:14PM |
G23.00002: Hollow-Fiber Microfiltration Systems: Stokes Flow Solution in a Semi-Infinite Channel with Permeable Walls Francesca Bernardi, Nicholas G. Cogan, M. Nicholas J. Moore Most wastewater management facilities aimed at water purification in the United States utilize hollow-fiber microfiltration. In these systems, pipes are split into thousands of micrometer-scale capped tubes with permeable walls. As wastewater flows through the filter, foulants are captured by the membraned walls allowing clean water to exit. Understanding the fluid dynamics is a fundamental step towards controlling the fouling process and enhancing the efficiency of microfiltration. We investigate the flow of wastewater through a single hollow-fiber tube. Starting from an infinite channel with permeable walls, we solve the Stokes flow problem in the channel interior for all permeability regimes. Then, we generalize the result to a semi-infinite channel with permeable walls capped at one end to mimic a single hollow-fiber system. Comparison with experiments and future directions will be discussed. [Preview Abstract] |
Sunday, November 24, 2019 4:14PM - 4:27PM |
G23.00003: Three-dimensional Hiemenz Stagnation-Point Flows Patrick Weidman A modification of Hiemenz's two-dimensional outer potential stagnation-point flow of strain rate $a$ is obtained by adding periodic radial and azimuthal velocities of the form $b r \sin 2 \theta$ and $b r \cos 2 \theta$, respectively, where $b$ is a shear rate. This leads to the discovery of a new family of three-dimensional viscous stagnation-point flows depending on the shear-to-strain rate ratio $\gamma = b/a$ that exist over the range $-\infty < \gamma < \infty$ with reflectional symmetry about $\gamma = 0$. Numerical solutions for the wall shear stress parameters and the displacement thicknesses are given and compared with their large-$\gamma$ asymptotic behaviors. Sample similarity profiles are also presented. [Preview Abstract] |
Sunday, November 24, 2019 4:27PM - 4:40PM |
G23.00004: Levitation by thin viscous layers. Tom Mullin, Hilary Ockendon, John Ockendon We consider the levitation of cuboidal blocks by means of the viscous stresses that are generated when the block adheres to a vertically moving wall that is coated with oil. We then describe an experimental procedure that reveals the parameter regimes in which long-time levitation can occur. Then a simple model for the relevant lubrication flows is used to explain the theoretical basis for these observations. [Preview Abstract] |
Sunday, November 24, 2019 4:40PM - 4:53PM |
G23.00005: Helical buckling of flexible filaments in viscous flow Brato Chakrabarti, Yanan Liu, John Lagrone, Ricardo Cortez, Lisa Fauci, Olivia du Roure, David Saintillan, Anke Lindner Helical morphologies of slender structures in flow are generic and have been observed in various experiments and manufacturing processes over a range of length scales. In contrast with the classical helical buckling of elastic rods that requires application of end moments, helical buckling of freely suspended filaments is a spontaneous symmetry breaking induced by distributed viscous forces. In a step towards elucidating this phenomenon, we demonstrate using microfluidic experiments that actin filaments first buckle in compressional flow due to viscous stresses and subsequently form coiled conformations, and two complementary sets of simulations in different geometries also reveal the same. The radius of the emerging helices is found to be independent of filament length, which we explain using a scaling law. To explain the origin of helical buckling, we also perform a weakly nonlinear stability analysis. Following a linear Euler buckling regime induced by compressive stresses, unstable planar modes are shown to interact in the presence of geometric nonlinearities and spontaneously give rise to three-dimensional helical morphologies. Our theory highlights why helical coiling is so ubiquitous in strain-dominated flows. [Preview Abstract] |
Sunday, November 24, 2019 4:53PM - 5:06PM |
G23.00006: Chiral micro-printed particles in viscous shear flow Francesca Tesser, Andreas ZĂ¶ttl, Justine Laurent, Olivia du Roure, Anke Lindner Particles in the form of helices in viscous shear flows migrate across streamlines as a result of their chiral shape and the shear flow. This chirality-induced drift can be used to sort micro-helices and other chiral objects in microfluidic channels, and it is also known to produce the rheotactic behavior of \textit{E. coli} bacteria. In this case, the drift in combination with viscous friction on the bacterial head induces a rheotactic torque, acting as a bias on the orientation of the cell. High resolution micro-printing techniques allow nowadays to fabricate micro-particles with a controlled shape and enable to perform experiments where the re-orientation dynamics can be observed under shear flow, providing new insight in this fluid-structure interaction problem. We print both left- and right-handed helices attached to a spherical body and follow them individually as they are passively transported in a microfluidic channel. The resulting dynamics is a modified Jeffery tumbling, in which we recognize the effect of the particle handedness on the stabilization of the particle orientation. Finally we show how this stabilization mechanism can be optimized, by varying the helix geometry. [Preview Abstract] |
Sunday, November 24, 2019 5:06PM - 5:19PM |
G23.00007: Sedimentation of polygonal tiles Narayanan Menon, Alyssa Conway, Rahul Chajwa, Rintaro Kirikawa, Sriram Ramaswamy We study the stokesian sedimentation of planar shapes by experiments in which polygonal tiles are placed in a vertical plane and sedimented at low Reynolds number in a quasi-two-dimensional container. We first focus on the effect of shape-polarity by studying isosceles triangles of varying apex angles. Unlike nonpolar shapes, a triangle rotates as it sediments due to coupling between the orientational and translational degrees of freedom, and asymptotically approaches a stable orientation [Jayaweera, Mason, J. Fluid Mech. 22 (1965)]. For small apex angles the triangle is stable with apex pointing down along the gravity direction. As the apex angle is increased we find a transition at $\pi $/3 for which all orientations of the triangle are stable and for apex angles greater than $\pi $/3, the triangle is stable with apex pointing up. We understand the experimental results with a model of three stokeslets fixed to the vertices of a triangle. The transition described above, and the coupling of orientation to horizontal drift are captured by this model. We also test generalizations of this discrete-stokeslet model to other regular and irregular polygons and to concave shapes. [Preview Abstract] |
Sunday, November 24, 2019 5:19PM - 5:32PM |
G23.00008: Motion of an approximate sphere in a Brinkman medium D. Palaniappan, O. S. Pak The motion of an approximate sphere through a porous medium modeled using the Brinkman equation is investigated. Analytic solutions for the velocity and pressure fields due to the translation of a perturbed sphere in a Brinkman medium are found via the Stokes stream function approach. Explicit expression for the stream function is obtained to the first and second order in the small parameter characterizing the deformation. The cases of prolate and oblate spheroids, which depart only slightly from the spherical shape form, are considered as particular examples and the hydrodynamic force on these non-spherical bodies are evaluated. Beyond the first order of deformation, it is found that the hydrodynamic drag on a non-spherical body depends on the permeability coefficient in manners different from the case of a perfect sphere. These differences suggest the complex interactions between non-sphericity and permeability. Several special cases are deduced from our exact solutions. The results may be applied to investigate the effects of particle geometry in transport and locomotion in porous media. [Preview Abstract] |
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