Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session A33: Micro/Nano Flows: Channels |
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Chair: Ivan Christov, Purdue University Room: 242 |
Sunday, November 20, 2022 8:00AM - 8:13AM |
A33.00001: Lucas-Washburn theory revisited for capillary rise in nanotubes Mohammad Heiranian, Narayana R Aluru In the 1920s, Edward Wight Washburn derived an equation, known as the Lucas-Washburn formula, based on the Hagen-Poiseille (HP) law to describe capillary flow or fluid filling dynamics in circular tubes. However, the HP law, which was incorporated in the Lucas-Washburn theory, only works for flow in infinitely long tubes where end effects are neglected. The entrance effects are important for large-slip flows such as water flow in carbon nanotubes (CNTs). With the recent experimental advances in water filling of isolated CNTs and the fact that CNTs have recently drawn a great deal of attention in a variety of applications, such as water desalination, power generation and biosensing, there is a need for an accurate theory describing flow in CNTs. Here, we revisit the Lucas-Washburn theory to account for the hydrodynamic entrance effects as well as the variation of capillary pressure and key hydrodynamic properties with the radius and length of CNTs. We show that our modified Lucas-Washburn theory is able to accurately describe filling dynamics in CNTs when compared to the data from molecular dynamics simulations. Using our modified theory, slip lengths in CNTs could potentially be estimated from experimental data in isolated CNTs. We believe that our findings are a leap forward in the field of nanofluidics. |
Sunday, November 20, 2022 8:13AM - 8:26AM Not Participating |
A33.00002: Evaporation during Liquid Imbibition into Micro-Channels Rick Spijkers, Jan Willem Mijnheer, Markus Schremb, Srinivas Vanapalli Imbibition of liquids into porous materials is of relevance for many fields and applications such as filtration, geology, heat pipe design, etc. The one-dimensional absorption process is well described for isothermal conditions using the Lucas-Washburn model, considering surface tension, permeability, and gravity. The present study expands on this existing work by studying the effect of evaporation on imbibition of liquids into capillaries with smaller dimensions. A gradual change in behavior during imbibition depending on temperature is observed and presented. Starting at low channel temperature with isothermal imbibition which is well-described using the Lucas-Washburn model, the effect of evaporation increases with increasing temperature until the liquid no longer contacts the capillary due to the Leidenforst effect. Using a temperature controlled capillary channel the relevance of evaporation and its effect on the imbibition velocity is examined for varying channel dimensions. In particular, the current knowledge will be extended to capillary channels with very small dimensions down to a depth of the order of 10 μm, which are more comparable to the pore and channel sizes found in relevant porous materials. |
Sunday, November 20, 2022 8:26AM - 8:39AM |
A33.00003: Molecular anatomy and macroscopic behavior of oil extraction from nanopores by CO2 and CH4 Hongwei Zhang, Rui Qiao, Shuyu Sun, Do Yoon Moh Oil production from unconventional reservoirs dominated by nanoscale pores contributes substantially to the liquid petroleum production in the US, but its recovery factor remains very low. Gas injection is a promising method to enhance oil production, but its underlying processes at the nanoscale are not well understood. This study focuses on the extraction of decane from single calcite nanopores under reservoir conditions. CO2 and CH4 with very different wall adsorption strengths are chosen as the injection gases for comparison. The results demonstrate that decane and injected gas exist as two populations (adsorbed and free phase) inside the pore. When CO2 is injected, the transport of the adsorbed populations initially dominates the oil extraction, but the transport of the free populations eventually governs oil extraction; the opposite trends are observed when CH4 is injected. Despite the evolving dominance by different populations, the overall decane extractions and gas accumulations in both cases can be described by a diffusive law. The effective diffusivities of decane extractions and gas accumulations, however, do not always align well with their self-diffusivities. |
Sunday, November 20, 2022 8:39AM - 8:52AM |
A33.00004: Joint use of fluidic and elastic reciprocal theorems to find the flow rate–pressure drop relation for deformable microchannels Ivan C Christov, Evgeniy Boyko, Howard A Stone Viscous flows through compliant conduits apply forces at the fluid-solid interface, leading to deformation of the conduit's cross-section, which affects the flow rate–pressure drop relation. Conventionally, calculating this relation requires solving the two-way coupled elastohydrodynamic problem of flow and deformation. Instead, we employ reciprocal theorems for Stokes flow and linear elasticity to derive a closed-form expression for the flow rate-pressure drop relation in deformable channels, using a domain perturbation expansion that that only requires the fluid flow solution and the elastic deformation due to the fluid stress distribution in an undeformed channel. Thus, we bypass solving the coupled fluid-structure-interaction problem. Unlike previous results, our approach shows a trade-off between the compliance of the deformable wall and the drag due to rigid sidewalls on the pressure drop. We find that compliance decreases the pressure drop, while drag due to sidewalls increases it. |
Sunday, November 20, 2022 8:52AM - 9:05AM |
A33.00005: Nonlinear flow rate–pressure drop relations in slender compliant microtubes Xiaojia Wang, Shrihari D Pande, Ivan C Christov We investigate the steady-state fluid–structure interaction between a Newtonian fluid flow and a deformable microtube, in two new configurations inspired by microfluidics experiments. Specifically, we derive a mathematical theory for the nonlinear flow rate–pressure drop relation by coupling lubrication theory for the flow with linear elasticity for the inner tube wall's deformation. Using the flow conduit's axial slenderness and its axisymmetry, we obtain an analytical expression for the radial displacement of the tube wall from a plane-strain configuration. We apply the theory to two novel geometries: (i) a cylindrical fluidic channel enclosed by an annulus of soft material with a rigid outer wall and (ii) a cylindrical fluidic channel extruded from a large rectangular slab of soft material. The predicted displacement fields, and the resulting closed-form flow rate--pressure drop relations, are each validated against 3D direct numerical simulations via SimVascular's two-way-coupled fluid–structure interaction solver, svFSI, showing good agreement. We also incorporate weak flow inertia into theory, further improving the agreement between theory and simulations for larger imposed flow rates. |
Sunday, November 20, 2022 9:05AM - 9:18AM |
A33.00006: Stokesian image systems and Lorentz' reflection formula Nicholas G Chisholm, Sarah D Olson Lorentz' reflection formula, a corollary of the Lorentz reciprocal theorem (1896), allows one to compute the creeping-flow motion of a fluid near a no-slip plane wall given a known solution to the Stokes equations in an unbounded fluid. This theorem may be applied to obtain the drag on colloidal particles or droplets near the wall. A related concept is that of an "image system", which is an auxiliary fluid flow that, when added to a Stokeslet---the point-force solution of the Stokes equations in an infinite medium---produces a new point-force solution subject to a desired boundary condition. The image system for a no-slip plane wall was first derived by Blake (1971), who noted that, while Lorentz' formula could be used to obtain a similar result, it did not produce his image system in a convenient form. Image systems have been used extensively to improve the efficiency of numerical boundary integral methods for Stokes flow. |
Sunday, November 20, 2022 9:18AM - 9:31AM |
A33.00007: Characterising fluid flow and solute transport in a gravity driven microfluidic system with surface tension effects Barnum Swannell, Michal Rudnik, Olivier Frey, Daniela Ortiz Franyuti, James M Oliver, Sarah L Waters Advanced microfluidic systems are increasingly important for evaluating safety and efficacy in pharmaceutical drug development. For drugs with complex mechanisms of action, it is crucial to understand and control the mixing of relevant compounds and biomolecules in these systems, which in turn requires a detailed understanding of the fluid flow. |
Sunday, November 20, 2022 9:31AM - 9:44AM |
A33.00008: Symmetry-Protected Stressless Microfluidics Jeremias M Gonzalez, Ajay Gopinathan, Bin Liu Flows under spatial confinement have often been regarded as possessing nonuniform structures accompanied by deformations and rotations. Symmetries of the system can however provide a powerful tool to both understand and manipulate the structure of the flow. Here, we studied flows confined by three-dimensional (3D) microfluidic devices with polyhedral symmetries. We show that all characteristic flows following an Octahedral symmetry can be classified into strain-full and strain-free groups, corresponding to distinct subgroups of the Octahedral symmetry group. Interestingly, the strain-free group of flow modes corresponds to uniform flow in arbitrary directions, which suggest exploiting them for 3D stress-free manipulations of flows. To demonstrate the robustness of these symmetry-protected flows, we built a microfluidic device with these symmetries and successfully realized stress-free manipulations by entraining several microparticles in the bulk fluid and forcing them to follow a variety of parallel and identical, user-specified 3D paths. |
Sunday, November 20, 2022 9:44AM - 9:57AM |
A33.00009: Fluid physics of telescoping cardboard boxes Kaare Hartvig Jensen, Emil Østergaard, Sean Marker, Jolet De Ruiter The economics, environmental impact, and mechanical properties of paper-based storage containers have been widely studied. However, knowledge of the physical processes relevant to the end-user experience is unavailable. This presentation outlines the main effects associated with the closing and opening of telescoping boxes, which are used, for instance, to store and transport board games, footwear, mobile phones, and tablet computers. The sliding motion of the lid is controlled by flow in a thin film of air in the gap separating the top and base of the box. Based on a broad comparison between theory and experiments on natural and synthetic boxes, we find that the process is primarily controlled by the detailed shape of the gap between the base and the lid. Three distinct experimental regimes are observed, and an optimal design for a rapidly closing box is identified. |
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