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Daivis PJ, Hansen JS, Todd BD. Electropumping of nanofluidic water by linear and angular momentum coupling: theoretical foundations and molecular dynamics simulations. Phys Chem Chem Phys 2021; 23:25003-25018. [PMID: 34739012 DOI: 10.1039/d1cp04139h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
In this article we review the relatively new phenomenon of electropumping in nanofluidic systems, in which nonzero net flow results when polar molecules are rotated by external electric fields. The flow is a consequence of coupling of the spin angular momentum of molecules with their linear streaming momentum. By devising confining surfaces that are asymmetric - specifically one surface is more hydrophobic compared to the other - unidirectional flow results and so pumping can be achieved without the use of pressure gradients. We first cover the historical background to this phenomenon and follow that with a detailed theoretical description of the governing hydrodynamics. Following that we summarise work that has applied this phenomenon to pump water confined to planar nanochannels, semi-functionalised single carbon nanotubes and concentric carbon nanotubes. We also report on the energy efficiency of this pumping technique by comparisons with traditional flows of planar Couette and Poiseuille flow, with the surprising conclusion that electropumping at the nanoscale is some 4 orders of magnitude more efficient than pumping by Poiseuille flow.
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Affiliation(s)
- Peter J Daivis
- School of Science, RMIT University, GPO Box 2476, Melbourne, Victoria 3001, Australia.
| | - J S Hansen
- "Glass and Time", IMFUFA, Department of Science and Environment, Roskilde University, Roskilde 4000, Denmark.
| | - B D Todd
- Department of Mathematics, School of Science, Computing and Engineering Technologies, Swinburne University of Technology, PO Box 218, Hawthorn, Victoria 3122, Australia.
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Ostler D, Kannam SK, Frascoli F, Daivis PJ, D Todd B. Inducing a Net Positive Flow of Water in Functionalized Concentric Carbon Nanotubes Using Rotating Electric Fields. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2019; 35:14742-14749. [PMID: 31614091 DOI: 10.1021/acs.langmuir.9b02594] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Electropumping has shown great potential as an effective means of inducing a net positive flow of water in confined channels. In this paper we present the first nonequilibrium molecular dynamics study and continuum based numerical solutions that demonstrate an effective net positive flow between concentric carbon nanotubes (CNT) using electropumping. We apply a spatially uniform rotating electric field that couples to the water's permanent dipole moment. Taking advantage of the coupling between the spin angular momentum and the linear momentum we break the symmetry of the channel radius by functionalizing the inner CNT's outer surface with carboxyl groups to induce a net positive flow. We also show that our results for concentric nanotubes are consistent with our previous work where we demonstrated that an increase in functionalization beyond an optimal point in a single walled carbon nanotube resulted in a decrease in positive net flow. We then numerically solve the coupled hydrodynamic momentum equations to show that the nonequilibrium molecular dynamics results are consistent with the continuum theory.
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Affiliation(s)
- David Ostler
- Department of Mathematics, School of Science, Faculty of Science, Engineering and Technology , Swinburne University of Technology , Melbourne , Victoria 3122 , Australia
| | - Sridhar Kumar Kannam
- Department of Mathematics, School of Science, Faculty of Science, Engineering and Technology , Swinburne University of Technology , Melbourne , Victoria 3122 , Australia
| | - Federico Frascoli
- Department of Mathematics, School of Science, Faculty of Science, Engineering and Technology , Swinburne University of Technology , Melbourne , Victoria 3122 , Australia
| | - Peter J Daivis
- School of Science and Centre for Molecular and Nanoscale Physics , RMIT University , Melbourne , Victoria 3001 , Australia
| | - B D Todd
- Department of Mathematics, School of Science, Faculty of Science, Engineering and Technology , Swinburne University of Technology , Melbourne , Victoria 3122 , Australia
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Abstract
The fluid dynamics of macroscopic and microscopic systems is well developed and has been extensively validated. Its extraordinary success makes it tempting to apply Navier–Stokes fluid dynamics without modification to systems of ever decreasing dimensions as studies of nanofluidics become more prevalent. However, this can result in serious error. In this paper, we discuss several ways in which nanoconfined fluid flow differs from macroscopic flow. We give particular attention to several topics that have recently received attention in the literature: slip, spin angular momentum coupling, nonlocal stress response and density inhomogeneity. In principle, all of these effects can now be accurately modelled using validated theories. Although the basic principles are now fairly well understood, much work remains to be done in their application.
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Dyrby TB, Innocenti GM, Bech M, Lundell H. Validation strategies for the interpretation of microstructure imaging using diffusion MRI. Neuroimage 2018; 182:62-79. [PMID: 29920374 DOI: 10.1016/j.neuroimage.2018.06.049] [Citation(s) in RCA: 52] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2017] [Revised: 06/08/2018] [Accepted: 06/15/2018] [Indexed: 12/19/2022] Open
Abstract
Extracting microanatomical information beyond the image resolution of MRI would provide valuable tools for diagnostics and neuroscientific research. A number of mathematical models already suggest microstructural interpretations of diffusion MRI (dMRI) data. Examples of such microstructural features could be cell bodies and neurites, e.g. the axon's diameter or their orientational distribution for global connectivity analysis using tractography, and have previously only been possible to access through conventional histology of post mortem tissue or invasive biopsies. The prospect of gaining the same knowledge non-invasively from the whole living human brain could push the frontiers for the diagnosis of neurological and psychiatric diseases. It could also provide a general understanding of the development and natural variability in the healthy brain across a population. However, due to a limited image resolution, most of the dMRI measures are indirect estimations and may depend on the whole chain from experimental parameter settings to model assumptions and implementation. Here, we review current literature in this field and highlight the integrative work across anatomical length scales that is needed to validate and trust a new dMRI method. We encourage interdisciplinary collaborations and data sharing in regards to applying and developing new validation techniques to improve the specificity of future dMRI methods.
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Affiliation(s)
- Tim B Dyrby
- Danish Research Centre for Magnetic Resonance, Center for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre, Hvidovre, Denmark; Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark.
| | - Giorgio M Innocenti
- Karolinska Institutet, Department of Neuroscience, Stockholm, Sweden; Brain and Mind Institute, Swiss Federal Institute of Technology in Lausanne, Lausanne, Switzerland
| | - Martin Bech
- Medical Radiation Physics, Lund University, Lund, Sweden
| | - Henrik Lundell
- Danish Research Centre for Magnetic Resonance, Center for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre, Hvidovre, Denmark
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De Luca S, Kannam SK, Todd BD, Frascoli F, Hansen JS, Daivis PJ. Effects of Confinement on the Dielectric Response of Water Extends up to Mesoscale Dimensions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2016; 32:4765-4773. [PMID: 27115841 DOI: 10.1021/acs.langmuir.6b00791] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The extent of confinement effects on water is not clear in the literature. While some properties are affected only within a few nanometers from the wall surface, others are affected over long length scales, but the range is not clear. In this work, we have examined the dielectric response of confined water under the influence of external electric fields along with the dipolar fluctuations at equilibrium. The confinement induces a strong anisotropic effect which is evident up to 100 nm channel width, and may extend to macroscopic dimensions. The root-mean-square fluctuations of the total orientational dipole moment in the direction perpendicular to the surfaces is 1 order of magnitude smaller than the value attained in the parallel direction and is independent of the channel width. Consequently, the isotropic condition is unlikely to be recovered until the channel width reaches macroscopic dimensions. Consistent with dipole moment fluctuations, the effect of confinement on the dielectric response also persists up to channel widths considerably beyond 100 nm. When an electric field is applied in the perpendicular direction, the orientational relaxation is 3 orders of magnitude faster than the dipolar relaxation in the parallel direction and independent of temperature.
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Affiliation(s)
- Sergio De Luca
- School of Chemical Engineering, Integrated Material Design Centre (IMDC), University of New South Wales , Sydney, NSW 2033, Australia
| | | | | | | | - J S Hansen
- DNRF Center "Glass and Time", IMFUFA, Department of Science and Environment, Roskilde University , DK-4000 Roskilde, Denmark
| | - Peter J Daivis
- School of Applied Sciences, RMIT University , Melbourne, Victoria 3001, Australia
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Felderhof BU. Self-propulsion of a spherical electric or magnetic microbot in a polar viscous fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:023014. [PMID: 25768604 DOI: 10.1103/physreve.91.023014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2014] [Indexed: 06/04/2023]
Abstract
The self-propulsion of a sphere immersed in a polar liquid or ferrofluid is studied on the basis of ferrohydrodynamics. In the electrical case an oscillating charge density located inside the sphere generates an electrical field that polarizes the fluid. The lag of polarization with respect to the electrical field due to relaxation generates a time-independent electrical torque density acting on the fluid, causing it to move. The resulting propulsion velocity of the sphere is calculated in perturbation theory to second order in powers of the charge density.
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Affiliation(s)
- B U Felderhof
- Institut für Theorie der Statistischen Physik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany
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De Luca S, Todd BD, Hansen JS, Daivis PJ. Molecular dynamics study of nanoconfined water flow driven by rotating electric fields under realistic experimental conditions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2014; 30:3095-3109. [PMID: 24575940 DOI: 10.1021/la404805s] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
In our recent work, J. Chem. Phys. 2013, 138, 154712, we demonstrated the feasibility of unidirectional pumping of water, exploiting translational-rotational momentum coupling using nonequilibrium molecular dynamics simulations. Flow can be sustained when the fluid is driven out of equilibrium by an external spatially uniform rotating electric field and confined between two planar surfaces exposing different degrees of hydrophobicity. The permanent dipole moment of water follows the rotating field, thus inducing the molecules to spin, and the torque exerted by the field is continuously injected into the fluid, enabling a steady conversion of spin angular momentum into linear momentum. The translational-rotational coupling is a sensitive function of the rotating electric field parameters. In this work, we have found that there exists a small energy dissipation region attainable when the frequency of the rotating electric field matches the inverse of the dielectric relaxation time of water and when its amplitude lies in a range just before dielectric saturation effects take place. In this region, that is, when the frequency lies in a small window of the microwave region around ∼20 GHz and amplitude ∼0.03 V Å(-1), the translational-rotational coupling is most effective, yielding fluid velocities of magnitudes of ∼2 ms(-1) with only moderate fluid heating. In this work, we also confine water to a realistic nanochannel made of graphene giving a hydrophobic surface on one side and β-cristobalite giving a hydrophilic surface on the other, reproducing slip-and-stick velocity boundary conditions, respectively. This enables us to demonstrate that in a realistic environment, the coupling can be effectively exploited to achieve noncontact pumping of water at the nanoscale. A quantitative comparison between nonequilibrium molecular dynamics and analytical solutions of the extended Navier-Stokes equations, including an external rotating electric field has been performed, showing excellent agreement when the electric field parameters match the aforementioned small energy dissipation region.
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Affiliation(s)
- Sergio De Luca
- Department of Mathematics, Faculty of Science, Engineering and Technology, and Centre for Molecular Simulation, Swinburne University of Technology , Melbourne, Victoria 3122, Australia
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De Luca S, Todd BD, Hansen JS, Daivis PJ. Electropumping of water with rotating electric fields. J Chem Phys 2013; 138:154712. [PMID: 23614441 DOI: 10.1063/1.4801033] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Pumping of fluids confined to nanometer dimension spaces is a technically challenging yet vitally important technological application with far reaching consequences for lab-on-a-chip devices, biomimetic nanoscale reactors, nanoscale filtration devices and the like. All current pumping mechanisms require some sort of direct intrusion into the nanofluidic system, and involve mechanical or electronic components. In this paper, we present the first nonequilibrium molecular dynamics results to demonstrate that non-intrusive electropumping of liquid water on the nanoscale can be performed by subtly exploiting the coupling of spin angular momentum to linear streaming momentum. A spatially uniform rotating electric field is applied to water molecules, which couples to their permanent electric dipole moments. The resulting molecular rotational momentum is converted into linear streaming momentum of the fluid. By selectively tuning the degree of hydrophobicity of the solid walls one can generate a net unidirectional flow. Our results for the linear streaming and angular velocities of the confined water are in general agreement with the extended hydrodynamical theory for this process, though also suggest refinements to the theory are required. These numerical experiments confirm that this new concept for pumping of polar nanofluids can be employed under laboratory conditions, opening up significant new technological possibilities.
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Affiliation(s)
- Sergio De Luca
- Mathematics, Faculty of Engineering and Industrial Sciences, and Centre for Molecular Simulation, Swinburne University of Technology, Melbourne, Victoria 3122, Australia
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Hansen JS. Generalized extended Navier-Stokes theory: multiscale spin relaxation in molecular fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032101. [PMID: 24125208 DOI: 10.1103/physreve.88.032101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2013] [Indexed: 06/02/2023]
Abstract
This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia per unit mass. In the regime of large moment of inertia the fast relaxation is wave-vector independent and dominated by the coupling between spin and the fluid streaming velocity, whereas for small inertia the relaxation is slow and spin diffusion plays a significant role. The fast wave-vector-independent relaxation is also observed for highly packed systems. The transverse and longitudinal spin modes have, to a good approximation, identical relaxation, indicating that the longitudinal and transverse spin viscosities have same value. The relaxation is also shown to be isomorphic invariant. Finally, the effect of the coupling in the zero frequency and wave-vector limit is quantified by a characteristic length scale; if the system dimension is comparable to this length the coupling must be included into the fluid dynamical description. It is found that the length scale is independent of moment of inertia but dependent on the state point.
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Affiliation(s)
- J S Hansen
- DNRF Centre "Glass and Time," IMFUFA Department of Nature, Systems and Models Roskilde University, DK-4000 Denmark
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Hansen JS, Daivis PJ, Dyre JC, Todd BD, Bruus H. Generalized extended Navier-Stokes theory: correlations in molecular fluids with intrinsic angular momentum. J Chem Phys 2013; 138:034503. [PMID: 23343281 DOI: 10.1063/1.4774095] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The extended Navier-Stokes theory accounts for the coupling between the translational and rotational molecular degrees of freedom. In this paper, we generalize this theory to non-zero frequencies and wavevectors, which enables a new study of spatio-temporal correlation phenomena present in molecular fluids. To discuss these phenomena in detail, molecular dynamics simulations of molecular chlorine are performed for three different state points. In general, the theory captures the behavior for small wavevector and frequencies as expected. For example, in the hydrodynamic regime and for molecular fluids with small moment of inertia like chlorine, the theory predicts that the longitudinal and transverse intrinsic angular velocity correlation functions are almost identical, which is also seen in the molecular dynamics simulations. However, the theory fails at large wavevector and frequencies. To account for the correlations at these scales, we derive a phenomenological expression for the frequency dependent rotational viscosity and wavevector and frequency dependent longitudinal spin viscosity. From this we observe a significant coupling enhancement between the molecular angular velocity and translational velocity for large frequencies in the gas phase; this is not observed for the supercritical fluid and liquid state points.
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Affiliation(s)
- J S Hansen
- DNRF Centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark.
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11
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The Wolf method applied to the type I methane and carbon dioxide gas hydrates. J Mol Graph Model 2012; 38:455-64. [DOI: 10.1016/j.jmgm.2012.10.002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2012] [Revised: 09/29/2012] [Accepted: 10/05/2012] [Indexed: 11/23/2022]
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Hansen JS, Schrøder TB, Dyre JC. Simplistic Coulomb Forces in Molecular Dynamics: Comparing the Wolf and Shifted-Force Approximations. J Phys Chem B 2012; 116:5738-43. [DOI: 10.1021/jp300750g] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- J. S. Hansen
- DNRF Centre “Glass and Time”, IMFUFA,
Department of Science, Systems and Models, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
| | - Thomas B. Schrøder
- DNRF Centre “Glass and Time”, IMFUFA,
Department of Science, Systems and Models, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
| | - Jeppe C. Dyre
- DNRF Centre “Glass and Time”, IMFUFA,
Department of Science, Systems and Models, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
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Kumar Kannam S, Todd BD, Hansen JS, Daivis PJ. Slip length of water on graphene: Limitations of non-equilibrium molecular dynamics simulations. J Chem Phys 2012; 136:024705. [DOI: 10.1063/1.3675904] [Citation(s) in RCA: 145] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
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Felderhof BU. Steady-state hydrodynamics of a viscous incompressible fluid with spinning particles. J Chem Phys 2011; 135:234901. [PMID: 22191899 DOI: 10.1063/1.3669422] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The steady-state hydrodynamics of a viscous incompressible fluid with spinning particles is studied on the basis of extended Stokes equations. The profiles of flow velocity and spin velocity in simple flow situations may be used to determine the vortex viscosity and spin viscosity of the molecular liquid or fluid suspension. As an example, one situation studied is the flow generated by a uniform torque density in a planar layer of infinite fluid. The spinning particles drive a nearly uniform flow on either side of the layer, in opposite directions on the two sides. The Green function of the extended Stokes equations is derived. The translational and rotational friction coefficients of a sphere with no-slip boundary conditions, and the corresponding flow profiles, are calculated.
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Affiliation(s)
- B U Felderhof
- Institut für Theoretische Physik A, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany.
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Scocchi G, Sergi D, D'Angelo C, Ortona A. Wetting and contact-line effects for spherical and cylindrical droplets on graphene layers: a comparative molecular-dynamics investigation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:061602. [PMID: 22304097 DOI: 10.1103/physreve.84.061602] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2011] [Revised: 07/27/2011] [Indexed: 05/31/2023]
Abstract
In molecular dynamics (MD) simulations, interactions between water molecules and graphitic surfaces are often modeled as a simple Lennard-Jones potential between oxygen and carbon atoms. A possible method for tuning this parameter consists of simulating a water nanodroplet on a flat graphitic surface, measuring the equilibrium contact angle, extrapolating it to the limit of a macroscopic droplet, and finally matching this quantity to experimental results. Considering recent evidence demonstrating that the contact angle of water on a graphitic plane is much higher than what was previously reported, we estimate the oxygen-carbon interaction for the recent SPC/Fw water model. Results indicate a value of about 0.2 kJ/mol, much lower than previous estimations. We then perform simulations of cylindrical water filaments on graphitic surfaces, in order to compare and correlate contact angles resulting from these two different systems. Results suggest that a modified Young's equation does not describe the relation between contact angle and drop size in the case of extremely small systems and that contributions different from the one deriving from contact line tension should be taken into account.
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Affiliation(s)
- Giulio Scocchi
- University of Applied Sciences, SUPSI, iCIMSI Research Institute, Galleria 2, CH-6928 Manno, Switzerland.
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Hansen JS, Dyre JC, Daivis PJ, Todd BD, Bruus H. Nanoflow hydrodynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:036311. [PMID: 22060496 DOI: 10.1103/physreve.84.036311] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2011] [Revised: 08/04/2011] [Indexed: 05/31/2023]
Abstract
We show by nonequilibrium molecular dynamics simulations that the Navier-Stokes equation does not correctly describe water flow in a nanoscale geometry. It is argued that this failure reflects the fact that the coupling between the intrinsic rotational and translational degrees of freedom becomes important for nanoflows. The coupling is correctly accounted for by the extended Navier-Stokes equations that include the intrinsic angular momentum as an independent hydrodynamic degree of freedom.
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Affiliation(s)
- J S Hansen
- Danish National Research Foundation (DNRF) Centre Glass and Time, IMFUFA, Department of Science, Systems and Models, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark.
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Felderhof BU. Entrainment by a rotating magnetic field of a ferrofluid contained in a cylinder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:026312. [PMID: 21929095 DOI: 10.1103/physreve.84.026312] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2011] [Indexed: 05/31/2023]
Abstract
Entrainment by a rotating magnetic field of a ferrofluid contained in a cylinder is studied on the basis of spin-diffusion theory. The equations for flow velocity and spin velocity, coupled to Maxwell's equations of magnetostatics, are solved in first-harmonic approximation under the assumption that the magnetic field is small compared to the saturation magnetization. The solution leads to a coupled set of nonlinear integral equations, which can be solved numerically by iteration in a recursive scheme by use of the analytic lowest order perturbation theory solution as the initial state. At a critical applied field, the recursive scheme shows bifurcation. At sufficiently high field, the solution with the lower rate of dissipation shows flow in the direction opposite to the rotating applied field.
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Affiliation(s)
- B U Felderhof
- Institut für Theoretische Physik A, RWTH Aachen University, Templergraben 55, DE-52056 Aachen, Germany.
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Felderhof BU. Self-propulsion of a planar electric or magnetic microbot immersed in a polar viscous fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:056315. [PMID: 21728655 DOI: 10.1103/physreve.83.056315] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2011] [Indexed: 05/31/2023]
Abstract
A planar sheet immersed in an electrically polar liquid like water can propel itself by means of a plane wave charge density propagating in the sheet. The corresponding running electric wave polarizes the fluid and causes an electrical torque density to act on the fluid. The sheet is convected by the fluid motion resulting from the conversion of rotational particle motion, generated by the torque density, into translational fluid motion by the mechanism of friction and spin diffusion. Similarly, a planar sheet immersed in a magnetic ferrofluid can propel itself by means of a plane wave current density in the sheet and the torque density acting on the fluid corresponding to the running wave magnetic field and magnetization. The effect is studied on the basis of the micropolar fluid equations of motion and Maxwell's equations of electrostatics or magnetostatics, respectively. An analytic expression is derived for the velocity of the sheet by perturbation theory to second order in powers of the amplitude of the driving charge or current density. Under the assumption that the equilibrium magnetic equation of state may be used in linearized form and that higher harmonics than the first may be neglected, a set of self-consistent integral equations is derived which can be solved numerically by iteration. In typical situations the second-order perturbation theory turns out to be quite accurate.
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Affiliation(s)
- B U Felderhof
- Institut für Theoretische Physik A, RWTH Aachen University, Templergraben 55, D-52056 Aachen, Germany.
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