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Fei C, Dunkel J. Fly embryo nuclei riding on two-fluid flow. Proc Natl Acad Sci U S A 2023; 120:e2317219120. [PMID: 37939065 PMCID: PMC10665796 DOI: 10.1073/pnas.2317219120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2023] Open
Affiliation(s)
- Chenyi Fei
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA02139
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2
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Brand HR, Pleiner H. A two-fluid model for the macroscopic behavior of polar nematic fluids and gels in a nonchiral or a chiral solvent. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:17. [PMID: 35218411 PMCID: PMC8882122 DOI: 10.1140/epje/s10189-022-00172-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Accepted: 02/14/2022] [Indexed: 06/14/2023]
Abstract
We present the macroscopic dynamics of polar nematic liquid crystals in a two-fluid context. We investigate the case of a nonchiral as well as of a chiral solvent. In addition, we analyze how the incorporation of a strain field for polar nematic gels and elastomers in a solvent modifies the macroscopic dynamics. It turns out that the relative velocity between the polar subsystem and the solvent gives rise to a number of cross-coupling terms, reversible as well as irreversible, unknown from the other two-fluid systems considered so far. Possible experiments to study those novel dynamic cross-coupling terms are suggested. As examples we just mention that gradients of the relative velocity lead, in polar nematics to heat currents and in polar cholesterics to temporal changes of the polarization. In polar cholesterics, shear flows give rise to a temporal variation in the velocity difference perpendicular to the shear plane, and in polar nematic gels uniaxial stresses or strains generate temporal variations of the velocity difference.
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Affiliation(s)
- Helmut R. Brand
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
| | - Harald Pleiner
- Max Planck Institute for Polymer Research, 55021 Mainz, Germany
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Adar RM, Joanny JF. Permeation Instabilities in Active Polar Gels. PHYSICAL REVIEW LETTERS 2021; 127:188001. [PMID: 34767387 DOI: 10.1103/physrevlett.127.188001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2021] [Accepted: 09/28/2021] [Indexed: 06/13/2023]
Abstract
We present a theory of active, permeating, polar gels, based on a two-fluid model. An active relative force between the gel components creates a steady-state current. We analyze its stability, while considering two polar coupling terms to the relative current: a permeation-deformation term, which describes network deformation by the solvent flow, and a permeation-alignment term, which describes the alignment of the polarization field by the network deformation and flow. Novel instability mechanisms emerge at finite wave vectors, suggesting the formation of periodic domains and mesophases. Our results can be used to determine the physical conditions required for various types of multicellular migration across tissues.
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Affiliation(s)
- Ram M Adar
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
- Laboratoire Physico-Chimie Curie, Institut Curie, Centre de Recherche, Paris Sciences et Lettres Research University, Centre National de la Recherche Scientifique, 75005 Paris, France
- Université Pierre et Marie Curie, Sorbonne Universités, 75248 Paris, France
| | - Jean-François Joanny
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
- Laboratoire Physico-Chimie Curie, Institut Curie, Centre de Recherche, Paris Sciences et Lettres Research University, Centre National de la Recherche Scientifique, 75005 Paris, France
- Université Pierre et Marie Curie, Sorbonne Universités, 75248 Paris, France
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4
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Brand HR, Pleiner H. Two-fluid model for the breakdown of flow alignment in nematic liquid crystals. Phys Rev E 2021; 103:012705. [PMID: 33601508 DOI: 10.1103/physreve.103.012705] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Accepted: 01/05/2021] [Indexed: 06/12/2023]
Abstract
We present a macroscopic two-fluid model to explain the breakdown of flow alignment in nematic liquid crystals under shear flow due to smectic clusters. We find that the velocity difference of the two fluids plays a key role to mediate the time-dependent behavior as soon as a large enough amount of smectic order is induced by flow. For the minimal model it is sufficient to keep the nematic degrees of freedom, the mass density of the smectic clusters and the degree of smectic order, the density, and two velocities as macroscopic variables. While frequently a smectic A or C phase arises at lower temperatures, this is not required for the applicability of the present model. Indeed, as pointed out before by Gähwiller, there are compounds showing a breakdown of flow alignment over a large temperature range and no smectic phase, but a solid phase at lower temperatures. We also demonstrate that, using a one velocity model, there is no coupling under shear flow between induced smectic order and the director orientation in stationary situations thus rendering such a model to be unsuitable to describe the breakdown of flow alignment. In a two-fluid description, flow alignment breaks down and becomes unstable with regard to a space- and time-dependent state due to an induced finite velocity difference. In an Appendix we outline a mesoscopic model to account for the sign change in the anisotropy of the electric conductivity observed in nematics with smectic clusters.
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Affiliation(s)
- Helmut R Brand
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
- Max Planck Institute for Polymer Research, 55021 Mainz, Germany
| | - Harald Pleiner
- Max Planck Institute for Polymer Research, 55021 Mainz, Germany
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Pleiner H, Brand HR. Symmetry aspects in the macroscopic dynamics of magnetorheological gels and general liquid crystalline magnetic elastomers. PHYSICAL SCIENCES REVIEWS 2020. [DOI: 10.1515/psr-2019-0109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Abstract
We investigate theoretically the macroscopic dynamics of various types of ordered magnetic fluid, gel, and elastomeric phases. We take a symmetry point of view and emphasize its importance for a macroscopic description. The interactions and couplings among the relevant variables are based on their individual symmetry behavior, irrespective of the detailed nature of the microscopic interactions involved. Concerning the variables we discriminate between conserved variables related to a local conservation law, symmetry variables describing a (spontaneously) broken continuous symmetry (e.g., due to a preferred direction) and slowly relaxing ones that arise from special conditions of the system are considered. Among the relevant symmetries, we consider the behavior under spatial rotations (e.g., discriminating scalars, vectors or tensors), under spatial inversion (discriminating e.g., polar and axial vectors), and under time reversal symmetry (discriminating e.g., velocities from polarizations, or electric fields from magnetic ones). Those symmetries are crucial not only to find the possible cross-couplings correctly but also to get a description of the macroscopic dynamics that is compatible with thermodynamics. In particular, time reversal symmetry is decisive to get the second law of thermodynamics right. We discuss (conventional quadrupolar) nematic order, polar order, active polar order, as well as ferromagnetic order and tetrahedral (octupolar) order. In a second step, we show some of the consequences of the symmetry properties for the various systems that we have worked on within the SPP1681, including magnetic nematic (and cholesteric) elastomers, ferromagnetic nematics (also with tetrahedral order), ferromagnetic elastomers with tetrahedral order, gels and elastomers with polar or active polar order, and finally magnetorheological fluids and gels in a one- and two-fluid description.
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Affiliation(s)
- Harald Pleiner
- Max Planck Institute for Polymer Research , Mainz , Germany
| | - Helmut R. Brand
- Department of Physics , University of Bayreuth , Bayreuth , Germany
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6
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Pleiner H, Svenšek D, Potisk T, Brand HR. Macroscopic two-fluid effects in magnetorheological fluids. Phys Rev E 2020; 101:032601. [PMID: 32289924 DOI: 10.1103/physreve.101.032601] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2019] [Accepted: 02/11/2020] [Indexed: 11/07/2022]
Abstract
We investigate macroscopic two-fluid effects in magnetorheological fluids generalizing a one-fluid model studied before. In the bulk of the paper we use a model in which the carrier fluid, with density ρ_{1}, moves with velocity v_{1}, while the magnetic component (density ρ_{2}) and, therefore, the magnetization and the magnetic-field-induced relaxing strain field move with velocity v_{2}. In the framework of macroscopic dynamics we find, in particular, reversible dynamic and dissipative cross-coupling terms between the magnetization and the velocity difference. Experiments to detect some of these cross-coupling terms are suggested. We also compare the results of the two-fluid model presented here with two-fluid models available for electrorheological fluids. In two appendices we discuss the simplifying assumptions made to arrive at the model used in this paper and we also outline how to detect potential deviations from this model.
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Affiliation(s)
- Harald Pleiner
- Max Planck Institute for Polymer Research, 55021 Mainz, Germany
| | - Daniel Svenšek
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Tilen Potisk
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
| | - Helmut R Brand
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
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Svenšek D, Pleiner H, Brand HR. A dynamic preferred direction model for the self-organization dynamics of bacterial microfluidic pumping. SOFT MATTER 2019; 15:2032-2042. [PMID: 30724307 DOI: 10.1039/c9sm00023b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
It is known that some flagellated bacteria like Serratia marcescens, when deposited and affixed onto a surface to form a "bacterial carpet", self-organize in a collective motion of the flagella that is capable of pumping fluid through microfluidic channels. We set up a continuum model comprising two macroscopic variables that is capable of describing this self-organization mechanism as well as quantifying it to the extent that an agreement with the experimentally observed channel width dependence of the pumping is reached. The activity is introduced through a collective angular velocity of the helical flagella rotation, which is an example of a dynamic macroscopic preferred direction. Our model supports and quantifies the view that the self-coordination is due to a positive feedback loop between the bacterial flagella and the local flow generated by their rotation. Moreover, our results indicate that this biological active system is operating close to the self-organization threshold.
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Affiliation(s)
- Daniel Svenšek
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia.
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Puljiz M, Orlishausen M, Köhler W, Menzel AM. Thermophoretically induced large-scale deformations around microscopic heat centers. J Chem Phys 2017; 144:184903. [PMID: 27179505 DOI: 10.1063/1.4948729] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Selectively heating a microscopic colloidal particle embedded in a soft elastic matrix is a situation of high practical relevance. For instance, during hyperthermic cancer treatment, cell tissue surrounding heated magnetic colloidal particles is destroyed. Experiments on soft elastic polymeric matrices suggest a very long-ranged, non-decaying radial component of the thermophoretically induced displacement fields around the microscopic heat centers. We theoretically confirm this conjecture using a macroscopic hydrodynamic two-fluid description. Both thermophoretic and elastic effects are included in this theory. Indeed, we find that the elasticity of the environment can cause the experimentally observed large-scale radial displacements in the embedding matrix. Additional experiments confirm the central role of elasticity. Finally, a linearly decaying radial component of the displacement field in the experiments is attributed to the finite size of the experimental sample. Similar results are obtained from our theoretical analysis under modified boundary conditions.
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Affiliation(s)
- Mate Puljiz
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | | | - Werner Köhler
- Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Andreas M Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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Menzel AM. Hydrodynamic description of elastic or viscoelastic composite materials: Relative strains as macroscopic variables. Phys Rev E 2016; 94:023003. [PMID: 27627384 DOI: 10.1103/physreve.94.023003] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2016] [Indexed: 06/06/2023]
Abstract
One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)elastic substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we present a hydrodynamic description of (visco)elastic composite materials. For this purpose, additional strain variables reflect the state of the inclusions and their immediate environment. These additional strain variables in general are not set by a coarse-grained macroscopic displacement field. Apart from that, during our derivation, we also include the macroscopic variables of relative translations and relative rotations that were previously introduced in different contexts. As a central point, our approach reveals and classifies the importance of a macroscopic variable termed relative strains. We analyze two simplified minimal example geometries as an illustration.
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Affiliation(s)
- Andreas M Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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Menzel AM, Saha A, Hoell C, Löwen H. Dynamical density functional theory for microswimmers. J Chem Phys 2016; 144:024115. [DOI: 10.1063/1.4939630] [Citation(s) in RCA: 66] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andreas M. Menzel
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Arnab Saha
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Christian Hoell
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
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Brand HR, Pleiner H, Svenšek D. Reversible and dissipative macroscopic contributions to the stress tensor: active or passive? THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:40. [PMID: 25260325 DOI: 10.1140/epje/i2014-14083-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2014] [Accepted: 08/29/2014] [Indexed: 06/03/2023]
Abstract
The issue of dynamic contributions to the macroscopic stress tensor has been of high interest in the field of bio-inspired active systems over the last few years. Of particular interest is a direct coupling ("active term") of the stress tensor with the order parameter, the latter describing orientational order induced by active processes. Here we analyze more generally possible reversible and irreversible dynamic contributions to the stress tensor for various passive and active macroscopic systems. This includes systems with tetrahedral/octupolar order, polar and non-polar (chiral) nematic and smectic liquid crystals, as well as active fluids with a dynamic preferred (polar or non-polar) direction. We show that it cannot a priori be seen, neither from the symmetry properties of the macroscopic variables involved, nor from the structure of the cross-coupling contributions to the stress tensor, whether the system studied is active or passive. Rather, that depends on whether the variables that give rise to those cross-couplings in the stress tensor are driven or not. We demonstrate that several simplified descriptions of active systems in the literature that neglect the necessary counter term to the active term violate linear irreversible thermodynamics and lead to an unphysical contribution to the entropy production.
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Affiliation(s)
- H R Brand
- Theoretische Physik III, Universität Bayreuth, 95440, Bayreuth, Germany,
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