Vortex Dynamics in a Hybrid Aligned Nematic Microvolume with an Orientational Defect
The aim of this theoretical paper is to investigate the physical mechanism responsible for the appearance of vortex flow in a hybrid aligned nematic (HAN) microvolume with an orientational defect, excited by a temperature gradient <inline-formula><math xmlns="http://www.w3.org/1998/Mat...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/2/324 |
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| author | Izabela Śliwa Pavel V. Maslennikov Alex V. Zakharov |
| author_facet | Izabela Śliwa Pavel V. Maslennikov Alex V. Zakharov |
| author_sort | Izabela Śliwa |
| collection | DOAJ |
| description | The aim of this theoretical paper is to investigate the physical mechanism responsible for the appearance of vortex flow in a hybrid aligned nematic (HAN) microvolume with an orientational defect, excited by a temperature gradient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∇</mo><mi>T</mi></mrow></semantics></math></inline-formula>. This was done in the framework of the classical Ericksen-Leslie theory, supplemented by thermomechanical correction of the shear stress and Rayleigh dissipation function, as well as taking into account the entropy balance equation. We have carried out a numerical study of the system of hydrodynamic equations including director reorientation, fluid flow <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">v</mi></semantics></math></inline-formula>, and the temperature redistribution across the HAN microvolume under the influence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∇</mo><mi>T</mi></mrow></semantics></math></inline-formula>, when the HAN microvolume is heated from above. Calculations show that, due to the interaction between the gradient of the director field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∇</mo><mover accent="true"><mi mathvariant="bold">n</mi><mo>^</mo></mover></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∇</mo><mi>T</mi></mrow></semantics></math></inline-formula>, the HAN microvolume settles down to a stationary complex vortex flow regime. |
| first_indexed | 2024-03-11T08:04:46Z |
| format | Article |
| id | doaj.art-49d28baac99647b6bbf24773dc482872 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T08:04:46Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-49d28baac99647b6bbf24773dc4828722023-11-16T23:31:48ZengMDPI AGSymmetry2073-89942023-01-0115232410.3390/sym15020324Vortex Dynamics in a Hybrid Aligned Nematic Microvolume with an Orientational DefectIzabela Śliwa0Pavel V. Maslennikov1Alex V. Zakharov2Department of Operations Research and Mathematical Economics, Poznan University of Economics and Business, Al. Niepodleglosci 10, 61-875 Poznan, PolandInstitute of Living Systems, Immanuel Kant Baltic Federal University, Str. Universitetskaya 2, 236040 Kaliningrad, RussiaSaint Petersburg Institute for Machine Sciences, The Russian Academy of Sciences, 199178 Saint Petersburg, RussiaThe aim of this theoretical paper is to investigate the physical mechanism responsible for the appearance of vortex flow in a hybrid aligned nematic (HAN) microvolume with an orientational defect, excited by a temperature gradient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∇</mo><mi>T</mi></mrow></semantics></math></inline-formula>. This was done in the framework of the classical Ericksen-Leslie theory, supplemented by thermomechanical correction of the shear stress and Rayleigh dissipation function, as well as taking into account the entropy balance equation. We have carried out a numerical study of the system of hydrodynamic equations including director reorientation, fluid flow <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">v</mi></semantics></math></inline-formula>, and the temperature redistribution across the HAN microvolume under the influence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∇</mo><mi>T</mi></mrow></semantics></math></inline-formula>, when the HAN microvolume is heated from above. Calculations show that, due to the interaction between the gradient of the director field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∇</mo><mover accent="true"><mi mathvariant="bold">n</mi><mo>^</mo></mover></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∇</mo><mi>T</mi></mrow></semantics></math></inline-formula>, the HAN microvolume settles down to a stationary complex vortex flow regime.https://www.mdpi.com/2073-8994/15/2/324liquid crystalshydrodynamics of anisotropic systemthermomechanical effect |
| spellingShingle | Izabela Śliwa Pavel V. Maslennikov Alex V. Zakharov Vortex Dynamics in a Hybrid Aligned Nematic Microvolume with an Orientational Defect Symmetry liquid crystals hydrodynamics of anisotropic system thermomechanical effect |
| title | Vortex Dynamics in a Hybrid Aligned Nematic Microvolume with an Orientational Defect |
| title_full | Vortex Dynamics in a Hybrid Aligned Nematic Microvolume with an Orientational Defect |
| title_fullStr | Vortex Dynamics in a Hybrid Aligned Nematic Microvolume with an Orientational Defect |
| title_full_unstemmed | Vortex Dynamics in a Hybrid Aligned Nematic Microvolume with an Orientational Defect |
| title_short | Vortex Dynamics in a Hybrid Aligned Nematic Microvolume with an Orientational Defect |
| title_sort | vortex dynamics in a hybrid aligned nematic microvolume with an orientational defect |
| topic | liquid crystals hydrodynamics of anisotropic system thermomechanical effect |
| url | https://www.mdpi.com/2073-8994/15/2/324 |
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