Dissipation of Energy in a Compressible Nematic Microvolume Under Effect of a Temperature Gradient
We have carried out a numerical study of hydrodynamic processes in the hybrid-aligned channel of a compressible liquid crystal (HACLC) under the effect of a temperature gradient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><sema...
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2025-02-01
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| author | Izabela Śliwa Pavel V. Maslennikov Alex V. Zakharov |
| author_facet | Izabela Śliwa Pavel V. Maslennikov Alex V. Zakharov |
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| description | We have carried out a numerical study of hydrodynamic processes in the hybrid-aligned channel of a compressible liquid crystal (HACLC) under the effect of 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> applied across a liquid crystal film. Calculations based on the classical Leslie–Ericksen theory showed that under the effect 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>, the HACLC sample settles down to a stationary flow regime with both horizontal <i>u</i> and vertical <i>w</i> components of velocity <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 direction and magnitude of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">v</mi></semantics></math></inline-formula> are strongly effected by the direction 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>. Calculations also showed that the relaxation of the stress tensor components <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mi>ij</mi></msub><mrow><mo>(</mo><mi>z</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mspace width="3.33333pt"></mspace><mrow><mo>(</mo><mi mathvariant="normal">i</mi><mo>,</mo><mi mathvariant="normal">j</mi><mo>=</mo><mi mathvariant="normal">x</mi><mo>,</mo><mi mathvariant="normal">z</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> in the hybrid-aligned compressible nematic microvolume is determined by the direction and magnitude of the thermomechanical force. |
| format | Article |
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| language | English |
| publishDate | 2025-02-01 |
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| spelling | doaj-art-86d93ae5675b41839e8af709c5f2edbe2025-08-20T02:11:09ZengMDPI AGCrystals2073-43522025-02-0115323510.3390/cryst15030235Dissipation of Energy in a Compressible Nematic Microvolume Under Effect of a Temperature GradientIzabela Śliwa0Pavel V. Maslennikov1Alex V. Zakharov2Department of Operations Research and Mathematical Economics, Poznan University of Economics and Business, 61-875 Poznan, PolandInstitute of Living Systems, Immanuel Kant Baltic Federal University, 236040 Kaliningrad, RussiaInstitute for Problems in Mechanical Engineering, Russian Academy of Science (IPME RAS), 199178 St. Petersburg, RussiaWe have carried out a numerical study of hydrodynamic processes in the hybrid-aligned channel of a compressible liquid crystal (HACLC) under the effect of 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> applied across a liquid crystal film. Calculations based on the classical Leslie–Ericksen theory showed that under the effect 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>, the HACLC sample settles down to a stationary flow regime with both horizontal <i>u</i> and vertical <i>w</i> components of velocity <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 direction and magnitude of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">v</mi></semantics></math></inline-formula> are strongly effected by the direction 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>. Calculations also showed that the relaxation of the stress tensor components <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mi>ij</mi></msub><mrow><mo>(</mo><mi>z</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mspace width="3.33333pt"></mspace><mrow><mo>(</mo><mi mathvariant="normal">i</mi><mo>,</mo><mi mathvariant="normal">j</mi><mo>=</mo><mi mathvariant="normal">x</mi><mo>,</mo><mi mathvariant="normal">z</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> in the hybrid-aligned compressible nematic microvolume is determined by the direction and magnitude of the thermomechanical force.https://www.mdpi.com/2073-4352/15/3/235liquid crystalsmicrofluidicshydrodynamics of anisotropic systemsthermomechanical effect |
| spellingShingle | Izabela Śliwa Pavel V. Maslennikov Alex V. Zakharov Dissipation of Energy in a Compressible Nematic Microvolume Under Effect of a Temperature Gradient Crystals liquid crystals microfluidics hydrodynamics of anisotropic systems thermomechanical effect |
| title | Dissipation of Energy in a Compressible Nematic Microvolume Under Effect of a Temperature Gradient |
| title_full | Dissipation of Energy in a Compressible Nematic Microvolume Under Effect of a Temperature Gradient |
| title_fullStr | Dissipation of Energy in a Compressible Nematic Microvolume Under Effect of a Temperature Gradient |
| title_full_unstemmed | Dissipation of Energy in a Compressible Nematic Microvolume Under Effect of a Temperature Gradient |
| title_short | Dissipation of Energy in a Compressible Nematic Microvolume Under Effect of a Temperature Gradient |
| title_sort | dissipation of energy in a compressible nematic microvolume under effect of a temperature gradient |
| topic | liquid crystals microfluidics hydrodynamics of anisotropic systems thermomechanical effect |
| url | https://www.mdpi.com/2073-4352/15/3/235 |
| work_keys_str_mv | AT izabelasliwa dissipationofenergyinacompressiblenematicmicrovolumeundereffectofatemperaturegradient AT pavelvmaslennikov dissipationofenergyinacompressiblenematicmicrovolumeundereffectofatemperaturegradient AT alexvzakharov dissipationofenergyinacompressiblenematicmicrovolumeundereffectofatemperaturegradient |