{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T18:47:35Z","timestamp":1769021255359,"version":"3.49.0"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,2]],"date-time":"2023-02-02T00:00:00Z","timestamp":1675296000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of the Russian Federation"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The stability problem solution of the manufacturing (drawing) of the quartz capillaries (pipes) for microstructured optical fibers (hole-assisted fiber) is important for determining the effective technological production modes. This importance is also caused by the high cost of fiber production and strict requirements for the accuracy of the fiber\u2019s geometric characteristics. Therefore, a theoretical approach to this problem is relevant and necessary. A modified capillary drawing model that takes into account inertial, viscous, and surface tension forces, as well as all types of heat transfer is proposed in the research. Within the framework of the linear theory of stability, a mathematical model of isothermal and nonisothermal capillary drawing has been developed. The stability of the process is studied depending on the drawing ratio and the Reynolds number. The analysis of the sensitivity of the process to perturbations in the boundary conditions is carried out. The secondary flow that occurs upon transition to the region of instability is also studied. It has been found that at draw ratios above critical values (instability region), undamped oscillations arise. The existence of optimal parameters of the heating element is shown: temperature distribution over the furnace surface and furnace radius, at which the stability of the process of drawing quartz tubes increases significantly (several times).<\/jats:p>","DOI":"10.3390\/a16020083","type":"journal-article","created":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T03:36:57Z","timestamp":1675395417000},"page":"83","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Mathematical Modeling of Capillary Drawing Stability for Hollow Optical Fibers"],"prefix":"10.3390","volume":"16","author":[{"given":"Vladimir","family":"Pervadchuk","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Perm National Research Polytechnic University, 614990 Perm, Russia"}]},{"given":"Daria","family":"Vladimirova","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Perm National Research Polytechnic University, 614990 Perm, Russia"}]},{"given":"Anna","family":"Derevyankina","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Perm National Research Polytechnic University, 614990 Perm, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"063002","DOI":"10.1088\/2040-8978\/18\/6\/063002","article-title":"Roadmap of optical communications","volume":"18","author":"Agrell","year":"2016","journal-title":"J. Opt."},{"key":"ref_2","unstructured":"Ferreira, M.F.S. (2017). Optical Fibers: Technology, Communications and Recent Advances, Nova Science Publishers."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Xie, W.G., Zhang, Y.N., Wang, P.Z., and Wang, J.Z. (2018). Optical Fiber Sensors Based on Fiber Ring Laser Demodulation Technology. Sensors, 18.","DOI":"10.3390\/s18020505"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sayed, A.E., Pilz, S., Najafi, H., Alexander, D.T.L., Hochstrasser, M., and Romano, V. (2018). Fabrication and Characteristics of Yb-Doped Silica Fibers Produced by the Sol-Gel Based Granulated Silica Method. Fibers, 6.","DOI":"10.3390\/fib6040082"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Mat Sharif, K.A., Omar, N.Y.M., Zulkifli, M.I., Muhamad Yassin, S.Z., and Abdul-Rashid, H.A. (2020). Fabrication of Alumina-Doped Optical Fiber Preforms by an MCVD-Metal Chelate Doping Method. Appl. Sci., 10.","DOI":"10.20944\/preprints202008.0666.v1"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Liu, Z., Zhang, Z.F., Tam, H.Y., and Tao, X. (2019). Multifunctional Smart Optical Fibers: Materials, Fabrication, and Sensing. Appl. Photonics, 6.","DOI":"10.3390\/photonics6020048"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Yu, Y., Lian, Y., Hu, Q., Xie, L., Ding, J., Wang, Y., and Lu, Z. (2022). Design of PCF Supporting 86 OAM Modes with High Mode Quality and Low Nonlinear Coefficient. Photonics, 9.","DOI":"10.3390\/photonics9040266"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7566","DOI":"10.3390\/ma7117566","article-title":"Microfluidic Flows and Heat Transfer and Their Influence on Optical Modes in Microstructure Fibers","volume":"7","author":"Davies","year":"2014","journal-title":"Materials"},{"key":"ref_9","first-page":"251","article-title":"Photonic Crystal Fibers for Sensing Applications","volume":"9","author":"Riyadh","year":"2018","journal-title":"J. Biosens. Bioelectron."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Pervadchuk, V., Vladimirova, D., Gordeeva, I., Kuchumov Alex, G., and Dektyarev, D. (2021). Fabrication of Silica Optical Fibers: Optimal Control Problem Solution. Fibers, 9.","DOI":"10.3390\/fib9120077"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/S1631-0705(03)00004-5","article-title":"Holey optical fibres: Fundamental properties and device applications","volume":"4","author":"Monro","year":"2003","journal-title":"Comptes Rendus Phys."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Maidi, A.M., Yakasai, I., Abas, P.E., Nauman, M.M., Apong, R.A., Kaijage, S., and Begum, F. (2021). Design and Simulation of Photonic Crystal Fiber for Liquid Sensing. Photonics, 8.","DOI":"10.3390\/photonics8010016"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"9014","DOI":"10.1364\/OPEX.13.009014","article-title":"Fabrication of selective injection microstructured optical fibers with a conventional fusion splicer","volume":"13","author":"Xiao","year":"2005","journal-title":"Opt. Express"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1109\/JLT.2005.862427","article-title":"Role of Material Properties and Drawing Conditions in the Fabrication of Microstructured Optical Fibers","volume":"24","author":"Xue","year":"2006","journal-title":"J. Light. Technol."},{"key":"ref_15","unstructured":"Yang, J. (2008). Numerical Modeling of Hollow Optical Fiber Drawing Process. [Ph.D Thesis, Mechanical and Aerospace Engineering, University of New Jersey]."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1016\/S0301-9322(97)00016-5","article-title":"Draw resonance of optical microcapillaries in non-isothermal drawing","volume":"23","author":"Gospodinov","year":"1997","journal-title":"Int. J. Multiph. Flow"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1454","DOI":"10.1063\/1.868260","article-title":"Stability loss and sensitivity in hollow fiber drawing","volume":"6","author":"Yarin","year":"1994","journal-title":"Phys. Fluids"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2245","DOI":"10.1109\/JLT.2005.850055","article-title":"Fabrication of microstructured optical fibers\u2014Part I: Problem formulation and numerical modeling of transient draw process","volume":"23","author":"Xue","year":"2005","journal-title":"J. Lightw. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2255","DOI":"10.1109\/JLT.2005.850058","article-title":"Fabrication of microstructured optical fibers\u2014Part II: Numerical modeling of steady-state draw process","volume":"23","author":"Xue","year":"2005","journal-title":"J. Lightw. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1023\/A:1020328606157","article-title":"The mathematical modelling of capillary drawing for holey fibre manufacture","volume":"43","author":"Fitt","year":"2002","journal-title":"J. Eng. Math."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1007\/BF00870743","article-title":"Nonstationary processes in optical fiber formation. 1. Stability of the drawing process","volume":"55","author":"Naumchik","year":"1988","journal-title":"J. Eng. Phys."},{"key":"ref_22","unstructured":"Lienard, I.V., and John, H. (2017). A Heat Transfer Textbook, Phlogiston Press."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1924","DOI":"10.1109\/50.971686","article-title":"Modeling the fabrication of hollow fibers: Capillary drawing","volume":"19","author":"Fitt","year":"2001","journal-title":"J. Light. Technol."},{"key":"ref_24","unstructured":"Drazin, P.G., and Reid, W.H. (2010). Hydrodynamic Stability, Cambridge University Press."},{"key":"ref_25","first-page":"67","article-title":"Linearization and Stability Analysis of Nonlinear Problems","volume":"16","author":"Morgan","year":"2015","journal-title":"Rose-Hulman Undergrad. Math. J."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Rodr\u00edguez, R.S., Avalos, G.G., Gallegos, N.B., Ayala-jaimes, G., and Garcia, A.P. (2021). Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization. Symmetry, 13.","DOI":"10.3390\/sym13050854"},{"key":"ref_27","unstructured":"Jung, H.W., and Hyun, J.C. (2006). Instabilities in extensional deformation polymer processing. Rheol. Rev., 131\u2013164."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"113905","DOI":"10.1103\/PhysRevFluids.2.113905","article-title":"Combined influence of inertia, gravity and surface tension on the linear stability of Newtonian fiber spinning","volume":"2","author":"Bechert","year":"2017","journal-title":"Phys. Rev. Fluids"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1017\/S0956792599004118","article-title":"Draw resonance in isothermal fibre spinning of Newtonian and power-law fluids","volume":"11","year":"2000","journal-title":"Eur. J. Appl. Math."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1002\/zamm.200410225","article-title":"numerical study on the suppression of draw resonance by inertia","volume":"86","author":"Hagen","year":"2006","journal-title":"ZAMM\u00b7Z. Angew. Math. Mech."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/2\/83\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:22:23Z","timestamp":1760120543000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/2\/83"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,2]]},"references-count":30,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["a16020083"],"URL":"https:\/\/doi.org\/10.3390\/a16020083","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,2]]}}}