{"title":"利用弹性湍流在粘弹性流体中进行混合","authors":"Reinier van Buel, Holger Stark","doi":"arxiv-2409.06391","DOIUrl":null,"url":null,"abstract":"We investigate the influence of elastic turbulence on mixing {of a scalar\nconcentration field} within a viscoelastic fluid in a two-dimensional\nTaylor-Couette geometry using numerical solutions of the Oldroyd-B model. The\nflow state is determined through the secondary-flow order parameter indicating\nthat the transition at the critical Weissenberg number $\\text{Wi}_c$ is\nsubcritical. When {starting in the turbulent state and subsequently} lowering\nthe Weissenberg number, a weakly-chaotic flow occurs below $\\text{Wi}_c$.\nAdvection in both {the turbulent and weakly-chaotic} flow states induces\nmixing, which we illustrate by the time evolution of the standard deviation of\nthe solute concentration from the uniform distribution. In particular, in the\nelastic turbulent state mixing is strong and we quantify it by the mixing rate,\nthe mixing time, and the mixing efficiency. All three quantities follow scaling\nlaws. Importantly, we show that the order parameter is strongly correlated to\nthe mixing rate and hence is also a good indication of mixing within the fluid.","PeriodicalId":501125,"journal":{"name":"arXiv - PHYS - Fluid Dynamics","volume":"8 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mixing in viscoelastic fluids using elastic turbulence\",\"authors\":\"Reinier van Buel, Holger Stark\",\"doi\":\"arxiv-2409.06391\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the influence of elastic turbulence on mixing {of a scalar\\nconcentration field} within a viscoelastic fluid in a two-dimensional\\nTaylor-Couette geometry using numerical solutions of the Oldroyd-B model. The\\nflow state is determined through the secondary-flow order parameter indicating\\nthat the transition at the critical Weissenberg number $\\\\text{Wi}_c$ is\\nsubcritical. When {starting in the turbulent state and subsequently} lowering\\nthe Weissenberg number, a weakly-chaotic flow occurs below $\\\\text{Wi}_c$.\\nAdvection in both {the turbulent and weakly-chaotic} flow states induces\\nmixing, which we illustrate by the time evolution of the standard deviation of\\nthe solute concentration from the uniform distribution. In particular, in the\\nelastic turbulent state mixing is strong and we quantify it by the mixing rate,\\nthe mixing time, and the mixing efficiency. All three quantities follow scaling\\nlaws. Importantly, we show that the order parameter is strongly correlated to\\nthe mixing rate and hence is also a good indication of mixing within the fluid.\",\"PeriodicalId\":501125,\"journal\":{\"name\":\"arXiv - PHYS - Fluid Dynamics\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Fluid Dynamics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06391\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Fluid Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06391","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Mixing in viscoelastic fluids using elastic turbulence
We investigate the influence of elastic turbulence on mixing {of a scalar
concentration field} within a viscoelastic fluid in a two-dimensional
Taylor-Couette geometry using numerical solutions of the Oldroyd-B model. The
flow state is determined through the secondary-flow order parameter indicating
that the transition at the critical Weissenberg number $\text{Wi}_c$ is
subcritical. When {starting in the turbulent state and subsequently} lowering
the Weissenberg number, a weakly-chaotic flow occurs below $\text{Wi}_c$.
Advection in both {the turbulent and weakly-chaotic} flow states induces
mixing, which we illustrate by the time evolution of the standard deviation of
the solute concentration from the uniform distribution. In particular, in the
elastic turbulent state mixing is strong and we quantify it by the mixing rate,
the mixing time, and the mixing efficiency. All three quantities follow scaling
laws. Importantly, we show that the order parameter is strongly correlated to
the mixing rate and hence is also a good indication of mixing within the fluid.