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M\u00f8ller, P., Fall, A., & Bonn, D. (2009). Origin of apparent viscosity in yield stress fluids below yielding EPL (Europhysics Letters), 87 (3) DOI: 10.1209\/0295-5075\/87\/38004[2] Barnes, H., & Walters, K. (1985). The yield stress myth? Rheologica Acta, 24 (4), 323-326 DOI: 10.1007\/BF01333960[3] Barnes, H. (1999). The yield stress\u2014a review\u2026","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":3934,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/3934","url_meta":{"origin":825,"position":1},"title":"\u80fd\u63cf\u8ff0\u5ef6\u8fdf\u5c48\u670d\u7684\u89e6\u53d8\u6027\u6a21\u578b","author":"Andrew","date":"2011\u5e749\u670820\u65e5","format":false,"excerpt":"\u6211\u7684\u6bd5\u4e1a\u8bba\u6587\u6253\u7b97\u6709\u4e00\u8282\u662f\u4f7f\u7528\u4e00\u4e2a\u89e6\u53d8\u6027\u6d41\u53d8\u5b66\u6a21\u578b\u6765\u7406\u89e3\u6211\u7684\u5b9e\u9a8c\u7ed3\u679c\uff08\u8c08\u4e0d\u4e0a\u62df\u5408\uff09\u3002\u7531\u4e8e\u5728\u8fd9\u65b9\u9762\u6211\u662f\u83dc\u9e1f\uff0c\u6240\u4ee5\u6709\u4e9b\u5931\u8d25\u4e0d\u77e5\u9053\u662f\u6a21\u578b\u7684\u95ee\u9898\u8fd8\u662f\u6211\u6570\u5b66\u5dee\u63a8\u4e0d\u51fa\u6765\u7684\u95ee\u9898\u3002\u5176\u4e2d\u4e00\u4e2a\u5c31\u662f\u5c48\u670d\u95ee\u9898\u3002Glassy polymers\u548ccolloidal gels\u4f53\u7cfb\u90fd\u6709\u5ef6\u8fdf\u5c48\u670d\uff08delayed yielding\uff09\u7684\u73b0\u8c61\u3002\u5728\u505a\u8815\u53d8\u5b9e\u9a8c\u65f6\uff0c\u5728\u4e2d\u7b49\u5927\u5c0f\u7684\u5e94\u529b\u03c3\u4e0b\uff0c\u6837\u54c1\u4e0d\u662f\u4e0d\u5c48\u670d\uff0c\u4f46\u53c8\u4e0d\u9a6c\u4e0a\u53d1\u751f\u5c48\u670d\uff0c\u800c\u662f\u6709\u4e00\u6bb5\u5ef6\u8fdf\u65f6\u95f4td\u3002td\u8ddf\u65bd\u52a0\u5e94\u529b\u03c3\u7684\u5927\u5c0f\u6709\u5173\uff0c\u03c3\u8db3\u591f\u5927\u7684\u8bdd\uff0c\u5c31\u770b\u4e0d\u5230\u5ef6\u8fdf\uff0ctd = 0\uff1b\u03c3\u8db3\u591f\u5c0f\u7684\u8bdd\uff0ctd\u8d8b\u4e8e\u65e0\u7a77\uff0c\u5e38\u89c4\u4e0a\u8bb2\u6cd5\u5c31\u662f\u8bf4\u65bd\u52a0\u5e94\u529b\u5c0f\u4e8e\u6837\u54c1\u7684\u5c48\u670d\u5e94\u529b\u03c3 < \u03c3y\u3002\u6240\u4ee5\uff0c\u5982\u679c\u8003\u8651\u5ef6\u8fdf\u5c48\u670d\u73b0\u8c61\u7684\u8bdd\uff0c\u6837\u54c1\u5176\u5b9e\u4e0d\u5b58\u5728\u4e00\u4e2a\u7279\u5b9a\u7684\u5c48\u670d\u5e94\u529b\u03c3y\u4f5c\u4e3a\u5c48\u670d\u524d\u540e\u7684\u754c\u7ebf\uff1b\u770b\u4e0d\u5230\u5c48\u670d\u6709\u53ef\u80fd\u53ea\u662f\u89c2\u5bdf\u65f6\u95f4\u4e0d\u591f\u957f\uff0c\u4f46\u4e0d\u4ee3\u8868\u6837\u54c1\u5185\u90e8\u6ca1\u6709\u4e8b\u60c5\u5728\u53d1\u751f\u3002\u8fd9\u5c31\u9ebb\u70e6\u5927\u4e86\u3002\u4e8e\u662f\u8fd9\u6bb5\u65f6\u95f4\u91cc\u5230\u5e95\u53d1\u751f\u4e86\u4ec0\u4e48\u4e8b\uff0c\u9700\u8981\u7ed9\u4e2a\u89e3\u91ca\u3002\u89e6\u53d8\u6027\u6d41\u53d8\u5b66\u6a21\u578b\u6709\u51e0\u5927\u7c7b\uff0c\u5177\u4f53\u53ef\u4ee5\u770b\u5173\u4e8ethixotropy\u7684review\u3002\u6211\u91c7\u7528\u7684\u5e94\u8be5\u662f\u6bd4\u8f83\u7b80\u5355\u7684\u90a3\u4e00\u7c7b\uff0c\u53ebstructural kinetic modal\u3002\u5c31\u662f\u628a\u89e6\u53d8\u6027\u6d41\u4f53\u770b\u6210\u4e00\u4e2a\u542b\u6709\u7ed3\u6784\u53c2\u6570\u03bb\u7684\u5e73\u8861\u6001\u6a21\u578b\uff0c\u800c\u7ed3\u6784\u53c2\u6570\u8ddf\u65f6\u95f4\u548c\u526a\u5207\u573a\u6709\u5173\uff0c\u5b58\u5728\u5efa\u7acb\u548c\u7834\u574f\u4e4b\u95f4\u7684\u7ade\u4e89\u3002\u6709\u4e00\u5927\u90e8\u5206\u8fd9\u7c7b\u6a21\u578b\u5bf9\u8fd9\u4e2a\u7ed3\u6784\u53c2\u6570\u7684\u5904\u7406\u662f\u4eff\u6548\u7ade\u4e89\u53cd\u5e94\u52a8\u529b\u5b66\u7684\u505a\u6cd5\uff0c\u628a\u5b83\u5199\u6210\u8ddf\u7ed3\u6784\u5efa\u7acb\u901f\u7387\u5e38\u6570k1\u548c\u7834\u574f\u901f\u7387\u5e38\u6570k2\u6709\u5173\u7684\u4e00\u4e2a\u901f\u7387\u65b9\u7a0b\u3002\u8fd9\u6837\u7684\u6a21\u578b\u81ea\u7136\u662f\u53ef\u4ee5\u63cf\u8ff0\u57fa\u672c\u89e6\u53d8\u6027\u73b0\u8c61\uff0c\u4f8b\u5982thixtropic loop\u548cstress overshoot\u3002\u4f46\u662f\uff0c\u6211\u5728MATLAB\u91cc\u73a9\u8fc7\u51e0\u4e2a\u8fd9\u79cd\u6a21\u578b\uff0c\u90fd\u6ca1\u529e\u6cd5\u6574\u51fa\u5ef6\u8fdf\u5c48\u670d\u73b0\u8c61\u3002\u5c48\u670d\u662f\u6709\u7684\uff0c\u4f46\u662f\u90fd\u662f\u4ecet = 0\u5f00\u59cb\u53d1\u751f\uff0c\u6211\u80fd\u8c03\u7684\u53ea\u662f\u5c48\u670d\u8fc7\u7a0b\u7684\u5feb\u6162\uff0c\u800c\u4e0d\u662f\u4f55\u65f6\u5f00\u59cb\u53d1\u751f\u3002\u6211\u6ca1\u529e\u6cd5\u8ba9\u5b83\u65f6\u957f\u4e3atd\u7684\u65f6\u95f4\u5185\u4e0d\u53d1\u751f\u4efb\u4f55\u4e8b\u60c5\uff0c\u7136\u540e\u8d85\u8fc7\u6b64\u65f6\u95f4\u4e4b\u540e\u518d\u53d1\u751f\u5c48\u670d\u3002\u66f4\u8c08\u4e0d\u4e0a\u8c03\u6574td\u7684\u957f\u77ed\u4e86\u3002\u76ee\u524d\u6211\u6000\u7591\u5982\u679c\u8981\u63cf\u8ff0\u5ef6\u8fdf\u5c48\u670d\uff0c\u5149\u7b80\u5355\u5730\u7528\u4e00\u4e2a\u6570\u503c\u4ee3\u8fdbk1\u6216k2\u662f\u4e0d\u591f\u7684\u3002k1\u548ck2\u9700\u8981\u8fdb\u4e00\u6b65\u5efa\u6a21\u3002\u4e0d\u8fc7\uff0c\u6211\u5fc5\u987b\u60f3\u51fa\u4e00\u4e2aidea\u5230\u5e95\u5ef6\u8fdf\u5c48\u670d\u7684td\u65f6\u95f4\u5185\u6837\u54c1\u5230\u5e95\u53d1\u751f\u4ec0\u4e48\u7ed3\u6784\u53d8\u5316\uff0c\u80fd\u65e2\u4e0d\u5bfc\u81f4\u4efb\u4f55\u6d41\u53d8\u5b66\u73b0\u8c61\uff0c\u53c8\u63a7\u5236\u7740td\u7684\u957f\u77ed\u3002","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":5118,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5118","url_meta":{"origin":825,"position":2},"title":"\u4e73\u6db2\u4f53\u7cfb\u6d41\u53d8\u5b66","author":"Andrew","date":"2013\u5e741\u670824\u65e5","format":false,"excerpt":"[mathjax]\u524d\u6bb5\u65f6\u95f4\u56e0\u4fee\u6539\u4e00\u7bc7\u4e73\u6db2\u6d41\u53d8\u5b66\u6587\u7ae0\u7684\u7f18\u6545\uff0c\u81ea\u5df1\u67e5\u9605\u4e86\u4e00\u756a\u76f8\u5173\u6587\u732e\uff0c\u5728\u51e0\u5f20\u8349\u7a3f\u7eb8\u4e0a\u505a\u4e86\u4e9b\u4e0d\u592a\u5b8c\u6574\u7684\u603b\u7ed3\uff0c\u4e00\u76f4\u7b80\u5355\u585e\u5728\u67d0\u4e2a\u5730\u65b9\u3002\u73b0\u5728\u89c9\u5f97\u8fd8\u662f\u6b63\u5f0f\u8bb0\u5f55\u4e0b\u6765\u6bd4\u8f83\u597d\uff0c\u4e0d\u7136\u5c06\u6765\u7eb8\u6389\u4e86\u5c31\u5de5\u592b\u5c31\u767d\u8d39\u4e86\u3002\u5206\u6563\u4f53\u7cfb\u7684\u6d41\u53d8\u5b66\u5927\u81f4\u4e0a\u9700\u8981\u8ba8\u8bba\u7684\u5185\u5bb9\u5206\u51e0\u5757\uff1a\u96f6\u5207\u7c98\u5ea6\\(\\eta_{0}\\)\u5bf9\u586b\u5145\u4f53\u79ef\u5206\u6570\\(\\phi\\)\u7684\u5173\u7cfb\u3002\u526a\u5207\u7c98\u5ea6\u5bf9\u526a\u5207\u901f\u7387\u7684\u5173\u7cfb\uff0c\\(\\eta\\sim\\dot{\\gamma}\\)\u7ebf\u6027\u7c98\u5f39\u6027\u975e\u7ebf\u6027\u77ac\u6001\u884c\u4e3a\u6bcf\u5757\u5185\u5bb9\u90fd\u9700\u8981\u6309\u7167\u7a00\u3001\u534a\u7a00\u548c\u6d53\u6765\u8ba8\u8bba\u3002\u4e73\u6db2\u4e0e\u786c\u7403\u60ac\u6d6e\u6db2\u4f53\u7cfb\u6709\u76f8\u4f3c\u4e4b\u5904\uff0c\u4f46\u4e5f\u6709\u533a\u522b\u3002\u4e00\u662f\u754c\u9762\u5f20\u529b\u7684\u8d21\u732e\uff0c\u4e8c\u662f\u6db2\u6ef4\u662f\u6db2\u6001\uff0c\u672c\u8eab\u53ef\u6d41\u52a8\u548c\u53d8\u5f62\uff08\u5176\u5b9e\u7b2c\u4e00\u4e5f\u53ef\u5f52\u4e3a\u7b2c\u4e8c\uff09\u3002\u6240\u4ee5\uff0c\u5148\u7b80\u5355\u603b\u7ed3\u786c\u7403\u7684\u60c5\u51b5\uff0c\u4ee5\u4fbf\u5206\u6e05\u4e73\u6db2\u6709\u54ea\u4e9b\u60c5\u51b5\u4e0d\u662f\u5b83\u7684\u7279\u6b8a\u6027\u3002\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u672c\u6587\u7684\u5185\u5bb9\u5728The Structure and Rheology of Complex Fluids\uff08Ronald G. Larson, Oxford University Press, 1999\uff09\u4e00\u4e66\u91cc\u5df2\u7ecf\u6709\u5f88\u7cfb\u7edf\u7684\u603b\u7ed3\u4e86\u3002\u6211\u5728\u8fd9\u91cc\u662f\u628a\u5b9e\u9645\u5927\u5bb6\u6700\u559c\u6b22\u7528\u7684\u5f0f\u5b50\u6311\u51fa\u6765\uff0c\u4e5f\u5bf9\u8be5\u4e66\u6ca1\u8bb2\u5230\u7684\u90e8\u5206\u505a\u4e86\u4e00\u4e9b\u8865\u5145\u3002\u65e0\u76f8\u4e92\u4f5c\u7528\u786c\u7403\u4f53\u7cfb\u96f6\u5207\u7c98\u5ea6\\(\\eta_0\\sim\\phi\\)\uff0c\u4e09\u4e2a\u65b9\u7a0b\uff1aEinstein\u3001Bachelor\u3001Krieger-Dougherty\u3002\u8fd9\u4e09\u4e2a\u65b9\u7a0b\u975e\u5e38\u5e38\u89c1\uff0c\u4e0a\u7f51\u641c\u4e00\u4e0b\u90fd\u6709\u3002\u4e8b\u5b9e\u4e0a\u53ea\u6709Einstein\u662ffirst principle\u7684\u3002\u8fd9\u4e09\u4e2a\u65b9\u7a0b\u5e38\u5e38\u88ab\u7528\u6765\u6807\u5b9a\u60ac\u6d6e\u6db2\u7684\u4f53\u79ef\u5206\u6570\u3002\u6211\u4e2a\u4eba\u89c9\u5f97\u53ea\u6709\u4fdd\u8bc1\u4f53\u7cfb\u662f\u5178\u578b\u7684\u65e0\u76f8\u4e92\u4f5c\u7528\u5355\u5206\u6563\u786c\u7403\u624d\u53ef\u9760\u3002\u4f46\u5f80\u5f80\u7528\u7684\u573a\u5408\u90fd\u662f\u5fae\u51dd\u80f6\u6216\u8005\u4e73\u6db2\u7684\u60c5\u51b5\u3002\u800c\u4e14\uff0c\u7528Krieger-Dougherty\u6765\u6807\u5b9a\u6d53\u60ac\u6d6e\u6db2\u4f53\u79ef\u5206\u6570\u7684\u65f6\u5019\uff0c\u4f60\u5fc5\u987b\u5148\u5047\u5b9a\u4e00\u4e2a\u6700\u5927\u4f53\u79ef\u5206\u6570\\(\\phi_\\textrm{max}\\)\uff08\u5b9e\u9645\u4e0a\u5c31\u662f\u4f7fKrieger-Dougherty\u5f0f\u4e2d\u7684\u7c98\u5ea6\u53d1\u6563\u7684\u4f53\u79ef\u5206\u6570\uff09\uff0c\u4f46\u662f\u8fd9\u4e2a\\(\\phi_\\textrm{max}\\)\u7684\u53d6\u503c\u6709\u4efb\u610f\u6027\uff0c\u75280.58\u30010.64\u3001\\(\\pi\\sqrt{2}\/6\\)\u7684\u90fd\u6709\uff0c\u90fd\u6709\u7406\u7531\uff08\u4f9d\u6b21\u662f\u73bb\u7483\u5316\u3001random close packing\u548crhomboidal dodecahedron packing\uff09\u3002\u6211\u5012\u662f\u6ca1\u8bd5\u8fc7\u5bf9\u4e8e\u540c\u4e00\u5957\u6570\u636e\uff0c\u5047\u5b9a\u4e0d\u540c\u7684\\(\\phi_\\textrm{max}\\)\u503c\u6765\u6807\u5b9a\\(\\phi\\)\u4f1a\u5dee\u591a\u5c11\u3002\u8ddf\u8fd9\u4e00\u5173\u7cfb\u76f8\u5e76\u5217\u7684\uff0c\u662f\u5f53\\(\\phi>\\phi_\\textrm{max}\\)\u65f6\u5e73\u53f0\u6a21\u91cf\\(G_\\textrm{p}\\)\u5bf9\\(\\phi\\)\u7684\u5173\u7cfb\u3002\u5012\u662f\u6709\u4e00\u4e2a\u8ddf\u7c92\u5b50\u76f8\u4e92\u4f5c\u7528\u52bf\u80fd\u6709\u5173\u7684\u7b80\u5355\u5173\u7cfb\uff1a$$G_\\textrm{p}\\propto\\frac{1}{r}\\left(\\frac{\\partial^2U\\left(r\\right)}{\\partial r^2}\\right)$$\u526a\u5207\u7c98\u5ea6\\(\\eta_\\textrm{r}\\sim\\textrm{Pe}\\)\u3002\u8fd9\u4e2a\u5173\u7cfb\uff0c\u597d\u50cf\u53ea\u6709\u8f83\u6d53\u7684\u60ac\u6d6e\u6db2\uff08\u53d1\u751f\u526a\u5207\u53d8\u7a00\uff09\u624d\u6709\u610f\u4e49\u3002\u552f\u8c61\u7684\u7eaf\u526a\u5207\u7684\u6d41\u53d8\u5b66\u6a21\u578b\u5f88\u5e38\u7528\u7684\u662fCasson\u6216\u8005Cross\u3002Casson\u65b9\u7a0b\u542b\u6709\u4e00\u4e2a\u201c\u5c48\u670d\u5e94\u529b\u201d$$\\sigma^{\\frac{1}{2}}=\\sigma_\\textrm{y}^{\\frac{1}{2}}+c\\dot{\\gamma}^{\\frac{1}{2}}$$\u4f46\u662f\u7528\u8fd9\u4e2a\u65b9\u7a0b\u62df\u5408\u5f97\u5230\u7684\u5c48\u670d\u5e94\u529b\u8ddf\u505a\u8815\u53d8\u5f97\u5230\u7684\u9759\u6001\u5c48\u670d\u5e94\u529b\u5f80\u5f80\u6709\u5dee\u3002Cross\u65b9\u7a0b\uff1a$$\\eta_\\textrm{r}=\\eta_{\\textrm{r}\\infty}+\\frac{\\eta_\\textrm{r0}-\\eta_{\\textrm{r}\\infty}}{1+\\left(b\\sigma_\\textrm{r}\\right)^m}$$\u5176\u4e2d\\(\\sigma_\\textrm{r}=a^3\\sigma\/k_\\textrm{B}T\\)\u3002\u81f3\u4e8e\u7ed3\u6784\u6a21\u578b\u5c31\u6d89\u53ca\u5230\u80f6\u4f53\u73bb\u7483\u7684\u95ee\u9898\u4e86\u3002\u5982\u679c\u662f\u786c\u7403\u4f53\u7cfb\u53ef\u4ee5\u5229\u7528schematic MCT\u7684\u7ed3\u679c\u6765\u8bd5\u8bd5\u3002\u7ebf\u6027\u7c98\u5f39\u6027\u5bf9\u4e8e\u6d53\u4f53\u7cfb\u8fd8\u662f\u53ef\u4ee5\u8bd5\u7528schematic MCT\u7684\uff0c\u6216\u8005\u7528\u8fd9\u4e00\u4e2a\u66f4\u7b80\u5355\u7684\u7248\u672c\uff1aPRL 75, 2770 (1995)\u3002\u8fd9\u4e2a\u5f0f\u5b50\u5b9e\u9645\u62df\u5408\u53c2\u6570\u5f88\u591a\uff0c\u4efb\u610f\u5ea6\u5f88\u5927\u3002\u7a00\u548c\u534a\u7a00\u4f53\u7cfb\u7684\u7ebf\u6027\u7c98\u5f39\u6027\u600e\u6837\uff0c\u6211\u6ca1\u6709\u67e5\u9605\u548c\u603b\u7ed3\u3002\u975e\u7ebf\u6027\u77ac\u6001\u884c\u4e3a\u540c\u6837\uff0cschematic MCT\u7684\u63a8\u5e7f\u4e5f\u6709\u5230time-dependent shear\u7684\u60c5\u5f62\uff0c\u6240\u4ee5\u80fd\u628aschematic MCT\u770b\u61c2\u7684\u8bdd\uff0c\u65e0\u76f8\u4e92\u4f5c\u7528\u786c\u7403jamming\u4f53\u7cfb\u7684\u6d41\u53d8\u5b66\u662f\u53ef\u4ee5\u83b7\u5f97\u7406\u8bba\u63cf\u8ff0\u7684\u3002\u95ee\u9898\u662f\uff0c\u5177\u6709\u7c7b\u4f3c\u6d41\u53d8\u5b66\u884c\u4e3a\u7684\u8fd8\u6709\u80f6\u4f53\u51dd\u80f6\u4f53\u7cfb\uff0c\u7528MCT\u53bb\u7b97\u5c31\u6ca1\u4ec0\u4e48\u7406\u7531\u3002\u6211\u6ca1\u6709\u67e5\u6700\u8fd1\u7684\u6587\u732e\u3002\u4eceLarson\u7684\u4e66\u91cc\u770b\u5230\uff0c\u51dd\u80f6\u4f53\u7cfb\u4e5f\u6709\u4e00\u4e9b\u4ece\u7c92\u5b50\u76f8\u4e92\u4f5c\u7528\u51fa\u53d1\u534a\u7ecf\u9a8c\u7684\u7ed3\u6784\u6a21\u578b\uff0c\u4f46\u591a\u6570\u662f\u9884\u6d4b\u4e00\u4e0b\u5c48\u670d\u5e94\u529b\uff0c\u6ca1\u6709\u5230\u9884\u6d4btime-dependent shear\u8fd9\u4e48\u5b8c\u6574\u3002\u7528\u6d41\u53d8\u5b66\u672c\u6784\u65b9\u7a0b\u7684\u5c31\u4e0d\u5728\u6b64\u603b\u7ed3\u4e86\uff0c\u6211\u7684\u5174\u8da3\u662f\u5982\u4f55\u80fd\u5c06\u6d41\u53d8\u5b66\u8ddf\u7ed3\u6784\u8054\u7cfb\u8d77\u6765\u3002\u4e73\u6db2\u4f53\u7cfb\u4e73\u6db2\u4f53\u7cfb\u8981\u8003\u8651Ca\u503c\u3002\u6211\u4e3b\u8981\u603b\u7ed3\\(\\textrm{Ca}\\ll1\\)\u7684\u60c5\u51b5\u3002\u96f6\u5207\u7c98\u5ea6\u7a00\u4e73\u6db2\uff0c\u8ddf\u786c\u7403\u5df2\u7ecf\u5f88\u63a5\u8fd1\u4e86\u3002Talor\u8003\u8651\u4e86\u6db2\u6ef4\u76f8\u672c\u8eab\u5728\u6d41\u573a\u4e2d\u4f1a\u6253\u8f6c\uff0c\u4f7f\u7c98\u5ea6\u964d\u4f4e\uff0c\u5f0f\u5b50\u662f\uff1a$$\\eta_\\textrm{r}=1+\\frac{1+\\frac{5}{2}M}{1+M}\\phi$$\u5176\u4e2d\\(M=\\eta_\\textrm{d}\/\\eta_\\textrm{s}\\)\u3002\u6d53\u4e00\u70b9\u7684\uff0c\u7528Pal\u7684\u51e0\u4e2a\u5f0f\u5b50\u3002\u6d53\u6d6e\u6db2\u4ea7\u751f\u7684\u53e6\u4e00\u4e2a\u4e0e\u786c\u7403\u4e0d\u540c\u7684\u56e0\u7d20\u5c31\u662f\u6db2\u6ef4\u7c98\u5728\u4e00\u8d77\u6709\u4e00\u5b9a\u7684\u63a5\u89e6\u89d2\uff0c\u63a5\u89e6\u754c\u9762\u7531\u4e24\u5c42\u6d3b\u6027\u5242\u5206\u5b50\uff0c\u6709\u4e00\u5b9a\u539a\u5ea6\u3002\u6709\u6548\u4f53\u79ef\u5206\u6570\u7684\u8ba8\u8bba\u89c1Princen\u7b49\u3002\u53e6\u5916\uff0c\u867d\u7136\\(\\textrm{Ca}\\ll1\\)\uff0c\u4f46\u662f\u6d53\u4e86\u4e4b\u540e\u6db2\u6ef4\u8fd8\u662f\u4f1a\u6324\u538b\u53d1\u751f\u53d8\u5f62\uff0c\u8fd9\u65f6\u54ea\u6015\u4e0d\u53d8\u5f62\u65f6\u5df2\u8fbe\u5230\u751a\u81f3\u8d85\u8fc7\\(\\phi_\\textrm{max}\\)\uff0c\u4f46\u901a\u8fc7\u53d8\u5f62\u4ecd\u7136\u53ef\u4ee5\u6ed1\u79fb\uff0c\u6240\u4ee5\u7c98\u5ea6\u4e0d\u4f1a\u53d1\u6563\u3002\u8fd9\u4e00\u6548\u5e94\u6ca1\u6709\u8fd8\u6ca1\u67e5\u5230\u7ed3\u6784\u7406\u8bba\u6a21\u578b\uff0c\u5b9e\u9a8c\u53ef\u53c2\u8003Colloids Surf. A 299, 65 (2007)\u3002\\(\\phi_\\textrm{max}\\)\u4ee5\u4e0a\uff0c\u6a21\u91cf\u968f\\(\\phi\\)\u7684\u53d8\u5316\uff0c\u53c2\u89c1J. Non-Newt. Fluid Mech. 105, 21 (2002)\u3002\u6216\u8005Princen\u526a\u5207\u7c98\u5ea6Princen\u3002\u7ebf\u6027\u7c98\u5f39\u6027\u7a00\u7684\u7528Palierne\u7684\u6a21\u578b\uff0c\u592a\u51fa\u540d\u4e86\uff0c\u4e0d\u5f15\u4e86\u3002\u6d53\u7684\u6ca1\u6709\uff0c\u53ef\u80fd\u53ef\u4ee5\u7528MCT\uff1f\u975e\u7ebf\u6027\u77ac\u6001\u884c\u4e3a\u518d\u6b21\u5f3a\u8c03\u6211\u53ea\u603b\u7ed3\\(\\textrm{Ca}\\ll1\\)\u7684\u60c5\u51b5\u3002\u6db2\u6ef4\u53d8\u5f62\u90a3\u4e00\u5927\u5757\u6709\u5f88\u591a\u6a21\u578b\u53ef\u4ee5\u505a\u5230time-dependent shear\u3002Princen\u7ed9\u8fc7\u4e00\u4e2a\u6d53\u6d6e\u6db2\u5c48\u670d\u5e94\u529b\u7684\u5f0f\u5b50[backref name=\"118\"]\u3002\u800c\u5bf9\u4e8etime-dependent shear\uff0c\u6211\u627e\u5230\u4e00\u7bc7J. 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Educ.\u62a5\u9053\u4e86\u6d41\u53d8\u5b66\u4f1a\u5728\u7f8e\u56fd\u56fd\u5bb6\u6807\u51c6\u5c40\u53ec\u5f00\u7684\u6d88\u606f\uff0c\u5217\u51fa\u4e86\u90e8\u5206\u4f1a\u8bae\u8bba\u6587\u53ca\u4f5c\u8005\uff0c\u5176\u4e2d\u6709Bingham\u3001Reiner\u548cScott-Blair\u8fd9\u51e0\u4e2a\u8457\u540d\u7684\u7b2c\u4e00\u4ee3\u6d41\u53d8\u5b66\u5bb6\u3002\u5176\u4e2dReiner\u6f14\u8bb2\u9898\u76ee\u7adf\u7136\u53eb\u505aThe General Equation of Flow!\uff08\u539f\u6807\u9898\u5c31\u542b\u611f\u53f9\u53f7\uff09\uff0c\u8ba9\u6211\u5f88\u597d\u5947\u6f14\u8bb2\u7684\u5185\u5bb9\u662f\u600e\u4e48\u6837\u7684\u3002 \u65f6\u95f4\u4e00\u4e0b\u5b50\u8df3\u5230\u4e8660\u5e74\u4ee3\uff0cFerry\u5728J. Chem. Educ.\u4e0a\u4ecb\u7ecd\u6d41\u53d8\u5b66\uff0c\u4e3b\u8981\u5173\u6ce8\u70b9\u5c31\u662f\u9ad8\u5206\u5b50\u6d41\u53d8\u5b66\u4e86\u3002\u4ed6\u5b9e\u8d28\u4e0a\u4ecb\u7ecd\u4e86\u7c98\u5f39\u6027\u7684\u6982\u5ff5\uff0c\u4f46\u8bed\u8a00\u4e0a\u662f\u8bf4\u201c\u6d41\u4f53\u4e5f\u80fd\u50a8\u5b58\u80fd\u91cf\u201d\uff0c\u539f\u56e0\u5c31\u662f\u201c\u5206\u5b50\u94fe\u88ab\u63a5\u4f38\u201d\u3002\u6587\u7ae0\u4e0d\u53ef\u907f\u514d\u5730\u4e5f\u89e3\u91ca\u4e86\u4e00\u4e9b\u201c\u71b5\u5f39\u6027\u201d\u6982\u5ff5\u3002\u6700\u540e\u4ecb\u7ecd\u4e86\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u677e\u5f1b\u8c31\u3002 Weissenberg\u6548\u5e94\u662f1940\u5e74\u4ee3\u53d1\u73b0\u7684\u3002\u4f46\u662f\u5176\u539f\u56e0\u4e00\u76f4\u523060\u5e74\u4ee3\u8fd8\u4e0d\u662f\u5f88\u6e05\u695a\uff0c\u8fd8\u5904\u4e8e\u53d1\u73b0\u54ea\u4e9b\u7269\u8d28\u4f1a\u6709\u8fd9\u4e2a\u6548\u5e94\u7684\u9636\u6bb5\u30021961\u5e74Nature\u4e0a\u7684\u4e00\u7bc7\u6587\u7ae0\uff0c\u5176\u5185\u5bb9\u5c31\u662f\u53d1\u73b0\u86cb\u767d\u6709Weissenberg\u6548\u5e94\u3002\u5728J. Chem. Educ.\u4e0a\u4e5f\u6709\u4e00\u7bc7\u6587\u7ae0\uff0c\u8bf4\u660e\u80f6\u53ef\u4ee5\u4f5c\u4e3a\u6f14\u793aWeissenberg\u6548\u5e94\u7684\u65b9\u4fbf\u7684\u6750\u6599\u3002 \u6d41\u53d8\u5b66\u6b63\u5f0f\u63d0\u51fa\u662f1920\u5e74\u3002\u8fd9\u521a\u597d\u4e5f\u662fStaudinger\u53d1\u8868\u300a\u8bba\u805a\u5408\u300b\u7684\u90a3\u5e74\uff0c\u9ad8\u5206\u5b50\u6982\u5ff5\u8fd8\u6ca1\u6709\u88ab\u5e7f\u6cdb\u63a5\u53d7\u3002\u6240\u4ee5\uff0c\u5f15\u8d77\u5b66\u8005\u5173\u6ce8\u590d\u6742\u6d41\u4f53\u7684\u6d41\u53d8\u73b0\u8c61\u7684\uff0c\u90fd\u662f\u80f6\u4f53\u4f53\u7cfb\u6837\u54c1\uff08\u6216\u8005\u8bf4\u5728\u5f53\u65f6\u90fd\u53eb\u80f6\u4f53\uff09\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5173\u4e8e\u7c98\u5f39\u6027\uff08\u5f53\u53ebelastic aftereffect\uff09\u3001\u7c98\u5ea6\u7684\u526a\u5207\u901f\u7387\u4f9d\u8d56\u6027\uff0c\u4eba\u4eec\u57281920\u5e74\u4ee5\u524d\u5df2\u7ecf\u8ba4\u8bc6\u5f97\u6bd4\u597d\u4e86\uff08\u4ee5Maxwell\u7528\u5fae\u5206\u65b9\u7a0b\u7684\u5f62\u5f0f\u63cf\u8ff0\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u666e\u904d\u5f62\u5f0f\u4e3a\u6807\u5fd7\uff09\u3002\u8fd9\u4e9b\u7814\u7a76\u4ee5\u864e\u514b\u548c\u725b\u987f\u4e3a\u6e90\u5934\uff0c\u7ecf\u8fc7\u6cca\u8083\u53f6\u3001\u67ef\u897f\u3001Maxwell\u548cBoltzmann\u7b49\u4eba\u8fdb\u5165\u5230\u4e8c\u5341\u4e16\u7eaa\uff0c\u672c\u6765\u5c31\u5df2\u7ecf\u5c5e\u4e8e\u6d41\u4f53\u529b\u5b66\u6216\u8005\u8fde\u7eed\u4f53\u529b\u5b66\u7684\u7814\u7a76\u8303\u56f4\u3002Reiner\u5728\u542c\u8bf4Bingham\u8981\u63d0\u51fa\u6d41\u53d8\u5b66\u4f5c\u4e3a\u4e00\u4e2a\u65b0\u7684\u5b66\u79d1\u65f6\u4e5f\u662f\u8fd9\u4e48\u56de\u590d\u7684\u3002\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u4e00\u7ebf\u7684\u7814\u7a76\u540e\u7eed\u8fd8\u6709Rivlin\u3001Oldroyd\u3001Noll\u3001Truesdell\u7b49\u4eba\u6cbf\u7740\u4f53\u529b\u5b66\u548c\u7406\u6027\u529b\u5b66\u7684\u8def\u5b50\u8d70\u4e0b\u53bb\uff0c\u53ea\u662f\u540e\u6765\u6d41\u53d8\u5b66\u771f\u7684\u5f62\u6210\u4e00\u4e2a\u5b66\u79d1\u4e4b\u540e\u628a\u4ed6\u4eec\u7684\u4e00\u4e9b\u5de5\u4f5c\u7eb3\u5165\u5230\u4e86\u81ea\u5df1\u5b66\u79d1\u7684\u7406\u8bba\u57fa\u7840\u800c\u5df2\u3002\u53ef\u4ee5\u8bf4\uff0c\u8fd9\u4e00\u7ebf\u7814\u7a76\u786e\u5b9e\u4e0d\u9700\u8981\u53e6\u5916\u518d\u8bbe\u7acb\u4e00\u4e2a\u5b66\u79d1\u3002\u6240\u4ee5Bingham\u5728J. Chem. Educ.\u4e0a\u7684\u6587\u7ae0\uff0c\u4e3a\u4e86\u786e\u7acb\u6d41\u53d8\u5b66\u8fd9\u4e00\u5b66\u79d1\uff0c\u660e\u786e\u5730\u6307\u51fa\u5927\u5bb6\u6240\u5ffd\u89c6\u7684\u6d41\u52a8\u662f\u5851\u6027\u6d41\u52a8\uff0c\u5373\u8ddf\u5f53\u65f6\u5173\u4e8e\u7c98\u5f39\u6027\u7684\u8fde\u7eed\u4ecb\u8d28\u672c\u6784\u65b9\u7a0b\u7814\u7a76\u65e0\u5173\u7684\u3001\u90a3\u79cd\u5177\u6709\u5c48\u670d\u5e94\u529b\u7684\u7ed3\u6784\u6d41\u4f53\u7684\u6d41\u52a8\uff08\u5728Bingham\u7684\u6587\u7ae0\u4e2d\u7684\u4f8b\u5b50\u662f\u4e00\u4e2a\u4e73\u6db2\u6837\u54c1\uff09\u3002\u4ed6\u8bf4\uff1a The hydraulicians were not aware that there is more than the one type of flow, and the type with which they were occupied did not\u2026","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":6668,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/6668","url_meta":{"origin":825,"position":5},"title":"\u5b8f\u89c2\u6d41\u53d8\u5b66\u7684\u8ba4\u8bc6\u5c40\u9650","author":"Andrew","date":"2015\u5e748\u670816\u65e5","format":"aside","excerpt":"\u9047\u5230\u4e00\u7bc7J. 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