{"id":5118,"date":"2013-01-24T16:32:47","date_gmt":"2013-01-24T08:32:47","guid":{"rendered":"http:\/\/www.andrewsun.net\/panta_rhei\/?p=5118"},"modified":"2013-01-26T04:36:15","modified_gmt":"2013-01-25T20:36:15","slug":"%e4%b9%b3%e6%b6%b2%e4%bd%93%e7%b3%bb%e6%b5%81%e5%8f%98%e5%ad%a6","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5118","title":{"rendered":"\u4e73\u6db2\u4f53\u7cfb\u6d41\u53d8\u5b66"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"5118\">\n<p>[mathjax]<\/p>\n<p>\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<\/p>\n<p>\u5206\u6563\u4f53\u7cfb\u7684\u6d41\u53d8\u5b66\u5927\u81f4\u4e0a\u9700\u8981\u8ba8\u8bba\u7684\u5185\u5bb9\u5206\u51e0\u5757\uff1a<\/p>\n<ul>\n<li>\u96f6\u5207\u7c98\u5ea6\\(\\eta_{0}\\)\u5bf9\u586b\u5145\u4f53\u79ef\u5206\u6570\\(\\phi\\)\u7684\u5173\u7cfb\u3002<\/li>\n<li>\u526a\u5207\u7c98\u5ea6\u5bf9\u526a\u5207\u901f\u7387\u7684\u5173\u7cfb\uff0c\\(\\eta\\sim\\dot{\\gamma}\\)<\/li>\n<li>\u7ebf\u6027\u7c98\u5f39\u6027<\/li>\n<li>\u975e\u7ebf\u6027\u77ac\u6001\u884c\u4e3a<\/li>\n<\/ul>\n<p>\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<\/p>\n<p>\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u672c\u6587\u7684\u5185\u5bb9\u5728<i>The Structure and Rheology of Complex Fluids<\/i>\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<\/p>\n<h2>\u65e0\u76f8\u4e92\u4f5c\u7528\u786c\u7403\u4f53\u7cfb<\/h2>\n<h3>\u96f6\u5207\u7c98\u5ea6<\/h3>\n<p>\\(\\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<\/p>\n<p>\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<\/p>\n<p>\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$$G_\\textrm{p}\\propto\\frac{1}{r}\\left(\\frac{\\partial^2U\\left(r\\right)}{\\partial r^2}\\right)$$<\/p>\n<h3>\u526a\u5207\u7c98\u5ea6<\/h3>\n<p>\\(\\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<\/p>\n<h3>\u7ebf\u6027\u7c98\u5f39\u6027<\/h3>\n<p>\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\uff1a<i>PRL<\/i> 75, 2770 (1995)\u3002\u8fd9\u4e2a\u5f0f\u5b50\u5b9e\u9645\u62df\u5408\u53c2\u6570\u5f88\u591a\uff0c\u4efb\u610f\u5ea6\u5f88\u5927\u3002<\/p>\n<p>\u7a00\u548c\u534a\u7a00\u4f53\u7cfb\u7684\u7ebf\u6027\u7c98\u5f39\u6027\u600e\u6837\uff0c\u6211\u6ca1\u6709\u67e5\u9605\u548c\u603b\u7ed3\u3002<\/p>\n<h3>\u975e\u7ebf\u6027\u77ac\u6001\u884c\u4e3a<\/h3>\n<p>\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<\/p>\n<p>\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<\/p>\n<h2>\u4e73\u6db2\u4f53\u7cfb<\/h2>\n<\/p>\n<p>\u4e73\u6db2\u4f53\u7cfb\u8981\u8003\u8651Ca\u503c\u3002\u6211\u4e3b\u8981\u603b\u7ed3\\(\\textrm{Ca}\\ll1\\)\u7684\u60c5\u51b5\u3002<\/p>\n<h3>\u96f6\u5207\u7c98\u5ea6<\/h3>\n<\/p>\n<p>\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<\/p>\n<p>\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\u8003<i>Colloids Surf. A<\/i> 299, 65 (2007)\u3002<\/p>\n<p>\\(\\phi_\\textrm{max}\\)\u4ee5\u4e0a\uff0c\u6a21\u91cf\u968f\\(\\phi\\)\u7684\u53d8\u5316\uff0c\u53c2\u89c1<i>J. Non-Newt. Fluid Mech.<\/i> 105, 21 (2002)\u3002\u6216\u8005Princen<\/p>\n<h3>\u526a\u5207\u7c98\u5ea6<\/h3>\n<p>Princen\u3002<\/p>\n<h3>\u7ebf\u6027\u7c98\u5f39\u6027<\/h3>\n<p>\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<\/p>\n<h3>\u975e\u7ebf\u6027\u77ac\u6001\u884c\u4e3a<\/h3>\n<p>\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\u3002<\/p>\n<p>Princen\u7ed9\u8fc7\u4e00\u4e2a\u6d53\u6d6e\u6db2\u5c48\u670d\u5e94\u529b\u7684\u5f0f\u5b50[backref name=&#8221;118&#8243;]\u3002\u800c\u5bf9\u4e8etime-dependent shear\uff0c\u6211\u627e\u5230\u4e00\u7bc7<i>J. Fluid Mech.<\/i> 463, 1 (2002)\u662f\u8003\u8651\u7a00\u6d6e\u6db2\u7684\u3002\u4f46\u597d\u50cf\u8fd8\u6ca1\u6709\u4eba\u53bb\u4f7f\u7528\u3002<\/p>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 5118 -->","protected":false},"excerpt":{"rendered":"<p>[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. 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Phys. 2008, 4, 420-424\uff09\u901a\u8fc7\u5efa\u6a21\u5728\u4e8c\u7ef4\u7a7a\u95f4\u91cd\u73b0\u4e86\u8fd9\u4e00\u73b0\u8c61\uff0c\u8868\u660e\u8fd9\u662f\u4e00\u79cd\u76f8\u53d8\uff0c\u6709\u6e1d\u6e17\u9608\u503c\u3002\u8fd9\u51e0\u5929\u53c8\u770b\u5230Menon\u5bf9\u8fd9\u4e00\u73b0\u8c61\u8fdb\u884c\u540e\u7eed\u7814\u7a76\uff08Phys. Rev. E 2009, 79, 061108\uff09\uff0c\u8c8c\u4f3c\u60f3\u8ba8\u8bbauniversality\u7684\u95ee\u9898\uff0c\u4f46\u5177\u4f53\u6211\u8fd8\u6ca1\u770b\u61c2\u3002\u8fd9\u4e00\u7cfb\u5217\u7814\u7a76\u5df2\u7ecf\u662f\u5728\u8ba8\u8bba\u632f\u8361\u526a\u5207\u7684\u5e45\u5ea6\u95ee\u9898\u4e86\uff0c\u53ea\u662f\u6ca1\u6709\u8ddf\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u8054\u7cfb\u8d77\u6765\u3002\u4f5c\u8005\u662f\u5177\u4f53\u5230\u60ac\u6d6e\u6db2\u8fd9\u4e00\u4f53\u7cfb\uff0c\u4ececreep flow\u7684\u65b9\u7a0b\u51fa\u53d1\u8003\u8651\u95ee\u9898\uff0c\u76f8\u53d8\u539f\u56e0\u89e3\u91ca\u4e3a\u7c92\u5b50\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u5bfc\u81f4\u7684\u975e\u5e73\u8861\u6001\u3002\u800c\u5728\u6d41\u53d8\u5b66\u4e2d\uff0c\u5927\u5e45\u5f62\u53d8\u4e0b\u8bd5\u6837\u51fa\u73b0\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u89e3\u91ca\u4e5f\u662f\u67d0\u79cd\u5e73\u8861\u7684\u7834\u574f\u3002\u6211\u731c\u6d4b\u8fd9\u4e24\u8005\u662f\u540c\u4e00\u4ef6\u4e8b\uff0c\u51fa\u73b0\u6df7\u6c8c\u7684\u90a3\u4e2a\u76f8\u53d8\u9608\u632f\u5e45\u5c31\u5bf9\u5e94\u7740\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u4e0d\u53ef\u5ffd\u7565\u7684\u90a3\u4e2a\u632f\u5e45\u3002Nat. Phys.\u90a3\u7bc7\u6587\u7ae0\u8fd8\u8bf4\u76f8\u53d8\u4e4b\u540e\u6709\u81ea\u7ec4\u7ec7\u884c\u4e3a\uff0c\u800c\u8bb8\u591a\u8bd5\u6837\u5728\u5927\u5e45\u526a\u5207\u4e0b\u4e5f\u7684\u786e\u51fa\u73b0\u8bf8\u5982shear banding\u3001shear-induced ordering\u7684\u73b0\u8c61\uff0c\u6211\u731c\u6d4b\u4e8c\u8005\u4e5f\u662f\u5bf9\u5e94\u7684\u3002\u4e0d\u8fc7\uff0c\u5176\u4ed6\u8bd5\u6837\u60ac\u6d6e\u4f53\u7cfb\uff0c\u5982\u679c\u8981\u8bc1\u660e\u8fd9\u4e9b\u90fd\u662f\u540c\u4e00\u7c7b\u76f8\u53d8\u7684universality\uff0c\u4f3c\u4e4e\u8981\u5728creep flow\u65b9\u7a0b\u7684\u57fa\u7840\u4e0a\u8fdb\u4e00\u6b65\u62bd\u8c61\u7684\u7406\u8bba\u624d\u884c\u3002\u6211\u662f\u505a\u5b9e\u9a8c\u7684\u4e0d\u662f\u505a\u7406\u8bba\u7684\uff0c\u6211\u7422\u78e8\u7740\u8fd9\u4e00\u76f8\u53d8\u5728\u6d41\u53d8\u5b66\u51fd\u6570\u4e2d\u80fd\u4e0d\u80fd\u4f53\u73b0\u51fa\u6765\uff0c\u80fd\u4e0d\u80fd\u628a\u5b83\u4ece\u5b9e\u9a8c\u4e0a\u505a\u51fa\u6765\u3002Menon, G., & Ramaswamy, S. (2009). Universality class of the reversible-irreversible transition in sheared suspensions Physical Review E, 79 (6) DOI: 10.1103\/PhysRevE.79.061108","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":6221,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/6221","url_meta":{"origin":5118,"position":2},"title":"J. Chem. Educ.\u4e0a\u7684\u6d41\u53d8\u5b66","author":"Andrew","date":"2015\u5e741\u670828\u65e5","format":"aside","excerpt":"\u6211\u4e00\u76f4\u90fd\u8ba2\u9605ACS\u7684J. Chem. Educ.\u671f\u520a\uff0c\u53d1\u73b0\u6700\u8fd1\u5bc6\u96c6\u51fa\u73b0\u4e86\u51e0\u7bc7\u5173\u4e8e\u6d41\u53d8\u5b66\u7684\u6587\u7ae0\uff0c\u8fd9\u5c31\u8ba9\u6211\u60f3\u8d77\u53bb\u627e\u627eJ. Chem. Educ.\u4ece\u521b\u520a\u4ee5\u6765\u5173\u4e8e\u6d41\u53d8\u5b66\u7684\u6587\u7ae0\u90fd\u6709\u54ea\u4e9b\u3002 \u7528rheology\u4e3a\u5173\u952e\u8bcd\uff0c\u641c\u51fa\u6765\u7684\u7ed3\u679c\u5176\u5b9e\u5e76\u4e0d\u591a\uff0c\u4f46\u662f\u91cc\u9762\u4e5f\u6709\u5f88\u591a\u6709\u610f\u601d\u7684\u4e1c\u897f\u3002\u6211\u6311\u9009\u4e86\u4e00\u4e9b\u51fa\u6765\u3002 1929\u5e74\u6b63\u662f\u7f8e\u56fd\u6d41\u53d8\u5b66\u4f1a\u6210\u7acb\u7684\u90a3\u5e74\uff0cBingham\u5728J. Chem. Educ.\u53d1\u8868\u4e86\u4e24\u7bc7\u6587\u7ae0\u6765\u4ecb\u7ecd\u8fd9\u4e2a\u65b0\u7684\u5b66\u79d1\u3002\u4ed6\u4e3b\u8981\u5f3a\u8c03\u4e86\u9664\u4e86\u5c42\u6d41\u548c\u6e4d\u6d41\u4e4b\u5916\u8fd8\u6709\u201c\u7b2c\u4e09\u79cd\u6d41\u201d\u5c31\u662f\u5c48\u670d\u548c\u5851\u6027\u6d41\u52a8\u3002\u4ed6\u5176\u5b9e\u4e5f\u5f3a\u8c03\u4e86\u8fd9\u79cd\u6d41\u52a8\u6027\u8d28\u662f\u80f6\u4f53\u7269\u8d28\u7684\u7279\u5f81\u3002\u6bd5\u7adf\uff0c\u5bbe\u6c49\u6d41\u4f53\u662f\u4ee5\u4ed6\u540d\u5b57\u547d\u540d\u7684\u30021930\u5e74\uff0cJ. Chem. 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 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\u9ad8\u5206\u5b50\u6eb6\u6db2\u65b9\u9762 Modern Theory of Polymer Solutions (Yamakawa) \u8fd9\u662f\u7ecf\u5178\uff0c\u4e0d\u4f5c\u6b63\u9762\u4ecb\u7ecd\u4e86\u3002\u5b83\u7684\u597d\u5904\u5728\u4e8e\u6570\u5b66\u63a8\u5bfc\u6e05\u6670\u7b80\u5355\uff0c\u6709\u5149\u6563\u5c04\u548c\u7c98\u5ea6\u5b9e\u9a8c\u7684\u5185\u5bb9\uff0c\u9002\u5408\u901a\u8bfb\u3002 The Theory of Polymer Dynamics (Doi) \u6b64\u4e66\u6bd4Polymer 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