{"id":2739,"date":"2011-03-26T19:07:07","date_gmt":"2011-03-26T11:07:07","guid":{"rendered":"http:\/\/www.andrewsun.net\/panta_rhei\/?p=2739"},"modified":"2011-03-26T21:44:18","modified_gmt":"2011-03-26T13:44:18","slug":"%e5%9b%bd%e5%86%85%e5%81%9ajamming%e7%9a%84%e8%80%81%e5%b8%88","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/2739","title":{"rendered":"\u56fd\u5185\u505ajamming\u7684\u8001\u5e08"},"content":{"rendered":"
\n

\u56e0\u4e3a\u6211\u5bfc\u5e08\u95ee\u8fc7\u51e0\u6b21\u56fd\u5185\u6709\u8c01\u505ajamming\uff0c\u6211\u4e4b\u524d\u7684\u5370\u8c61\u4e2d\u662f\u6ca1\u6709\u7684\u3002\u505ajamming\u548c\u505acolloid\u8fd8\u4e0d\u592a\u4e00\u6837\u3002\u867d\u7136jamming\u9886\u57df\u4e00\u6d89\u53ca\u5230\u5b9e\u9a8c\u5f80\u5f80\u8981\u627e\u7684\u4f53\u7cfb\u662fcolloid\u3002\u8981\u8bf4\u505acolloid\u7684\u8bdd\uff0c\u7edd\u5bf9\u4e0d\u53ef\u80fd\u6ca1\u6709\uff0c\u4f46\u4ed6\u4eec\u5e76\u4e0d\u662f\u6240\u6709\u90fd\u53bb\u642d\u4e58Andrea J. Liu<\/a>\u7684\u201c\u5feb\u8f66\u201d\u3002\u6211\u611f\u89c9\u5728\u975e\u6676\u51dd\u805a\u6001\u65b9\u9762\u4f3c\u4e4e\u8d8a\u4e0d\u7cbe\u786e\u7684\u63cf\u8ff0\u8d8a\u5403\u9999\u3002<\/p>\n

\u6700\u8fd1\u4e00\u6bb5\u65f6\u95f4\uff0c\u56fd\u5185\u81f3\u5c11\u6211\u6240\u77e5\u9053\u6709\u4e24\u4f4d\u8001\u5e08\u662f\u505a\u8fd9\u65b9\u9762\u7684\u7814\u7a76\u3002\u4ed6\u4eec\u5176\u5b9e\u90fd\u662fLiu\u7684\u535a\u58eb\u540e\u56de\u56fd\u3002\u4e00\u4f4d\u662f\u4e2d\u79d1\u5927\u7269\u7406\u7cfb\u7684\u5f90\u5b81<\/a>\u8001\u5e08\uff0c\u4e00\u4f4d\u662f\u82cf\u5dde\u5927\u5b66\u7684\u5f20\u6cfd\u65b0<\/a>\u8001\u5e08\u3002<\/p>\n

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UPDATE\uff1a\u867d\u7136\u4ee5\u6211\u80fd\u5199\u4e0a\u7b80\u5386\u4e0a\u7684\u5185\u5bb9\u80fd\u5f97\u5230\u56fd\u5916\u535a\u58eb\u540e\u7684\u673a\u4f1a\u4e0d\u5927\uff0c\u4f46\u6211\u73b0\u5728\u4e5f\u5728\u6536\u96c6\u4e00\u4e9b\u4e0e\u6211\u7814\u7a76\u5174\u8da3\u76f8\u8fd1\u7684\u56fd\u5916\u6559\u6388\u540d\u5355<\/a>\uff08\u8981\u7ffb\u5899\uff09\u3002<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

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Liu\u7684\u201c\u5feb\u8f66\u201d\u3002\u6211\u611f\u89c9\u5728\u975e\u6676\u51dd\u805a\u6001\u65b9\u9762\u4f3c\u4e4e\u8d8a\u4e0d\u7cbe\u786e\u7684\u63cf\u8ff0\u8d8a\u5403\u9999\u3002 \u6700\u8fd1\u4e00\u6bb5\u65f6\u95f4\uff0c\u56fd\u5185\u81f3\u5c11\u6211\u6240\u77e5\u9053\u6709\u4e24\u4f4d\u8001\u5e08\u662f\u505a\u8fd9\u65b9\u9762\u7684\u7814\u7a76\u3002\u4ed6\u4eec\u5176\u5b9e\u90fd\u662fLiu\u7684\u535a\u58eb\u540e\u56de\u56fd\u3002\u4e00\u4f4d\u662f\u4e2d\u79d1\u5927\u7269\u7406\u7cfb\u7684\u5f90\u5b81\u8001\u5e08\uff0c\u4e00\u4f4d\u662f\u82cf\u5dde\u5927\u5b66\u7684\u5f20\u6cfd\u65b0\u8001\u5e08\u3002 \u73bb\u7483\u6001\u805a\u5408\u7269\u4e5f\u662f\u975e\u6676\u4f53\u7cfb\u3002\u5982\u679c\u7b97\u4e0a\u8fd9\u4e2a\uff0c\u90a3\u4e48\u82cf\u5dde\u5927\u5b66\u7684\u9648\u5eb7\u8001\u5e08\u4e5f\u8981\u7b97\u5728\u5185\u3002\u4ed6\u662f\u539f\u672c\u662fKenneth S. 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\u7b2c\u4e09\uff0c\u6309\u7167 Jamming\u76f8\u56fe\u7684\u610f\u56fe\uff0c\uff08\u7ea6\u5316\uff09\u6e29\u5ea6\u964d\u5e95\u5bfc\u81f3\u51bb\u7ed3\uff0c\u8fd9\u662f\u53ea\u80fd\u5c40\u9650\u4e8e\u67d0\u79cd\u7c7b\u4f3c\u5e73\u8861\u6001\uff08\u6216\u8005\u8bf4\u5904\u4e8elocal\u7684\u5e73\u8861\u6001\uff09\u7684\u4f53\u7cfb\u7684\u3002\u5047\u5982\u4f53\u7cfb\u6b63\u5728aging\u7684\u8fc7\u7a0b\u4e2d\uff0cjamming\u76f8\u56fe\u662f\u4e0d\u9002\u7528\u7684\u3002\u6211\u4eec\u8fd8\u662f\u8ba8\u8bba\uff08\u7ea6\u5316\uff09\u6e29\u5ea6\u8fd9\u6761\u8f74\u3002\u5728jamming\u76f8\u56fe\u4e2d\uff0c\uff08\u7ea6\u5316\uff09\u6e29\u5ea6\u8d8a\u4f4e\uff0c\u8868\u793a\u4f53\u7cfb\u6dec\u706b\uff08quenching\uff09\u7a0b\u5ea6\u8d8a\u6df1\u3002\u5bf9\u4e8e\u975e\u96f6\u6e29\u7684\u4f53\u7cfb\uff08T>0\uff09\uff0cquench\u5230\u73bb\u7483\u5316\u6e29\u5ea6\u4ee5\u4e0b\u4e4b\u540e\u4f53\u7cfb\u662f\u4f1aaging\u7684\u3002\u4f46\u662faging rate\u8ddfdepth of quenching\u6ca1\u6709\u5355\u8c03\u7684\u5173\u7cfb\u3002\u8fd9\u4e2a\u5b9e\u9a8c\u5f88\u5c11\u6709\u4eba\u62a5\u5bfc\uff0c\u4f46\u6700\u65e9\u63d0\u51faaging\u6982\u5ff5\u7684Struik\u5728\u4ed61978\u5e74\u7684\u4e66\u4e2d\u5c31\u7ed9\u51fa\u4e86\u65e0\u5b9a\u5f62\u9ad8\u5206\u5b50\u7684\u5b9e\u9a8c\u7ed3\u679c\uff0c\u663e\u793aaging rate\u5bf9depth of quenching\u7684\u975e\u5355\u8c03\u7684\u4f9d\u8d56\u6027\u3002Quench\u5f97\u592a\u6df1\u6216\u592a\u6d45\uff0caging\u90fd\u6162\uff1b\u6781\u6df1\u7684\u4f53\u7cfb\u662f\u4e0daging\u7684\uff08\u4f53\u7cfb\u6839\u672c\u52a8\u4e0d\u4e86\uff09\uff0c\u6781\u6d45\u6d45\u5230\u4e00\u5b9a\u7a0b\u5ea6\u5c31\u662f\u6ca1quench\u4e0b\u53bb\uff0c\u90a3\u5f53\u7136\u4e5f\u4e0daging\uff0c\u6240\u4ee5\u53ea\u6709\u201c\u9002\u4e2d\u201d\u6df1\u5ea6\u7684quenching\u6709\u660e\u663e\u7684aging\uff0caging rate\u6700\u9ad8\u3002\u5bf9\u4e8e\u6392\u65a5\u52bf\u7684jamming\u76f8\u56fe\u800c\u8a00\uff0c\u5728T>0\u7684jamming\u533a\uff0c\u57fa\u672c\u5c31\u662faging\u7684\u4f53\u7cfb\uff0c\u800caging\u662f\u6c38\u8fdc\u6ca1\u6709\u5c3d\u5934\u7684\u3002\u8fd9\u65f6\uff0c\u6e29\u5ea6T\u5176\u5b9e\u5c31\u6709\u7740\u4e24\u65b9\u9762\u610f\u4e49\uff0c\u4e00\u662f\u8868\u5f81\u4f53\u7cfb\u7684depth of quenching\uff0cTg-T\uff1b\u4e8c\u662f\u8d4b\u4e88\u4f53\u7cfb\u5f53\u524d\u7684\u6d3b\u52a8\u80fd\u529b\u6216\u8005\u8bf4\u5e73\u5747\u7684dynamics\u3002\u6839\u636e\u524d\u9762\u8bf4aging rate\u8ddfdepth of quench\u6ca1\u6709\u5355\u8c03\u5173\u7cfb\uff0c\u90a3\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728\u67d0\u4e00\u4e2adepth of quenching\uff08\u65e2\u6e29\u5ea6T\uff09\uff0c\u5373\u53ef\u80fdaging rate\u968fT\u589e\u52a0\u800c\u589e\u52a0\uff0c\u53c8\u53ef\u80fdaging rate\u968fT\u589e\u52a0\u800c\u51cf\u5c0f\uff0c\u5c31\u770b\u4f53\u7cfb\u662fquench\u5230\u201c\u8fc7\u6df1\u201d\u533a\u8fd8\u662f\u201c\u8fc7\u6d45\u201d\u533a\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728jamming\u76f8\u56fe\u7684jamming\u533a\uff0c\u4f1a\u6709\u4e00\u4e2adepth of quenching\u533a\u57df\u4f53\u7cfb\u7ed3\u6784\u548c\u52a8\u6001\u5176\u5b9e\u662f\u660e\u663e\u968f\u65f6\u95f4\u53d8\u5316\u7684\u3002\u76ee\u524d\u5176\u5b9e\u8fd8\u4e0d\u6e05\u695a\uff0c\u4e00\u4e2a\u4f53\u7cfbaging\u5230\u5e95\u662f\u5411\u7740\u4ec0\u4e48\u6837\u7684\u65b9\u5411\u8dd1\u3002\u5982\u679c\u5b83\u65e0\u975e\u662f\u8dd1\u5230Jamming\u76f8\u56fe\u7684\u5176\u4ed6\u5730\u65b9\uff0c\u90a3\u4e48\u8fd9\u4e2a\u4f1aaging\u7684\u533a\u57df\u5176\u5b9e\u5c31\u662f\u6682\u65f6\u7684\uff0c\u5728\u201c\u6700\u7ec8\u201d\u7684jamming\u76f8\u56fe\u4e2d\u662f\u4e0d\u5b58\u5728\u7684\u3002\u4f46\u524d\u9762\u53c8\u8bf4\u4e86\uff0c\u6211\u4eec\u5f88\u96be\u7b49\u5230\u4f53\u7cfbaging\u5230\u201c\u6700\u7ec8\u201d\u7684\u90a3\u4e00\u5929\u3002\u6240\u4ee5\u76ee\u524d\u53ea\u80fd\u8bf4\uff0cjamming\u76f8\u56fe\u53ea\u9002\u7528\u4e8e\u8ba8\u8bba\u4f53\u7cfb\u4eceunjamming\u5230jamming\u7684\u8f6c\u53d8\u4f4d\u7f6e\uff0c\u5728Jamming\u8f6c\u53d8\u4ee5\u4e0b\u7684jamming\u533a\u5e94\u8be5\u662f\u4e00\u4e2a\u7a7a\u767d\uff0c\u65e0\u6cd5\u8ba8\u8bba\u3002\u5bf9\u4e8e\u5438\u5f15\u52bf\u7684jamming\u76f8\u56fe\uff0c\u8ba8\u8bba\u7ea6\u5316\u6e29\u5ea6\uff0c\u60c5\u51b5\u5c31\u66f4\u52a0\u590d\u6742\u3002\u56e0\u4e3a\u5438\u529b\u4f53\u7cfb\u7684jamming\u5b9e\u9645\u4e0a\u53d1\u751f\u7684\u662f\u51dd\u80f6\u5316\uff08\u4e0d\u662f\u73bb\u7483\u5316\uff09\uff0c\u5f80\u5f80\u7ecf\u8fc7\u4e00\u4e2a\u4ece\u5c11\u6570\u7c92\u5b50\u805a\u96c6\u7684clusters\u5230volume-spanning 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"\u5de5\u4f5c\u7b14\u8bb0"","block_context":{"text":"\u5de5\u4f5c\u7b14\u8bb0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/personal\/%e5%b7%a5%e4%bd%9c%e7%ac%94%e8%ae%b0"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":5118,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5118","url_meta":{"origin":2739,"position":5},"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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