{"id":5743,"date":"2014-01-09T03:01:05","date_gmt":"2014-01-08T19:01:05","guid":{"rendered":"http:\/\/www.andrewsun.net\/panta_rhei\/?p=5743"},"modified":"2014-01-09T03:01:05","modified_gmt":"2014-01-08T19:01:05","slug":"%e7%89%b9%e6%80%a7%e7%b2%98%e6%95%b0","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5743","title":{"rendered":"\u7279\u6027\u7c98\u6570"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"5743\">\n<p>\u4eca\u65f6\u4eca\u65e5\uff0c\u8fd8\u6709\u591a\u5c11\u7814\u7a76\u751f\u4f7f\u7528\u4e4c\u5f0f\u7c98\u5ea6\u8ba1\u6d4b\u91cf\u7279\u6027\u7c98\u6570\uff1f\u800c\u4e14\u80fd\u591f\u6d4b\u597d\u6765\uff1f<\/p>\n<p>\u89c9\u5f97\u81ea\u5df1\u7406\u8bba\u5dee\uff0c\u6570\u5b66\u5dee\uff0c\u6ca1sense\u3002\u4e8e\u662f\u6bcf\u6bcf\u8ddf\u4eba\u8bf4\u6211\u662f\u505a\u5b9e\u9a8c\u7684\uff0c\u6211\u662fexperimental 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aria-describedby=\"caption-attachment-5744\" data-attachment-id=\"5744\" data-permalink=\"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5743\/graph1\" data-orig-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2014\/01\/Graph1.png\" data-orig-size=\"3507,2479\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Intrinsic viscosity of a gelatin sample\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Intrinsic viscosity of a gelatin sample&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2014\/01\/Graph1-1024x723.png\" src=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2014\/01\/Graph1-480x339.png\" alt=\"Intrinsic viscosity of a gelatin sample\" width=\"480\" height=\"339\" class=\"size-medium wp-image-5744\" srcset=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2014\/01\/Graph1-480x339.png 480w, https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2014\/01\/Graph1-1024x723.png 1024w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a><p id=\"caption-attachment-5744\" class=\"wp-caption-text\">Intrinsic viscosity of a gelatin sample<\/p><\/div>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 5743 -->","protected":false},"excerpt":{"rendered":"<p>\u4eca\u65f6\u4eca\u65e5\uff0c\u8fd8\u6709\u591a\u5c11\u7814\u7a76\u751f\u4f7f\u7528\u4e4c\u5f0f\u7c98\u5ea6\u8ba1\u6d4b\u91cf\u7279\u6027\u7c98\u6570\uff1f\u800c\u4e14\u80fd\u591f\u6d4b\u597d\u6765\uff1f 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S^2\\right\\rangle_\\alpha$\u3002\u5c31\u7b97\u8bba\u6587\u7684\u6b63\u6587\u6ca1\u6709\u7ed9\u51fa\u503c\uff0c\u53ea\u8981\u7ed9\u4e86\u6570\u636e\u56fe\uff0c\u4f60\u81ea\u5df1\u4e5f\u53ef\u4ee5\u4ece\u56fe\u4e2d\u5f97\u5230\u3002\u8fd9\u90e8\u5206\u7684\u539f\u7406\u6bd4\u8f83\u57fa\u672c\uff0c\u4e00\u822c\u7684\u9ad8\u5206\u5b50\u6eb6\u6db2\u7406\u8bba\u7684\u4e66\u7684\u8bb2\u8ff0\u4e0d\u4f1a\u6709\u4ec0\u4e48\u4ee4\u4eba\u56f0\u60d1\u7684\u5dee\u5f02\uff0c\u5c31\u4e0d\u5728\u6b64\u89e3\u91ca\u4e86\u3002\u5982\u679c\u627e\u5230\u6587\u732e\u505a\u4e86\u4e0d\u6b62\u4e00\u4e2a\u5206\u5b50\u91cf\u7684\u6837\u54c1\uff0c\u4f46\u662f\u6ca1\u6709\u6d4b\u5b83\u4eec\u7684\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]_\\alpha$\u56e0\u6b64\u8fd8\u662f\u4e0d\u77e5\u9053Mark\u2014Houwink\u7cfb\u6570\uff0c\u90a3\u4f60\u4ecd\u7136\u53ef\u4ee5\u65b9\u4fbf\u5730\u6839\u636e$\\left\\langle S^2\\right\\rangle^{1\/2}_\\alpha\\sim M^{\\nu_\\alpha}$\u5f97\u5230\u6587\u732e\u6761\u4ef6\u4e0b\u7684$\\nu_\\alpha$\uff08\u54ea\u6015\u6587\u732e\u6ca1\u505a\u4f60\u4e5f\u53ef\u4ee5\u7528\u5b83\u7684\u6570\u636e\u81ea\u5df1\u505a\uff0c\u8fd9\u4e00\u70b9\u5728\u4e0b\u6587\u4e2d\u5c31\u4e0d\u518d\u91cd\u590d\u63d0\u793a\u4e86\uff09\u3002 \u5982\u679c\u6587\u732e\u53ea\u505a\u4e86\u4e00\u4e2a\u5206\u5b50\u91cf\u7684\u6837\u54c1\uff0c\u81f3\u5c11\u4e5f\u5df2\u7ecf\u6709$M$\u548c$A_2$\u4e86\u3002\u8fd9\u65f6\u53ef\u4ee5\u901a\u8fc7\u6269\u5f20\u7cfb\u6570\u6765\u6c42Flory\u6307\u6570\u3002\u5982\u679c\u6269\u5f20\u7cfb\u6570\u662f\u5173\u4e8e\u5747\u65b9\u672b\u7aef\u8ddd\u7684\uff0c\u5c31\u6709\uff1a$\\alpha_\\alpha=\\left\\langle h^2\\right\\rangle^{1\/2}_\\alpha\/\\left\\langle h^2\\right\\rangle_\\theta^{1\/2}$\uff0c\u5176\u4e2d\uff0c$\\left\\langle h^2\\right\\rangle^{1\/2} = b_\\alpha N_\\alpha^\\nu_\\alpha$\uff0c$\\left\\langle h^2\\right\\rangle_\\theta^{1\/2} = b_\\alpha N_\\alpha^{1\/2}$\uff0c$b_\\alpha$\u662fKuhn\u94fe\u6bb5\u957f\u5ea6\uff0c$N_\\alpha$\u662fKuhn\u94fe\u6bb5\u7684\u4e2a\u6570\u3002$N_\\alpha=M\/\\left(M_1 b_\\alpha\\right)$\u3002\u90a3\u4e48\u5c31\u53ef\u4ee5\u7531\u6269\u5f20\u7cfb\u6570\u8ba1\u7b97Flory\u6307\u6570\u4e86\uff0c\u6240\u7f3a\u7684\u53c2\u6570\u662f$\\alpha_\\alpha$\u548c$b_alpha$\u3002 $b_\\alpha$\u4e5f\u662f\u8981\u627e\u6587\u732e\u7684\u3002\u6587\u732e\u4e00\u822c\u6709\u4e24\u79cd\u505a\u6cd5\uff1a\u4e00\u662f\u5149\u6563\u5c04\u5f97\u5230\u4e86\u6bd4\u8f83\u5bbd\u6ce2\u77e2\u8303\u56f4\u7684form factor\uff0c\u53ef\u4ee5\u770b\u5230coil\u884c\u4e3a\u5411rod\u884c\u4e3a\u7684\u8f6c\u53d8\uff0c\u8fd9\u4e2a\u8f6c\u53d8\u6240\u5bf9\u5e94\u7684\u5c3a\u5ea6\u5c31\u662f$b$\u3002\u4e8c\u662f\u901a\u8fc7\u4e00\u4e9b\u542b\u6709\u6301\u7eed\u957f\u5ea6$l_\\mathrm{p}$\u53c2\u6570\u7684\u94fe\u6a21\u578b\u6765\u62df\u5408\u6d4b\u5f97\u7684$\\left\\langle S^2\\right\\rangle$\u6570\u636e\u5f97\u5230$l_\\mathrm{p}$\u4ece\u800c\u5f97\u5230$b$\u3002\u4e0d\u7ba1\u600e\u4e48\u6837\u4f60\u8981\u67e5\u5230\u8fd9\u4e2a\u6570\u636e\u3002\u7531\u4e8e$b_\\alpha$\u7684\u503c\u662f\u4f9d\u8d56\u6761\u4ef6\uff0c\u6240\u4ee5\u6700\u597d\u662f\u540c\u4e00\u4e2a\u62a5\u9053\u91cc\u4e0d\u4ec5\u4f5c\u4e86Zimm\u56fe\uff0c\u8fd8\u628a\u5149\u5f3a\u548c\u6ce2\u77e2\u66f2\u7ebf\u7ed9\u51fa\u6765\uff0c\u7136\u540e\u4f9b\u4f60\u7528\u7b2c\u4e00\u79cd\u65b9\u6cd5\u4f30\u7b97\u51fa$b$\u3002\u6587\u732e\u81ea\u5df1\u628a\u8fd9\u4ef6\u4e8b\u505a\u4e86\u7684\u8bdd\u5c31\u66f4\u597d\u4e86\u3002 \u81f3\u4e8e\u6269\u5f20\u7cfb\u6570\uff0c\u662f\u8fd9\u6837\u5f97\u5230\u7684\uff1a\u901a\u8fc7\u6bd4\u8f83\u53e6\u4e00\u79cd\u9ad8\u5206\u5b50B\u7684$M_\\mathrm{B}$\u3001$A_{2,\\mathrm{B}}$\u548c\u6269\u5f20\u7cfb\u6570$\\alpha_{B\\beta}$\u6765\u4f30\u7b97\u5f53\u524d\u7684\u9ad8\u5206\u5b50\u5728\u6761\u4ef6\u03b1\u7684\u6269\u5f20\u7cfb\u6570$\\alpha_\\alpha$\u3002\u5177\u4f53\u5730\u8bb2\uff0c\u4f60\u9700\u8981\u67e5\u627e\u53e6\u4e00\u79cd\u7814\u7a76\u5f97\u6bd4\u8f83\u591a\u7684\u9ad8\u5206\u5b50B\u7684\u6570\u636e\uff0c\u8fd9\u6837\u5c31\u6709\u671b\u627e\u5230\u540c\u65f6\u62a5\u9053\u4e86\u5176\u5206\u5b50\u91cf$M_\\mathrm{B}$\u548c\u67d0\u6761\u4ef6\uff08\u8bb0\u4e3a\u03b2\uff09\u4e0b\u7684$A_{2,\\mathrm{B}}$\u548c\u6269\u5f20\u6bd4$\\alpha_\\mathrm{B\\beta}$\u7684\u6587\u732e\u3002\u7136\u540e\uff0c\u6839\u636eFlory\u7684\u6269\u5f20\u7cfb\u6570\u5173\u7cfb\u5f0f$\\alpha^5-\\alpha^3=2C_\\mathrm{M}\\psi\\left(1-\\Theta\/T\\right)M^{1\/2}$\u53ef\u77e5\uff0c\u4e0d\u540c\u9ad8\u5206\u5b50\u5728\u540c\u4e00\u7b2c\u4e8c\u7ef4\u5229\u7cfb\u6570\u4e0b\u7684$\\left(\\alpha^5-\\alpha^3\\right)\/M^{1\/2}$\u503c\u662f\u5dee\u522b\u5f88\u5c0f\u7684\u3002\u4e8e\u662f\u4f60\u5c31\u53ef\u4ee5\u901a\u8fc7$\\frac{\\alpha_\\alpha^5-\\alpha_\\alpha^3}{M^{1\/2}}=\\frac{\\alpha_\\mathrm{B\\beta}^5-\\alpha_\\mathrm{B\\beta}^3}{M_\\mathrm{B}^{1\/2}}$\u6765\u8ba1\u7b97\u4f60\u8981\u7684\u6269\u5f20\u7cfb\u6570$\\alpha_\\alpha$\u4e86\u3002\u6709\u4e86$\\alpha_\\alpha$\u548c$b_\\alpha$\uff0c\u5c31\u53ef\u4ee5\u6c42$\\nu_\\alpha$\u4e86\u3002 \u77e5\u9053\u4e86$\\nu_\\alpha$\uff0c\u4e0b\u4e00\u6b65\u5c31\u662f\u8ba1\u7b97\u6211\u4eec\u624b\u5934\u4e0a\u7684\u6837\u54c1\u7684\u5206\u5b50\u91cf$M^\\prime$\u3002\u8fd9\u65f6\u5c31\u9700\u8981\u4f7f\u7528\u7279\u6027\u7c98\u6570\u7684\u6570\u636e\u4e86\u3002\u4f60\u9700\u8981\u518d\u4ece\u6587\u732e\u4e2d\u627e\u5230\u76f8\u540c\u6761\u4ef6\u4e0b\u7684\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]_\\alpha$\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u4f60\u4ece\u6587\u732e\u4e2d\u4e00\u5171\u8981\u627e\u5230\u5bf9\u67d0\u5206\u5b50\u91cf\u4e3a$M$\u7684\u6837\u54c1\u5728\u540c\u4e00\u6761\u4ef6\u03b1\u4e0b\u7684\uff1a$b_\\alpha$\u548c$\\left[\\eta\\right]_\\alpha$\uff0c\u6309\u4e0a\u8ff0\u7684\u8ba1\u7b97\u65b9\u6cd5\u7b97\u51fa$\\nu_\\alpha$\u3002\u540c\u65f6\uff0c\u4f60\u624b\u5934\u4e0a\u7684\u6837\u54c1\u4e5f\u8981\u81ea\u5df1\u62ff\u53bb\u5728\u76f8\u540c\u7684\u6761\u4ef6\u4e0b\u6d4b\u7279\u6027\u7c98\u6570\uff0c\u5f97\u5230$\\left[\\eta\\right]^\\prime_\\alpha$\u3002\u8fd9\u65f6\u6839\u636eFlory\u2014Fox\u5173\u7cfb\u6709$\\left[\\eta\\right]_\\alpha\/\\left[\\eta\\right]^\\prime_\\alpha=\\left(M\/M^\\prime\\right)^{\\left(3\\nu_\\alpha-1\\right)}$\uff0c\u4ece\u800c\u5f97\u5230\u4f60\u624b\u5934\u4e0a\u6837\u54c1\u7684\u5206\u5b50\u91cf$M^\\prime$\u3002 \u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u5982\u679c\u8981\u4f30\u7b97\u53e6\u4e00\u79cd\u6eb6\u5242\u6216\u6e29\u5ea6\u6761\u4ef6\uff08\u8bb0\u4e3a\u03b3\uff09\u4e0b\u7684\u5404\u79cd\u5c3a\u5bf8\uff0c\u5c31\u5fc5\u987b\u77e5\u9053\u65b0\u6761\u4ef6\u4e0b\u8fd9\u4e00\u9ad8\u5206\u5b50\u6837\u54c1\u7684\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]_\\gamma$\u548c\u5206\u5b50\u91cf$M$\uff0c\u8fd9\u540c\u6837\u8981\u4ece\u6587\u732e\u91cc\u627e\u3002\u7b80\u5355\u5730\u8bf4\uff0c\u5c31\u662f\u4f60\u60f3\u83b7\u5f97\u4f60\u624b\u5934\u4e0a\u6837\u54c1\u6761\u4ef6\u03b3\u7684\u4fe1\u606f\uff0c\u4f60\u5c31\u8981\u627e\u5230\u6709\u4eba\u4e5f\u5728\u6761\u4ef6\u03b3\u4e0b\u505a\u8fc7\u540c\u79cd\u9ad8\u5206\u5b50\u7684\u5b9e\u9a8c\uff0c\u5426\u5219\u5c31\u6ca1\u620f\u4e86\u3002\u5982\u679c\u6709\uff0c\u90a3\u4f60\u53ea\u9700\u8981\u518d\u5728\u6761\u4ef6\u03b3\u4e0b\u6d4b\u4e00\u6b21\u624b\u5934\u4e0a\u6837\u54c1\u7684\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]^\\prime_\\gamma$\uff0c\u5c31\u53ef\u4ee5\u7c7b\u4f3c\u5730\u7528\u5173\u7cfb$\\left[\\eta\\right]_\\gamma\/\\left[\\eta\\right]^\\prime_\\gamma=\\left(M\/M^\\prime\\right)^{\\left(3\\nu_\\gamma-1\\right)}$\u5f97\u5230\u65b0\u6761\u4ef6\u7684Flory\u6307\u6570\u3002\u7136\u540e\u53ef\u4ee5\u5229\u7528Flory\u2014Fox\u5173\u7cfb\u672c\u8eab\u5f97\u5230\u65b0\u6761\u4ef6\u4e0b\u7684Kuhn\u94fe\u6bb5\u6570\u91cf$N^\\prime_\\gamma$\u548c\u957f\u5ea6$b_\\gamma$\uff0c\u8fdb\u800c\u5f97\u5230\u5747\u65b9\u672b\u7aef\u8ddd$\\left\\langle h^2\\right\\rangle_\\gamma^\\prime$\u3002 \u6eb6\u80c0\u94fe\u7684\u5747\u65b9\u56de\u8f6c\u534a\u5f84$\\left\\langle S^2\\right\\rangle^{1\/2}$\u4e0e\u5747\u65b9\u672b\u7aef\u8ddd$\\left\\langle h^2\\right\\rangle^{1\/2}$\u4e4b\u95f4\u6ca1\u6709\u7b80\u5355\u7684\u7cbe\u786e\u5173\u7cfb\u3002\u4f46\u4ecd\u7136\u53ef\u4ee5\u6309\u6587\u672b\u5173\u4e8e\u6269\u5f20\u7cfb\u6570\u7684\u8865\u5145\u8bf4\u660e\u53ef\u4ee5\u4f5c\u6b64\u6362\u7b97\uff0c\u5f97\u5230\u4f60\u624b\u5934\u4e0a\u6837\u54c1\u7684\u5747\u65b9\u56de\u8f6c\u534a\u5f84$\\left\\langle S^2\\right\\rangle^\\prime_\\gamma$\u3002\u6709\u4e86\u5747\u65b9\u56de\u8f6c\u534a\u5f84\uff0c\u4f60\u5c31\u53ef\u4ee5\u8ba1\u7b97\u65b0\u6761\u4ef6\u4e0b\u5f53\u524d\u6837\u54c1\u7684\u5f88\u591a\u4fe1\u606f\uff0c\u4f8b\u5982\u534a\u6d53\u6eb6\u6db2\u7684\u63a5\u89e6\u6d53\u5ea6$c^*=3M\/\\left(4\\pi N_\\mathrm{A}\\left\\langle S^2\\right\\rangle^{1\/2}\\right)$\uff0c\u4ee5\u53ca\u76f8\u5173\u957f\u5ea6\uff08blob size\uff09$\\xi=\\left\\langle S^2\\right\\rangle^{1\/2}\\left(c\/c^*\\right)^{-\\nu\/\\left(3\\nu-1\\right)}$\u3002\u6ce8\u610f\u5f0f\u4e2d\u4f9d\u8d56\u6761\u4ef6\u7684\u91cf\u8981\u53d6\u540c\u4e00\u6761\u4ef6\u4e0b\u7684\u503c\u3002 \u5bf9\u4e8e\u9ad8\u5206\u5b50\u6eb6\u6db2\u4ea4\u8054\u5f62\u6210\u7684\u51dd\u80f6\uff0c\u4e5f\u53ef\u4ee5\u5728\u540c\u6837\u7684\u6eb6\u5242\u548c\u6e29\u5ea6\uff08\u5982\u6761\u4ef6\u03b3\uff0c\u4e0d\u518d\u6807\u793a\u4e86\uff09\u4e0b\u6d4b\u91cf\u5e73\u53f0\u6a21\u91cf$G_\\mathrm{p}$\uff0c\u7136\u540e\u7528Nijenhuis\u7684\u5f0f\u5b50\uff0c\u5f97\u5230\u4ea4\u8054\u70b9\u95f4\u5206\u5b50\u91cf$M_\\mathrm{c}$\u3002 \\begin{equation}G_\\mathrm{p}=\\frac{2cRT}{M}\\left(\\frac{M}{M_\\mathrm{c}}\\frac{f-1}{f}-1\\right)\\left(1-w_\\mathrm{s}\\right)\\end{equation}\\begin{equation}\\frac{M}{M_\\mathrm{c}}=-\\frac{\\mathrm{ln}w_\\mathrm{s}}{1-w_\\mathrm{s}}\\frac{1-w_\\mathrm{s}^{0.5f}}{1-w_\\mathrm{s}^{0.5f-1}}\\end{equation} $M$\u662f\u9ad8\u5206\u5b50\u7684\u5206\u5b50\u91cf\uff0c$c$\u662f\u9ad8\u5206\u5b50\u6d53\u5ea6\uff08\u5355\u4f4d\u4f53\u79ef\u7684\u9ad8\u5206\u5b50\u8d28\u91cf\uff09\u3002$f$\u662f\u4ea4\u8054\u70b9\u7684\u5b98\u80fd\u5ea6\uff0c$w_\\mathrm{s}$\u662f\u51dd\u80f6\u4e2d\u7684sol fraction\u3002 \u5f97\u5230\u4e86\u4ea4\u8054\u70b9\u95f4\u5e73\u5747\u5206\u5b50\u91cf\uff0c\u5c31\u53ef\u4ee5\u901a\u8fc7\u4e4b\u524d\u5f97\u5230\u7684\u540c\u6837\u6761\u4ef6\u4e0b\u7684\u6837\u54c1\u7684$M$\u3001$M_1$\u3001$\\nu$\u3001$b$\u8ba1\u7b97\u4ea4\u8054\u70b9\u95f4\u5e73\u5747Kuhn\u94fe\u6bb5\u6570$N_\\mathrm{c}$\uff0c\u8fdb\u800c\u5047\u8bbe\u7f51\u773c\u5c3a\u5bf8\u8fd1\u4f3c\u7b49\u4e8e\u4ea4\u8054\u70b9\u95f4\u94fe\u6bb5\u7684\u5747\u65b9\u672b\u7aef\u8ddd\uff0c\u53ef\u5f97\u7f51\u773c\u5c3a\u5bf8$\\xi=bN_\\mathrm{c}^\\nu$\u3002 \u529f\u80fd\u6027\u6c34\u51dd\u80f6\u7684\u6eb6\u5242\u6761\u4ef6\u5343\u53d8\u4e07\u5316\u3002\u6e29\u5ea6\u4f9d\u8d56\u6027\u5c1a\u4e14\u6709\u70ed\u529b\u5b66\u4e00\u822c\u5173\u7cfb\u53ef\u4f9d\u8d56\uff0c\u4f46\u662f\u4e0d\u540cpH\u6216\u76d0\u7684\u79cd\u7c7b\u3001\u6d53\u5ea6\uff0c\u4e0d\u53ef\u80fd\u90fd\u6709\u4eba\u505a\u8fc7\u5149\u6563\u5c04\u5b9e\u9a8c\u3002\u54ea\u6015\u81ea\u5df1\u6709\u5149\u6563\u5c04\uff0c\u4e5f\u4e0d\u53ef\u80fd\u53d8\u4e00\u4e0b\u76d0\u6d53\u5ea6\u5c31\u6d4b\u4e00\u6b21\u6216\u8005\u641e\u51fa\u4ec0\u4e48\u5de5\u4f5c\u66f2\u7ebf\u6765\u3002\u8fd9\u65f6\u6211\u4eec\u8981\u6709\u4e00\u79cd\u4e0d\u90a3\u4e48\u7ea0\u7ed3\u7684\u65b9\u5f0f\u3002\u5728\u5904\u7406\u8fd9\u79cd\u95ee\u9898\u7684\u65f6\u5019\uff0c\u53ea\u80fd\u628a\u6761\u4ef6\u4f9d\u8d56\u7684\u53c2\u6570\u90fd\u5f53\u4f5c\u53d8\u91cf\uff0c\u770b\u80fd\u4e0d\u80fd\u641e\u4e00\u4e9b\u62df\u5408\u4e86\u3002 \u5173\u4e8e\u6269\u5f20\u7cfb\u6570\u7684\u8865\u5145\u8bf4\u660e \u524d\u9762\u63d0\u5230\u5bf9\u4e8e\u6eb6\u80c0\u94fe\u7684\u5747\u65b9\u56de\u8f6c\u534a\u5f84$\\left\\langle S^2\\right\\rangle^{1\/2}$\u4e0e\u5747\u65b9\u672b\u7aef\u8ddd$\\left\\langle h^2\\right\\rangle^{1\/2}$\u4e4b\u95f4\u6ca1\u6709\u7b80\u5355\u7684\u7cbe\u786e\u5173\u7cfb\uff0c\u6269\u5f20\u7cfb\u6570\u4e5f\u9700\u8981\u5206\u5f00\u5b9a\u4e49\u3002\u5747\u65b9\u672b\u7aef\u8ddd\u7684\u6269\u5f20\u7cfb\u6570\u662f$\\alpha_h\\equiv\\left\\langle h^2\\right\\rangle^{1\/2}\/\\left\\langle h^2\\right\\rangle_\\mathrm{\\theta} ^{1\/2}$\uff1b\u5747\u65b9\u56de\u8f6c\u534a\u5f84\u7684\u6269\u5f20\u7cfb\u6570\u662f$\\alpha_S\\equiv\\left\\langle S^2\\right\\rangle^{1\/2}\/\\left\\langle\u2026","rel":"","context":"In 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Fluids\u5c31\u662f\u4e00\u672c\u5f88\u597d\u7684\u6559\u6750\u3002\u5e94\u8be5\u719f\u8bfb\u8fd9\u672c\u4e66\uff0c\u9996\u5148\u6e05\u695a\u5404\u7c7b\u4f53\u7cfb\u7684\u7ed3\u6784\uff08structure\uff09\u548c\u52a8\u6001\uff08dynamics\uff09\uff0c\u7136\u540e\u518d\u4e86\u89e3\u4ed6\u4eec\u5982\u4f55\u5f71\u54cd\u6d41\u53d8\u5b66\u6027\u8d28\uff08again\uff0c\u5206\u522b\u662f\u6d41\u52a8\u6027\u548c\u7ebf\u6027\u7c98\u5f39\u6027\uff09\u3002\u90a3\u4e48\uff0c\u9047\u5230\u5b9e\u9645\u7684\u6d4b\u91cf\u6837\u54c1\u7684\u65f6\u5019\uff0c\u624d\u80fd\u72ec\u7acb\u601d\u8003\uff1a\u5148\u8bd5\u56fe\u628a\u6837\u54c1\u5f52\u7c7b\u4e3aLarson\u4e66\u4e2d\u7684\u67d0\u79cd\u4f53\u7cfb\uff0c\u7136\u540e\u6839\u636e\u8fd9\u79cd\u4f53\u7cfb\u7684\u4e00\u822c\u6a21\u578b\u53bb\u4f30\u8ba1\u5b83\u7684\u6d41\u52a8\u6027\u548c\u7ebf\u6027\u7c98\u5f39\u6027\u5e94\u8be5\u662f\u600e\u6837\u7684\uff0c\u518d\u53bb\u6d4b\u91cf\u3002\u8fd9\u76f8\u5f53\u4e8e\u662f\u5148\u6709hypothesis\uff0c\u518d\u53bb\u505aexperiment\u3002\u5f88\u591a\u521d\u5b66\u8005\u5c31\u662f\u5728hypothesis\u5b8c\u5168\u7a7a\u767d\u7684\u60c5\u51b5\u4e0b\u4e71\u6d4b\uff0c\u5f97\u51fa\u7684\u7ed3\u679c\u4e5f\u5c31\u53ea\u80fd\u4e71\u89e3\u8bfb\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":9291,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9291","url_meta":{"origin":5743,"position":3},"title":"\u201c\u5fae\u6d41\u53d8\u201d\u672f\u8bed\u53f2","author":"Andrew","date":"2025\u5e7410\u670819\u65e5","format":false,"excerpt":"\u201c\u5fae\u6d41\u53d8\u201d\uff08microrheology\uff09\u5728\u6700\u8fd1\u51e0\u5e74\u7684\u6587\u732e\u4e2d\u662f\u4e13\u6307III. \u901a\u8fc7\u80f6\u4f53\u7c92\u5b50\u7684\u70ed\u8fd0\u52a8\u7edf\u8ba1\u89c4\u5f8b\u53cd\u63a8\u60ac\u6d6e\u4ecb\u8d28\u7684\u6d41\u53d8\u6027\u8d28\u7684\u4e00\u79cd\u5b9e\u9a8c\u7814\u7a76\u3002\u8fd9\u4e5f\u662f\u6211\u73b0\u5728\u7814\u7a76\u65b9\u5411\u4e4b\u4e00\u3002\u4f46\u662f\uff0c\u8fd9\u4e2a\u672f\u8bed\u6700\u65e9\u7684\u610f\u4e49\u8ddf\u73b0\u5728\u6709\u4e9b\u533a\u522b\u3002 \u6839\u636e\u6211\u67e5\u5230\u7684\u7ed3\u679c\uff0c\u201cmicrorheology\u201d\u4e00\u8bcd\u6700\u65e9\u51fa\u73b0\u5728M. Reiner\u7684\u6d41\u53d8\u5b66\u8bb2\u4e49\uff08Markus Reiner (1943), Ten Lectures on Theoretical Rheology, Rubin Mass\uff09\u4e2d\u7684\u7b2c\u4e03\u8bb2\u3002\u8fd9\u4e2a\u5957\u8bb2\u4e49\u540e\u6765\u5206\u522b\u57281949\u5e74\u548c1960\u5e74\u51fa\u4e86\u7b2c\u4e8c\u548c\u7b2c\u4e09\u7248\u3002\u7b2c\u4e09\u7248\u6709\u4e2d\u8bd1\u672c\uff1aM. \u96f7\u8bb7\u8457\uff0c\u90ed\u6709\u4e2d\u7b49\u8bd1\u300a\u7406\u8bba\u6d41\u53d8\u5b66\u8bb2\u4e49\u300b\uff0c\u7531\u79d1\u5b66\u51fa\u7248\u793e\u4e8e1965\u51fa\u7248\u3002\u5728\u5f53\u65f6\u8fd9\u4e2a\u8bcd\u5927\u6982\u662f\u6307I. \u4ece\u5fae\u89c2\u7ed3\u6784\u63a8\u51fa\u5b8f\u89c2\u7cfb\u7edf\u6d41\u53d8\u5b66\u6027\u8d28\u7684\u7406\u8bba\u7814\u7a76\uff0c\u4f3c\u4e4e\u662f\u7528\u4e8e\u4e0e\u57fa\u4e8e\u8fde\u7eed\u4ecb\u8d28\u5047\u5b9a\u7684\u7406\u8bba\u76f8\u533a\u522b\u3002\u540e\u8005\u88ab\u79f0\u4f5c\u201cmacrorheology\u201d\u3002 \u5927\u6982\u76f8\u540c\u7684\u65f6\u671f\uff0c\u80f6\u4f53\u7c92\u5b50\u60ac\u6d6e\u6db2\u6d41\u53d8\u5b66\u7684\u5148\u9a71Stanley G. Mason\uff081914-1987\uff09\u5927\u91cf\u4f7f\u7528\u8fd9\u4e2a\u8bcd\u6765\u63cf\u8ff0\u4ed6\u7814\u7a76\u7684\u95ee\u9898\u3002\u5173\u4e8eMason\u7ecf\u5386\u7684\u4e00\u4e9b\u8d44\u6599\u53ef\u89c1\u4ed6\u7684\u81ea\u8ff0\u548c\u540e\u8f88\u5199\u7684appreciation\u3002Mason\u57281950\u5e74\u4ee3\u5c31\u5f00\u59cb\u6b63\u5f0f\u7814\u7a76\u60ac\u6d6e\u7c92\u5b50\u7684\u6d41\u4f53\u52a8\u529b\u5b66\u3002\u4ed6\u521b\u7acb\u7684\u7814\u7a76\u65b9\u6cd5\u662fII. \u901a\u8fc7\u5b9e\u9a8c\u89c2\u5bdf\u7c92\u5b50\u5468\u56f4\u7684\u6d41\u573a\u6765\u9a8c\u8bc1\u6d41\u4f53\u52a8\u529b\u5b66\u7406\u8bba\u3002\u56e0\u6b64\uff0c\u5230\u4e86Mason\u8fd9\u91cc\uff0c\u201cmicrorheology\u201d\u7684\u610f\u4e49\u5c31\u4ece\u7406\u8bba\u6a21\u578b\u53d8\u4e3a\u5b9e\u9a8c\u624b\u6bb5\u3002Mason\u4e5f\u63a8\u5bfc\u8fc7\u80f6\u4f53\u6d41\u53d8\u5b66\u7406\u8bba\uff0c\u4f46\u4ed6\u548c\u4ed6\u7684\u5b66\u751f\u4e0d\u7528\u201cmicrorheology\u201d\u4e00\u8bcd\u63cf\u8481\u8fd9\u4e9b\u7406\u8bba\u5de5\u4f5c\u3002 Mason\u7684\u53ca\u5176\u5b66\u751f\u7684\u540e\u7eed\u5de5\u4f5c\u4e00\u76f4\u6301\u7eed\u52301970\u5e74\u4ee3\u3002\u5728\u8fd9\u6bb5\u65f6\u95f4\uff0c\u201cmicrorheology\u201d\u4e00\u8bcd\u51e0\u4e4e\u53ea\u51fa\u73b0\u5728\u4ed6\u4eec\u53d1\u8868\u7684\u5de5\u4f5c\u5f53\u4e2d\u3002\u4e5f\u6709\u96f6\u661f\u613f\u610f\u4f7f\u7528Reiner\u8bb2\u4e49\u7684\u8001\u610f\u4e49\u7684\u8bba\u6587\uff0c\u5305\u62ec\u51af\u5143\u6862\u5148\u751f\u30021970\u5e74\u4ee3\uff0c\u201cmicrorheology\u201d\u4e00\u8bcd\u88ab\u8840\u6db2\u6d41\u53d8\u5b66\u9886\u57df\u5927\u91cf\u91c7\u7528\uff0c\u8fd9\u4e5f\u4ecd\u662f\u5f52\u56e0\u4e8eMason\u7684\u5de5\u4f5c\u5bf9\u8fd9\u4e00\u9886\u57df\u7684\u5f71\u54cd\u529b\u3002 \u6211\u80fd\u627e\u5230\u7684\u7b2c\u4e00\u4e2a\u610f\u4e49\u53d8\u6210\u73b0\u5728\u7684\u7b2cIII\u79cd\u7684\u6700\u65e9\u8bba\u6587\u662f1985\u5e74\u7684\u4e00\u7bc7\u8bba\u6587\u3002 \u4e0e\u201cmicrorheology\u201d\u4e00\u8bcd\u5341\u5206\u76f8\u5173\u7684\u8fd8\u6709\u201cmicroviscosity\u201d\u3002\u8fd9\u4e2a\u8bcd\u53cd\u800c\u6700\u65e9\u5c31\u8fbe\u5230\u4e86\u4eca\u5929\u5bf9microrheology\u5e94\u8be5\u8fbe\u5230\u7684\u7406\u89e3\u3002\u57281929\u5e74\u7684\u7b2c\u4e00\u5c4a\u7f8e\u56fd\u6d41\u53d8\u5b66\u5e74\u4f1a\u4e0a\uff0cE. Kraemer & R. Williamson\u533a\u5206\u4e86\u51e0\u4e2a\u5c42\u6b21\u7684\u201c\u6469\u64e6\u201d\uff08friction\uff09\u3002\u4e00\u662f\u5b8f\u89c2\u4f53\u7cfb\u7684\u7c98\u5ea6\uff0c\u4e8c\u662f\u7c92\u5b50\u4e0e\u5468\u56f4\u6d41\u573a\u754c\u9762\u5904\u7684\u6469\u64e6\uff0c\u4e09\u662f\u7c92\u5b50\u5f62\u53d8\u7684\u5185\u90e8\u6469\u64e6\u3002\u201cmicroviscosity\u201d\u6307\u7684\u5c31\u662f\u5728IV. \u5fae\u89c2\u5c3a\u5ea6\u4e0b\u7684\u7c98\u5ea6\u2014\u2014\u5b83\u5e38\u5e38\u4e0e\u5b8f\u89c2\u5c3a\u5ea6\u4e0b\u5bf9\u540c\u4e00\u7cfb\u7edf\u6d4b\u5f97\u7684\u7c98\u5ea6\u660e\u663e\u4e0d\u540c\u3002\u8fd9\u4ef6\u4e8b\u65e9\u5728\u201c\u80f6\u4f53\u201d\uff08colloid\uff09\u4e00\u8bcd\u7684\u675c\u64b0\u8005Thomas Graham\u57281861\u5e74\u7684\u7814\u7a76\u4e2d\u5c31\u53d1\u73b0\u4e86\u3002\u76d0\u5728\u660e\u80f6\u6216\u743c\u8102\u51dd\u80f6\u4e2d\u7684\u6269\u6563\u6bd4\u5c11\u6162\u4e0d\u4e86\u591a\u5c11\uff0c\u4f46\u524d\u8005\u7684\u7c98\u5ea6\u6bd4\u6c34\u9ad8\u597d\u51e0\u4e2a\u6570\u91cf\u7ea7\u3002\u56e0\u6b64\u8fd9\u4ee4\u4eba\u76f8\u4fe1\uff0c\u5fae\u89c2\u5c3a\u5ea6\u7269\u4f53\u611f\u53d7\u5230\u7684\u6db2\u4f53\u7684\u7c98\u5ea6\u662f\u8ddf\u5b8f\u89c2\u6d4b\u91cf\u503c\u4e0d\u540c\u7684\u3002\u5177\u4f53\u5728\u8fd9\u4e00\u5b9e\u9a8c\u73b0\u8c61\u4e2d\uff0c\u7814\u7a76\u8005\u751a\u81f3\u662f\u901a\u8fc7\u6269\u6563\u7684\u6548\u679c\u6765\u7406\u89e3\u7c98\u5ea6\u3002\u8fd9\u662f\u5728Einstein--Stokes\u5173\u7cfb\u7684\u7406\u8bba\u57fa\u7840\u4e0a\u7684\u8ba4\u8bc6\u89d2\u5ea6\uff0c\u628a\u5b9e\u9a8c\u7ed3\u679c\u5173\u4e8eEinstein--Stokes\u5173\u7cfb\u7684\u504f\u79bb\u5f53\u4f5c\u7c98\u5ea6\u4e0d\u540c\u3002\u4eca\u5929\u6211\u4eec\u8fd8\u6709\u53e6\u4e00\u79cd\u505a\u6cd5\uff0c\u90a3\u5c31\u662f\u628a\u5b9e\u9a8c\u7ed3\u679c\u5173\u4e8eEinstein--Stokes\u5173\u7cfb\u7684\u504f\u79bb\u5f53\u4f5c\u534a\u5f84\u4e0d\u540c\uff0c\u5b9a\u4e49\u51fa\u201c\u6d41\u4f53\u52a8\u529b\u5b66\u534a\u5f84\u201d\u3002\u8fd9\u4e24\u54b1\u505a\u6cd5\u7684\u4eba\u4e4b\u95f4\u5f88\u5c11\u770b\u5230\u6709\u4ea4\u53c9\u7684\uff0c\u66f4\u522b\u8bf4\u6709\u4eba\u53bbreconcile\u8fd9\u4e24\u8005\u3002\u8fd9\u53ef\u80fd\u662f\u7531\u4e8e\u5b9e\u9a8c\u65b9\u6cd5\u4e0d\u540c\u3002\u4e00\u6d3e\u4eba\u6d4b\u91cf\u5b8f\u89c2\u7cfb\u7edf\u7684\u7c98\u5ea6\uff0c\u548c\u5206\u5b50\u7684\u6269\u6563\u7cfb\u6570\u3002\u7531\u4e8e\u5206\u5b50\u7ed3\u6784\u662f\u660e\u786e\u7684\uff0c\u8fd9\u6d3e\u4eba\u662f\u4e0d\u4f1a\u6000\u7591\u5206\u5b50\u8fd8\u6709\u53e6\u4e00\u79cd\u201c\u534a\u5f84\u201d\u3002\u53e6\u4e00\u6d3e\u4eba\u7528\u52a8\u6001\u5149\u6563\u5c04\u6d4b\u80f6\u4f53\u7c92\u5b50\u5728\u60ac\u6d6e\u6db2\u4e2d\u6216\u805a\u5408\u7269\u5728\u6eb6\u6db2\u4e2d\u7684\u534a\u5f84\uff0c\u5e76\u4e0e\u7535\u5b50\u663e\u5fae\u955c\u6216\u89d2\u5ea6\u4f9d\u8d56\u6563\u5c04\u7684\u7ed3\u679c\uff08\u5747\u65b9\u56de\u8f6c\u534a\u5f84\uff09\u76f8\u6bd4\u8f83\u3002\u7279\u522b\u662f\u5bf9\u4e8e\u805a\u5408\u7269\u8bd5\u6837\uff0c\u7531\u4e8e\u5176\u5206\u5b50\u5c3a\u5bf8\u53ea\u6709\u5e73\u5747\u6982\u5ff5\uff0c\u5728\u6eb6\u6db2\u4e2d\u7684\u5e73\u5747\u5c3a\u5bf8\u8fd8\u53d7\u6eb6\u5242\u6eb6\u8d28\u76f8\u4e92\u4f5c\u7528\u4ee5\u53ca\u6d41\u4f53\u52a8\u529b\u5b66\u76f8\u4e92\u4f5c\u7528\u7684\u5f71\u54cd\u3002\u800c\u6269\u6563\u7cfb\u6570\u88ab\u9690\u542b\u5728\u52a8\u6001\u5149\u6563\u5c04\u7684\u57fa\u672c\u539f\u7406\u5f53\u4e2d\u3002","rel":"","context":"In 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