{"id":3418,"date":"2011-07-21T23:58:56","date_gmt":"2011-07-21T15:58:56","guid":{"rendered":"http:\/\/www.andrewsun.net\/panta_rhei\/?p=3418"},"modified":"2011-07-22T23:52:45","modified_gmt":"2011-07-22T15:52:45","slug":"rheometry-of-laponitepeo-suspensions","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/3418","title":{"rendered":"Rheometry of Laponite\/PEO suspensions"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"3418\">\n<p>A full lest of rheometric investigation of Laponite\/PEG suspension. Parts of the tasks have been submitted or published.<\/p>\n<h1>Observation during preshear<\/h1>\n<h3>Comparison of different shear rates<\/h3>\n<p>Steady shear flow [math]\\eta[\/math] vs [math]\\dot{\\gamma}[\/math]. Procedure: steady preshear at [math]\\dot{\\gamma}[\/math] = 200 s<sup>-1<\/sup> for 200s, delay for 800s, steady state flow test.<\/p>\n<p>Samples: L2S5, L2S5P35k0.1, 0.25, 0.63, 0.8, 1.0<\/p>\n<p>Instrument: AR-G2<\/p>\n<h3>Comparison of different shear method: osc. vs cont.<\/h3>\n<p>Whether [math]\\gamma_0\\omega=\\dot{\\gamma}[\/math], by checking the Cox-Merz rule<\/p>\n<p>Sample: L2S5, L2S5P35k0.63<\/p>\n<p>Instrument: AR-G2<\/p>\n<h1>Aging<\/h1>\n<h2>Ageing under SAOS<\/h2>\n<h3>Comparison of different preshear rates<\/h3>\n<p>Procedure: Steady preshear at [math]\\dot{\\gamma}[\/math] = 1, 2.5, 6.3, 16, 40, 63, 160, 200 s<sup>-1<\/sup> for 200 s, oscillatory time sweep.<\/p>\n<p>Samples: L2S5, L2S5P35k0.1, 0.25, 0.63, 0.8, 1.0<\/p>\n<p>Instrument: AR-G2<\/p>\n<h3>Comparison of different preshear method: osc. vs cont.<\/h3>\n<p>Procedure: preshear at [math]\\dot{\\gamma}[\/math] = 200 s<sup>-1<\/sup> or <em>\u03b3<\/em> = 200 %, <em>\u03c9<\/em> = 10 rad\/s, for 200 s, oscillatory frequency sweep.<\/p>\n<p>Samples: L2S5, L2S5P35k0.63<\/p>\n<p>Instrument: AR-G2<\/p>\n<h3>Effect of PEG concentration<\/h3>\n<p>Submitted.<\/p>\n<h3>Time-resolved viscoelastic property<\/h3>\n<p>Procedure: steady preshear at [math]\\dot{\\gamma}[\/math] = 200 s<sup>-1<\/sup> for 200 s, oscillatory time sweep at \u03c9 = 1, 1.6, 2.5, 4, 6.3, 10, 16, 25, 40, 63 rad\/s for 400s.<\/p>\n<p>Samples: L2S5P35k0.1, 0.25, 0.63, 0.8, 1.0<\/p>\n<p>Instrument: AR-G2<\/p>\n<h2>Aging under LAOS<\/h2>\n<p>Procedure: steady preshear at [math]\\dot{\\gamma}[\/math] = 200 s<sup>-1<\/sup> for 200 s, dynamic time sweep at <em>\u03c9<\/em> = 6.283 rad\/s and <em>\u03b3<\/em><sub>0<\/sub> = 1 ~ 25 %, focusing on the yielding strain amplitude region.<\/p>\n<p>Samples: L2S5P35k0.063, 0.1, 0.25, 0.4, 0.63, 1.0<\/p>\n<p>Instrument: ARES<\/p>\n<h1>Aged gel<\/h1>\n<h2>Steady LAOS<\/h2>\n<p>Published.<\/p>\n<h2>Yielding under LAOS<\/h2>\n<p>References: <i>PRL<\/i> <b>2011<\/b>, <i>106<\/i>, 248303. <i>Soft Matter<\/i> <b>2010<\/b>, <i>6<\/i>, 3482.<br \/>\nProcedure: steady preshear at [math]\\dot{\\gamma}[\/math] = 200 s<sup>-1<\/sup> for 200s, delay 800s, arbitrary waveshape test at <em>\u03c9<\/em> = 6.283 rad\/s and <em>\u03b3<\/em><sub>0<\/sub> = 10 ~ 100 % focusing on the yielding regime.<\/p>\n<p>Samples: L2S5P35k0.1, 0.25, 0.4, 0.63, 0.8, 1.0<\/p>\n<p>Instrument: ARES<\/p>\n<h1>Schedule<\/h1>\n<p><iframe loading=\"lazy\" style=\"border-width: 0;\" src=\"https:\/\/www.google.com\/calendar\/embed?showNav=0&amp;showPrint=0&amp;showTabs=0&amp;showCalendars=0&amp;showTz=0&amp;height=600&amp;wkst=1&amp;bgcolor=%23FFFFFF&amp;src=5e8t8o9cr4qmopn8bb2604lkjg%40group.calendar.google.com&amp;color=%23A32929&amp;src=nt8tt12jh8mfuih0domgbnj9b4%40group.calendar.google.com&amp;color=%23528800&amp;ctz=Asia%2FShanghai\" frameborder=\"0\" scrolling=\"no\" width=\"600\" height=\"600\"><\/iframe><\/p>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 3418 -->","protected":false},"excerpt":{"rendered":"<p>A full lest of rheometric investigation of Laponite\/PEG suspension. Parts of the tasks have been submitted or published. Observation during preshear Comparison of different shear rates Steady shear flow [math]\\eta[\/math] vs [math]\\dot{\\gamma}[\/math]. Procedure: steady preshear at [math]\\dot{\\gamma}[\/math] = 200 s-1 for 200s, delay for 800s, steady state flow test. Samples: L2S5, L2S5P35k0.1, 0.25, 0.63, 0.8, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[264],"tags":[],"class_list":["post-3418","post","type-post","status-publish","format-standard","hentry","category-264"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p1aPvF-T8","jetpack-related-posts":[{"id":4296,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/4296","url_meta":{"origin":3418,"position":0},"title":"\u91cd\u65b0\u8003\u8651Laponite\u7c92\u5b50\u95f4\u4f5c\u7528\u52bf\u80fd","author":"Andrew","date":"2011\u5e7411\u67086\u65e5","format":false,"excerpt":"\u9000\u56de\u7684\u5ba1\u7a3f\u610f\u89c1\u53cd\u6620\u7a3f\u5b50\u7684\u6700\u5927\u95ee\u9898\u5728\u4e8e\u5bf9Laponite\u7c92\u5b50\u76f8\u4e92\u4f5c\u7528\u7684\u8003\u8651\u4e0d\u5468\u3002\u9700\u8981\u5bf9\u539f\u672c\u7684model\u8fdb\u884c\u6bd4\u8f83\u5927\u7684\u4fee\u6539\u3002 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\u7531\u4e8e\u771f\u5b9e\u4e16\u754c\uff08\u975e\u8ba1\u7b97\u673a\u6a21\u62df\uff09\u7684\u5b9e\u9a8c\u624b\u6bb5\u5927\u591a\u65e0\u6cd5\u5206\u8fa8Laponite\u7c92\u5b50\u53d6\u5411\u5206\u5e03\u3002\u5e38\u7528\u7684\u52a8\u6001\u5149\u6563\u5c04\u6cd5\u6d4b\u7c92\u5f84\u548c\u7535\u6cf3\u6cd5\u6d4b\u03b6-\u7535\u4f4d\u90fd\u662f\u5047\u8bbe\u7c92\u5b50\u4e3a\u7403\u5f62\u5f97\u5230\u5b9e\u9a8c\u7ed3\u679c\u7684\u3002\u6240\u4ee5\u5c31\u7b97\u4f60\u80fd\u4ece\u7406\u8bba\u4e0a\u7ed9\u51fa\u53d6\u5411\u5206\u5e03\u7684\u5b9a\u91cf\u5173\u7cfb\uff0c\u9664\u8ba1\u7b97\u673a\u6a21\u62df\u4ee5\u5916\u4e5f\u7f3a\u4e4f\u5b9e\u9a8c\u9a8c\u8bc1\u624b\u6bb5\uff0c\u8003\u8651\u4e86\u4e5f\u767d\u8003\u8651\u3002\u56e0\u6b64\u6211\u4e0d\u592a\u7406\u89e3\u5ba1\u7a3f\u4eba\u662f\u5426\u975e\u8981\u6211\u5b9e\u7259\u5b9e\u9f7f\u5730\u8003\u8651face-edge\u76f8\u4e92\u4f5c\u7528\u4e0d\u53ef\u3002\u6211\u770b\u5230University of Washington\u7684J. Berg\u7ec4\u6709\u4e00\u7bc7\u7814\u7a76Laponite\u6d41\u53d8\u5b66\u7684\u6587\u7ae0\u76f4\u63a5\u628a\u7c92\u5b50\u5f53\u7403\u5f62\u8003\u8651\u4e86\uff0c\u4f46\u6709\u4e00\u6bb5\u5173\u4e8eedge\u548cface\u7684\u89e3\u91ca\u6587\u5b57\u5982\u4e0b\uff08\u91cd\u70b9\u662f\u6211\u52a0\u7684\uff09\uff1a The electrical surface potential must now account for the face and edge potential separately. This gives the following estimate [math]\\mathit{\\Phi}_\\textup{e}\\approx 2\\pi\\epsilon\\epsilon_0 a\\psi _\\textup{face}\\psi_\\textup{edge}\\ln\\left[\\frac{1}{1-\\exp\\left(-\\kappa D \\right )} \\right ].[\/math] The Larson anlysis went from this point to replace the surface potential\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":3451,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/3451","url_meta":{"origin":3418,"position":1},"title":"DLS and zeta-potential measurement","author":"Andrew","date":"2011\u5e747\u670822\u65e5","format":false,"excerpt":"Aim: To aid the theoretical modeling of the rheological data. Viscosity of PEO solutions Used to calculate zeta-potentials. Samples: PEG 35k aqueous solutions at cp = 0, 0.063, 0.1, 0.25, 0.4, 0.63, 0.8, 1.0 wt% Instrument: AR-G2 DLS and zeta-potential measurement Procedure: yet to determine. Principles of zeta-potential measurement? http:\/\/goo.gl\/aQVDU\u2026","rel":"","context":"In &quot;\u5de5\u4f5c\u7b14\u8bb0&quot;","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":1303,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/1303","url_meta":{"origin":3418,"position":2},"title":"\u7b80\u5355\u51e0\u4f55\u4e0e\u529b\u5b66\u6a21\u578b\u80fd\u5426\u641e\u5b9aSoft Colloidal Glass\u6d41\u53d8\u5b66\uff1f","author":"Andrew","date":"2010\u5e747\u670828\u65e5","format":false,"excerpt":"Roger\u00a0T.\u00a0Bonnecaze, & Michel\u00a0Cloitre (2010). Micromechanics of Soft Particle Glasses Advances in Polymer Science : 10.1007\/12_2010_90\u8fd9\u662fAdv. Polym. 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Sci.\u63d0\u51fa\u7684\u6a21\u578b\uff0c\u53ef\u4ee5\u8bf4\u662f\u7b80\u76f4\u201c\u4e0d\u677e\u5f1b\u201d\uff0c\u6216\u8005\u50cf\u6587\u7ae0\u91cc\u89e3\u91ca\u7684\u90a3\u6837\u2014\u2014\u5047\u8bbe\u603b\u662f\u677e\u5f1b\u5230\u63a5\u8fd1\u5e73\u8861\uff08near equilibrium\uff09\u3002\u6240\u4ee5\u5728shear rheology\u90e8\u5206\uff0c\u8be5\u6a21\u578b\u4e5f\u53ea\u6562\u53bb\u62df\u5408steady state\u7684\u7ed3\u679c\u3002\u4e8b\u5b9e\u4e0a\u5bf9\u4e8e\u6574\u4e2a\u80f6\u4f53\u73bb\u7483\u7814\u7a76\u800c\u8a00\uff0c\u96be\u7684\u4e1c\u897f\u4e0d\u662f\u5728steady state\u3002\u6d41\u53d8\u5b66\u5982\u679c\u4ec5\u4ec5\u505a\u4e2asteady state flow\u5b9e\u9a8c\u5c31\u8bf4\u81ea\u5df1\u7814\u7a76\u975e\u7ebf\u6027\u6d41\u53d8\u5b66\u4e5f\u662f\u53d6\u5de7\u6216\u8005\u907f\u91cd\u5c31\u8f7b\u7684\u505a\u6cd5\u2014\u2014\u5c3d\u7ba1steady state flow\u786e\u5b9e\u662f\u975e\u7ebf\u6027\u6d41\u53d8\u5b66\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u7279\u96be\u770b\u61c2\u7684SGR\u53cd\u800c\u66f4\u591a\u4eba\u91c7\u7528\u2014\u2014\u5b83\u8003\u8651\u6e29\u5ea6\u3002\u800c\u4e14\u5b83\u786e\u5b9e\u5dee\u4e0d\u591a\u597d\u5730\u63cf\u8ff0\u5305\u62ec\u8815\u53d8\u548cLAOS\u5728\u5185\u7684\u591a\u79cd\u884c\u4e3a\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":3418,"position":3},"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. Fluid Mech. 463, 1 (2002)\u662f\u8003\u8651\u7a00\u6d6e\u6db2\u7684\u3002\u4f46\u597d\u50cf\u8fd8\u6ca1\u6709\u4eba\u53bb\u4f7f\u7528\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":772,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/772","url_meta":{"origin":3418,"position":4},"title":"\u5173\u4e8eStrain-Rate Frequency Superposition\u7684\u770b\u6cd5","author":"Andrew","date":"2010\u5e742\u67089\u65e5","format":false,"excerpt":"Brian M. Erwin, Simon A. Rogers, Michel Cloitre, & Dimitris Vlassopoulos (2010). Examining the validity of strain-rate frequency superposition when measuring the linear viscoelastic properties of soft materials Journal of Rheology, 54 (2), 187-195Strain-Rate Frequency Superposition\uff08SRFS\uff09\u7684\u6587\u7ae0\u4f1a\u4e0d\u4f1a\u5982\u96e8\u540e\u6625\u7b0b\u822c\u66b4\u53d1\u6211\u4e0d\u6e05\u695a\u3002\u6709\u5f88\u591a\u6211\u5f88\u4e0d\u4ee5\u4e3a\u7136\u7684\u4e1c\u897f\u90fd\u83ab\u540d\u5176\u5999\u5730\u66b4\u53d1\u8fc7\u4e86\uff0c\u6559\u8bad\u5c31\u662f\u5343\u4e07\u522b\u8ddf\u6587\u7ae0\u4e0a\u5199\u7684\u4e1c\u897f\u8f83\u771f\u3002SRFS\u662fH. Wyss\u7b49\u4eba\uff08D. Weitz\u5c0f\u7ec4\uff09\u53d1\u8868\u5728PRL 98:238303\u4e0a\u7684\u5de5\u4f5c\uff0c\u662f\u5728\u80f6\u4f53\u73bb\u7483\u7b49\u8bb8\u591a\u8f6f\u7269\u8d28\u4e0a\u53d1\u73b0\u7684\u53ef\u53e0\u52a0\u73b0\u8c61\u3002\u505a\u6d41\u53d8\u7684\u670b\u53cb\u5e94\u8be5\u591a\u591a\u5c11\u5c11\u4e5f\u7559\u610f\u5230\u8fd9\u9879\u7814\u7a76\u4e86\u3002\u5176\u4ed6\u7ec4\u540e\u7eed\u8ddf\u8e2a\u7684\u4e0d\u5c11\u3002\u6211\u4e5f\u7b97\u662f\u8ddf\u8e2a\u4e86\u4e00\u4e0b\uff0c\u6587\u7ae0\u8fd8\u6ca1\u51fa\u7089\u3002\u6240\u4ee5\u6211\u5728\u8fd9\u91cc\u8981\u8c08\u8c08\u770b\u6cd5\u3002\u8fd9\u4e1c\u897f\u5982\u679c\u4e0d\u662f\u4e00\u4e2a\u5f88\u82b1\u4fcf\u7684\u5e9f\u7269\uff0c\u90a3\u5c31\u662f\u91cd\u5927\u53d1\u73b0\u7684\u5f00\u7aef\u3002\u73b0\u5728\u770b\u6765\u50cf\u524d\u8005\u591a\u4e00\u70b9\u3002 \u7ed9\u5b9aPRL\u90a3\u7bc7\u6587\u7ae0\uff0c\u8d77\u7801\u8981\u6709\u4ee5\u4e0b\u7684\u7591\u95ee\uff1aPRL\u90a3\u7bc7\u6587\u7ae0\u662f\u8bf4\uff0cSRFS\u5728\u5f88\u591a\u8f6f\u7269\u8d28\u6750\u6599\u4f53\u7cfb\u4e0a\u90fd\u6709\uff0c\u751a\u81f3\u6309\u7167\u6211\u7406\u89e3H. Wyss\u7684\u610f\u601d\uff0c\u53ea\u8981\u4e00\u4e2a\u8f6f\u7269\u8d28\u5728dynamic strain sweep\u4e0b\u51fa\u73b0\u5178\u578b\u5982\u53f3\u56fe\u7684\u884c\u4e3a\uff0c\u5c31\u4e00\u5b9a\u7b26\u5408SRFS\uff08\u8be6\u89c1SRFS\u7684\u4ecb\u7ecd\u7f51\u9875\uff09\u3002\u8fd9\u5230\u5e95\u6709\u4ec0\u4e48\u7269\u7406\u4e0a\u7684\u6839\u636e\uff1f\u6700\u7ec8\u5230\u5e95\u6ee1\u8db3\u4ec0\u4e48\u6761\u4ef6\u7684\u6750\u6599\u5c31\u4f1a\u6709\uff0c\u4e0d\u6ee1\u8db3\u5c31\u6ca1\u6709\uff1f\u5de6\u56fe\u7684\u6570\u5b66\u5173\u7cfb\uff0c\u5df2\u7ecf\u5728\u8bb8\u591a\u5b9e\u9a8c\u4e2d\u8bc1\u5b9e\u4e86\uff0c\u5982\u679c\u8003\u8651\u7c98\u5ea6\u548c\u677e\u5f1b\u65f6\u95f4\u7b49\u4ef7\uff0c\u5b83\u5176\u5b9e\u5c31\u662f\u5e7f\u4e49\u5bbe\u6c49\u6d41\u4f53\u7684\u65b9\u7a0b\u3002\u800cSRFS\u7684\u6570\u5b66\u5173\u7cfb\uff0c\u662f\u8981\u628a\u5de6\u56fe\u7684\u7a33\u6001\u526a\u5207\u901f\u7387gamma-dot\u6362\u6210\u632f\u8361\u526a\u5207\u901f\u7387\u5e45\u5ea6gamma-dot-zero\u3002\u8fd9\u53c8\u662f\u4ec0\u4e48\u9053\u7406\uff1fdynamic strain sweep\u4e0b\u5927\u5e94\u53d8\u533a\u7684G''\u659c\u7387\u7edd\u5bf9\u503c\u5176\u5b9e\u662f\u7b49\u4e8e\u5e7f\u4e49\u5bbe\u6c49\u6d41\u4f53\u91cc\u9762\u90a3\u4e2a\u5e42\u03bd\u7684\uff0c\u8fd9\u4e2a\u5df2\u7ecf\u4ece\u6570\u5b66\u4e0a\u8bc1\u660e\u4e86\u3002MCT\u548cSGR\u7406\u8bba\u4e5f\u90fd\u5404\u81ea\u5bfc\u51fa\u4e86\u8fd9\u4e00\u5173\u7cfb\u3002\u5982\u679c\u4e0a\u8ff0SRFS\u7684\u5404\u65b9\u9762\u90fd\u6210\u7acb\uff0c\u90a3\u4e48SRFS\u4e0bG''\u5728\u4f4e\u9891\u533a\u7684\u659c\u7387\uff0c\u4e5f\u8981\u7b49\u4e8e\u03bd\uff0c\u800c\u4e14\u6c34\u5e73\u5e73\u79fb\u56e0\u5b50a\u540c\u5e94\u53d8\u901f\u7387\u5e45\u5ea6gamma-dot-zero\u4e4b\u95f4\u7684\u5e42\u7387\u5173\u7cfb\uff0c\u6307\u6570\u4e5f\u8981\u7b49\u4e8e\u03bd\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd9\u4e2a\u03bd\u51a5\u51a5\u4e2d\u7edf\u6cbb\u4e86\u8f6f\u7269\u8d28\u4e16\u754c\uff01\u5982\u679c\u4f60\u4e0d\u7ed9\u51fa\u4e00\u4e2a\u7edf\u6cbb\u8f6f\u7269\u8d28\u4e16\u754c\u7684\u6a21\u578b\u6765\u89e3\u91ca\u8fd9\u4e2a\u03bd\uff0c\u6211\u60c5\u613f\u76f8\u4fe1\u8fd9\u662f\u5de7\u5408\u3002PRL\u8fd9\u7bc7\u6587\u7ae0\u51fa\u6765\u4e4b\u540e\uff0c\u611f\u5174\u8da3\u7684\u4eba\u5f88\u591a\u3002\u6211\u597d\u50cf\u8bb0\u5f97Nature\u7684Journal Club\u90fd\u8d5e\u626c\u8fc7\uff0c\u53ea\u662f\u6211\u4e00\u65f6\u627e\u4e0d\u56de\u539f\u6587\u4e86\u3002\u540e\u7eed\u8ddf\u8e2a\u7684\u6587\u7ae0\u53d1\u8868\u5728Soft Matter\u3001Phys. Rev. E\u3001J. Phys.\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":"Yielding","src":"https:\/\/i0.wp.com\/www.seas.harvard.edu\/projects\/weitzlab\/srfs\/images\/typ_nonlin_rheo.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":4206,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/4206","url_meta":{"origin":3418,"position":5},"title":"\u5173\u4e8eCox-Merz\u89c4\u5219\u7684\u6709\u76ca\u8ba8\u8bba","author":"Andrew","date":"2011\u5e7410\u67089\u65e5","format":false,"excerpt":"\u6211\u4e4b\u524d\u4ece\u4e00\u7bc7paper\u51fa\u53d1\u8ba8\u8bba\u8fc7\u6211\u5bf9Cox-Merz\u89c4\u5219\u7684\u770b\u6cd5\u3002\u6211\u5728LinkedIn\u7684Society of Rheology\u7fa4\u91cc\u4e5f\u66fe\u7ecf\u53d1\u8d77\u8fc7\u76f8\u5173\u8ba8\u8bba\uff0c\u73b0\u5728\u8fd9\u4e2a\u8ba8\u8bba\u5f88\u957f\u4e86\uff0c\u800c\u4e14\u51fa\u73b0\u4e86\u4e00\u4e9b\u8ba9\u6211\u83b7\u76ca\u826f\u591a\u7684\u56de\u590d\u3002\u4f8b\u5982\uff1aI think the main \"killer\" of CM is when the (large) strains in a steady state measurement start to modify the structure. So colloidal & thixotropic systems, gels can be problematic. If the system can be assumed to be robust under large strains, like polymer solutions, low molar\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":[]}],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/posts\/3418","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/comments?post=3418"}],"version-history":[{"count":4,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/posts\/3418\/revisions"}],"predecessor-version":[{"id":3457,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/posts\/3418\/revisions\/3457"}],"wp:attachment":[{"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/media?parent=3418"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/categories?post=3418"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/tags?post=3418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}