{"id":81,"date":"2021-09-02T03:37:56","date_gmt":"2021-09-01T19:37:56","guid":{"rendered":"http:\/\/49.235.202.190\/?p=81"},"modified":"2021-09-10T15:07:55","modified_gmt":"2021-09-10T07:07:55","slug":"%e7%a7%91%e7%a0%94%e8%af%be%e5%a0%82%ef%bc%88%e4%b8%80%ef%bc%89-%e5%88%9d%e8%af%86%e7%9b%b8%e5%9c%ba%e6%a8%a1%e5%9e%8b","status":"publish","type":"post","link":"https:\/\/shuaiwang.cc\/?p=81","title":{"rendered":"\u79d1\u7814\u8bfe\u5802\uff08\u4e00\uff09\u2014\u2014\u521d\u8bc6\u76f8\u573a\u6a21\u578b"},"content":{"rendered":"\n<p>\u76f8\u573a\u6a21\u578b\uff08Phase field model\uff09\u4e3b\u8981\u662f\u4e3a\u4e86\u89e3\u51b3\u754c\u9762\u95ee\u9898\u3002\u601d\u60f3\u6765\u6e90\u6700\u65e9\u53ef\u4ee5\u8ffd\u6eaf\u5230Van der Waals\u5728\u5904\u7406\u6db2\u4f53\u8868\u9762\u5f20\u529b\u65f6\u5019\u7684\u975e\u5747\u5300\u754c\u9762\u5047\u8bbe\uff0c\u7ecf\u8fc7Landau&amp;Lifshitz\u3001Allen-Cahn\u3001Cahn-Hillard\u53d1\u5c55\uff0c\u65e5\u8d8b\u5b8c\u5584\u3002\u5bf9\u4e8e\u76f8\u573a\u6a21\u578b\u7684\u8868\u8fbe\u5f0f\uff0c\u5728\u7b80\u5355\u3001\u4f4e\u7ef4\u3001\u5e73\u8861\u7684\u6761\u4ef6\u4e0b\uff0c\u4eba\u4eec\u5df2\u7ecf\u7ed9\u51fa\u4e86\u89e3\u6790\u89e3\u3002\u4f46\u662f\u5bf9\u4e8e\u590d\u6742\u7684\u8fb9\u754c\u6761\u4ef6\u4ee5\u53ca\u975e\u5e73\u8861\u72b6\u6001\u4e0b\u5e8f\u53c2\u91cf\u7684\u6f14\u5316\u8fc7\u7a0b\uff0c\u8ba1\u7b97\u91cf\u5341\u5206\u5e9e\u5927\u3002<\/p>\n\n\n\n<p>\u968f\u7740\u8ba1\u7b97\u673a\u79d1\u5b66\u7684\u4e0d\u65ad\u53d1\u5c55\uff0c\u6c42\u89e3\u590d\u6742\u8fb9\u754c\u6761\u4ef6\u4e0b\u7684\u76f8\u573a\u65b9\u7a0b\u6210\u4e3a\u53ef\u80fd\u3002\u5178\u578b\u7684\u4f8b\u5b50\u662fR. Kayabushi\uff081993\uff09\u7684\u6676\u679d\u751f\u957f\u3001\u4ee5\u53caLQ Chen\u7b49\u7684\u94c1\u7535\u7574\u53d8\u7684\u7b97\u4f8b\u3002\u76ee\u524d\u76f8\u573a\u65b9\u6cd5\u5e94\u7528\u4e8e\u4f17\u591a\u9886\u57df\uff0c\u5982<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u94c1\u7535<\/li><li>\u94c1\u78c1<\/li><li>\u5408\u91d1<\/li><li>\u9a6c\u6c0f\u4f53\u76f8\u53d8<\/li><li>\u591a\u76f8\u5408\u91d1<\/li><li>\u7c89\u672b\u51b6\u91d1<\/li><\/ul>\n\n\n\n<p>\u7b49\u7b49\u3002<\/p>\n\n\n\n<p>\u90a3\u4e48\uff0c\u7a76\u7adf\u4ec0\u4e48\u662f\u76f8\u573a\u6a21\u578b\uff1f\u5bf9\u4e8e\u4e00\u4e2a\u754c\u9762\uff0c\u6211\u4eec\u53ef\u4ee5\u6709\u4e24\u79cd\u5904\u7406\u65b9\u5f0f\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"1093\" height=\"440\" src=\"http:\/\/49.235.202.190\/wp-content\/uploads\/2021\/09\/interface.jpg\" alt=\"\" class=\"wp-image-246\"\/><figcaption>diffusive interface v.s. sharp interface<\/figcaption><\/figure>\n\n\n\n<p>\u5bf9\u4e8e\u6c14\u3001\u6db2\u754c\u9762\uff0cTolman [1]  \u548cOno Kondo  [2] \u8bc1\u660e\uff0c\u91c7\u7528\u5982\u4e0b\u6240\u793a\u7684\u81ea\u7531\u80fd\u8868\u793a\u65b9\u5f0f\uff0c\u6700\u540e\u5f97\u5230\u7684\u754c\u9762\u7684\u5e8f\u53c2\u91cf\u662f\u95f4\u65ad\u53d8\u5316\u7684\u3002<\/p>\n\n\n\n<p>\\(\\psi(z) =  \\psi(z)  [\\rho(z), T]\\)      \uff081\uff09<\/p>\n\n\n\n<p>\u81ea\u7531\u80fd\u53d6\u6700\u4f4e\u7684\u6761\u4ef6\u4e3a\u8868\u9762\u5f20\u529b\u4e3a0\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p>Van der Waals \u63d0\u51fa\uff0c\u5728\u754c\u9762\u5904\u7684\u81ea\u7531\u80fd\u5206\u5e03\u4e0d\u662f\u5747\u5300\u7684\uff0c\u800c\u662f\u4e00\u4e2a\u8ddf\u7ec4\u4efd\u6bd4\u4f8b\u6709\u5173\u7684\u53c2\u6570\uff1a<\/p>\n\n\n\n<p> \\(\\Psi(z) =  \\psi(z)  [\\rho(z), T]\\) &#8211; \\psi(\\rho^{A,B}, T)   \uff082\uff09<\/p>\n\n\n\n<p>\u4e0e\u516c\u5f0f\uff081\uff09\u76f8\u6bd4\u589e\u52a0\u7684\u4e00\u90e8\u5206\u81ea\u7531\u80fd\u88ab\u79f0\u4e3asurface excess\u3002\u6ce8\u610f\u8fd9\u91cc\u81ea\u7531\u80fd\u7684\u5206\u5e03\u662f\u4f4d\u7f6e\u5750\u6807\u7684\u51fd\u6570\u3002<\/p>\n\n\n\n<p>Landau\u91c7\u7528\u76f8\u540c\u7684\u601d\u60f3\uff0c\u5c06\u94c1\u78c1\u4f53\u81ea\u7531\u80fd\u7684\u5206\u5e03\u5199\u4e3a\u5c40\u90e8<strong>\u5e8f\u53c2\u91cf<\/strong>\uff08\u5982magnetization\uff09\u68af\u5ea6\u7684\u51fd\u6570\u3002Cahn\u7b49\u5c06\u68af\u5ea6\u5f15\u5165\u4efb\u610f\u975e\u5747\u5300\u7cfb\u7edf\u3002\u5728\u6b64\u5047\u8bbe\u4e0b\uff0c\u81ea\u7531\u80fd\u5bc6\u5ea6\u53ef\u4ee5\u5199\u4e3a<\/p>\n\n\n\n<p> \\(\\psi(c,\\nabla c) = \\psi _0(c) + G|\\nabla c|^{2} \\)    \uff083\uff09<\/p>\n\n\n\n<p>\u5176\u4e2dc\u4e3a\u7cfb\u7edf\u7684\u5e8f\u53c2\u91cf\uff0c\\(  \\psi _0(c) \\) \u4e3a\u5c40\u90e8\u81ea\u7531\u80fd\u5bc6\u5ea6\uff0c \\( |\\nabla c|^{2} \\)\u4e3a\u56e0\u5e8f\u53c2\u91cf\u5728\u7a7a\u95f4\u5206\u5e03\u7684\u4e0d\u5747\u5300\u6240\u5bfc\u81f4\u7684\u81ea\u7531\u80fd\u7684\u589e\u52a0\u3002 \u516c\u5f0f\uff083\uff09\u5373\u4e3a\u5e73\u8861\u72b6\u6001\u5bf9\u5e94\u7684\u76f8\u573a\u516c\u5f0f\u3002<\/p>\n\n\n\n<p>\u4e0e\u5176\u4ed6\u5904\u7406\u975e\u5747\u5300\u7cfb\u7edf\u7684\u65b9\u6cd5\u76f8\u6bd4\uff0c \u76f8\u573a\u6cd5\u6709\u7740\u4ee5\u4e0b\u4f18\u70b9:\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u76f8\u573a\u65b9\u6cd5\u5bf9\u4e8e\u754c\u9762\u7684\u8ffd\u8e2a\u662f\u81ea\u52a8\u7684\u3002\u901a\u8fc7\u5c06\u4f53\u7cfb\u81ea\u7531\u80fd\u671d\u7740\u80fd\u91cf\u6700\u5c0f\u7684\u65b9\u5411\u6f14\u5316\uff0c\u53ef\u4ee5\u81ea\u52a8\u83b7\u5f97\u754c\u9762\u7684\u53d8\u5316\u3002<\/li><li>\u76f8\u573a\u65b9\u6cd5\u662f\u5904\u7406\u975e\u5e73\u8861\u72b6\u6001\u8fc7\u7a0b\u6709\u529b\u5de5\u5177\u3002<\/li><li>\u76f8\u573a\u7684\u76f8\u53c2\u6570\u53ef\u4ee5\u4e0e\u5176\u5b83\u5916\u573a\uff0c\u5982\u6e29\u5ea6\u573a\u3001\u7535\u573a\u7b49\u8fdb\u884c\u8026\u5408\u3002<\/li><\/ul>\n\n\n\n<p><\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p><strong>\u53c2\u8003\u6587\u732e<\/strong><\/p>\n\n\n\n<p>[1] Tolman, Richard C. &#8220;The effect of droplet size on surface tension.&#8221;\u00a0<em>The journal of chemical physics<\/em>\u00a017.3 (1949): 333-337.<\/p>\n\n\n\n<p>[2] Ono, Syu, and Sohei Kondo. &#8220;Molecular theory of surface tension in liquids.&#8221;\u00a0<em>Structure of  Liquids\/Struktur der Fl\u00fcssigkeiten<\/em>. Springer, Berlin, Heidelberg, 1960. 134-280.<\/p>\n\n\n\n<p>[3] Cahn, John W., and John E. Hilliard. &#8220;Free energy of a nonuniform system. I. Interfacial free energy.&#8221;\u00a0<em>The Journal of chemical physics<\/em>\u00a028.2 (1958): 258-267.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u76f8\u573a\u6a21\u578b\uff08Phase field model\uff09\u4e3b\u8981\u662f\u4e3a\u4e86\u89e3\u51b3\u754c\u9762\u95ee\u9898\u3002\u601d\u60f3\u6765\u6e90\u6700\u65e9\u53ef\u4ee5\u8ffd\u6eaf\u5230Van der W &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/shuaiwang.cc\/?p=81\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u201c\u79d1\u7814\u8bfe\u5802\uff08\u4e00\uff09\u2014\u2014\u521d\u8bc6\u76f8\u573a\u6a21\u578b\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,12],"tags":[],"class_list":["post-81","post","type-post","status-publish","format-standard","hentry","category-4","category-12","entry"],"_links":{"self":[{"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=\/wp\/v2\/posts\/81","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=81"}],"version-history":[{"count":6,"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=\/wp\/v2\/posts\/81\/revisions"}],"predecessor-version":[{"id":255,"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=\/wp\/v2\/posts\/81\/revisions\/255"}],"wp:attachment":[{"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=81"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=81"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=81"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}