{"id":157219,"date":"2023-09-05T12:02:19","date_gmt":"2023-09-05T06:32:19","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=157219"},"modified":"2023-09-05T12:02:20","modified_gmt":"2023-09-05T06:32:20","slug":"a-model-porous-medium-of-5-cylindrical-capillaries-of-radii-varying-from-60-to-100-micrometers-refer-table-is-subjected","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-model-porous-medium-of-5-cylindrical-capillaries-of-radii-varying-from-60-to-100-micrometers-refer-table-is-subjected\/","title":{"rendered":"A model porous medium of 5 cylindrical capillaries of radii varying from 60 to 100 micrometers (refer Table) is subjected"},"content":{"rendered":"\n

Q. A model porous medium of 5 cylindrical capillaries of radii varying from 60 to 100 micrometers (refer Table) is subjected to Mercury Injection Capillary Pressure (MICP) treatment. The capillaries are being filled in an increasing order of their entry pressure. The magnitude of (\u03c3 cos \ud835\udf03)ai\ud835\udc5f\u2212\ud835\udc3b\ud835\udc54 is 367 dyne\/cm, where \ud835\udf0e is the interfacial tension and \ud835\udf03 is the contact angle. The minimum applied mercury pressure to achieve 50% mercury saturation in the sample is______\u00d7 103<\/sup> dyne\/cm2 (round off to 1 decimal place).<\/p>\n\n\n\n

Radius<\/strong><\/strong> (\u03bcm)<\/strong><\/strong><\/td>Crossectional<\/strong><\/strong> Area (\u00b5m2<\/sup>)<\/strong><\/td>Crossectional Area<\/strong> (fraction)<\/strong><\/strong><\/td>Cumulative Area<\/strong> (fraction)<\/strong><\/strong><\/td><\/tr>
60<\/td>11304<\/td>0.11<\/td>1.00<\/td><\/tr>
70<\/td>15386<\/td>0.15<\/td>0.89<\/td><\/tr>
80<\/td>20096<\/td>0.19<\/td>0.74<\/td><\/tr>
90<\/td>25434<\/td>0.25<\/td>0.55<\/td><\/tr>
100<\/td>31400<\/td>0.30<\/td>0.30<\/td><\/tr>
Total Area =<\/td>103620<\/strong><\/strong><\/td> <\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Ans: 81-83<\/p>\n\n\n\n

Sol:<\/p>\n\n\n\n

Minimum applied mercury pressure to achieve 50% mercury saturation is when the cumulative area covered by mercury is 50%<\/p>\n\n\n\n

Therefore 50% of the cumulative area covered by Hg is when the radius is 90 \u00b5m <\/p>\n\n\n\n

Pc<\/sub> = 2\u03c3cos\u03b8\/r = (2 x 367)\/(9 x 10-3<\/sup>) = 81555.5 dyne\/cm2<\/sup> = 81.55 x 103<\/sup> dyne\/cm2<\/sup><\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Q. A model porous medium of 5 cylindrical capillaries of radii varying from 60 to 100 micrometers (refer Table) is subjected to Mercury Injection Capillary Pressure (MICP) treatment. The capillaries are being filled in an increasing order of their entry pressure. The magnitude of (\u03c3 cos \ud835\udf03)ai\ud835\udc5f\u2212\ud835\udc3b\ud835\udc54 is 367 dyne\/cm, where \ud835\udf0e is the interfacial […]<\/p>\n","protected":false},"author":419,"featured_media":157220,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-157219","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157219","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=157219"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157219\/revisions"}],"predecessor-version":[{"id":157221,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157219\/revisions\/157221"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/157220"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=157219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=157219"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=157219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}