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The microfluidic channels with large width to depth ratios (e.g., the expanded channel) can be approximated as two closely spaced parallel plates similar to a Hele-Shaw cell. At low Reynolds numbers, the depth averaged Navier-Stokes equation reduces to the Laplace equation for pressure (Darcy¡¯s law). This equation is a potential flow equation and based on this assumption, the streamlines will linearly expand with the channel dimensions. Nearly linear amplification of streamlines has also been experimentally observed by Yamada et al.,39 and therefore, the distance between the particle centers in the broadened section is given as where a is the aspect ratio of the device defined as the ratio of broadened section width and pinched section width (wb/wp) and ¢dp is the difference of the particle diameters. |
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yt.yutian.(½ð±Ò+10, ·ÒëEPI+1): лл 2011-05-28 21:37:51
| The microfluidic channels with large width to depth ratios (e.g., the expanded channel) can be approximated as two closely spaced parallel plates similar to a Hele-Shaw cell. ¾ßÓдóµÄ¿í¶È/Éî¶È±ÈµÄ΢Á÷ͨµÀ£¨¼´À©É¢Í¨µÀ£©¿ÉÒÔ´óÖ¿´×÷ÓëHele-Shaw СÊÒÀàËÆµÄÁ½¸öÃܼ¯ÅÅÁÐµÄÆ½Ðа塣At low Reynolds numbers, the depth averaged Navier-Stokes equation reduces to the Laplace equation for pressure (Darcy¡¯s law). Ôڵ͵ÄÀ×ŵÊý£¬Æ½¾ùÉî¶ÈNavier-Stokes ·½³ÌʽÑݱäΪѹÁ¦Laplace·½³Ìʽ¡£ This equation is a potential flow equation and based on this assumption, the streamlines will linearly expand with the channel dimensions. Õâ¸ö·½³ÌʽÊÇDZÁ÷·½³Ìʽ£¬»ùÓڴ˼ÙÉ裬Á÷Ïß½«ËæÍ¨µÀ³ß´çÏßÐÔÀ©Õ¹¡£ Nearly linear amplification of streamlines has also been experimentally observed by Yamada et al.,39 and therefore, the distance between the particle centers in the broadened section is given as where a is the aspect ratio of the device defined as the ratio of broadened section width and pinched section width (wb/wp) and ¢dp is the difference of the particle diameters. Á÷ÏߵĽüÏßÐÔÀ©ÔöҲȷʵÓÉYamadaÔÚÊÔÑéÖй۲⵽£¬Òò¶ø£¬µ±a±íʾÉ豸µÄ×ݺá±È£¨¶¨ÒåΪÀ©¿í²¿·Ö¿í¶ÈºÍËõ½ô²¿·Ö¿í¶ÈÖ®±Èwb/wp£©£¬¢dp±íʾÁ£×ÓÖ±¾¶µÄ²îÒìʱ£¬À©¿í²¿·ÖµÄÁ£×ÓÖÐÐļäµÄ¾àÀë±»¸ø¶¨¡£ |
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