A Geometry Model for Tortuosity of Flow Path in Porous Media

A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity a

ÀÁƺÈÀ˺ÄÌ̺

¾

½ÔÖØÑÒØÓÈÝ×׸ÀÙÞÓÒÍÒÚÖ×ØÝÓËÒÒÌÒÓÐÓݸÏÙÒ¿¼¼ÌËØØÃÝÄÓÖØÓÖÝÓÆÓÒÐÒÖÅÒ×´ÄÆŵ¸ÁÒ×ØØÙØÓÅÒ׸Ò×ÑÝÓËÒ׸ҽ¼¼¼¼¿Ê×ÖÒØÖÓÓÑÐÅØÖÐ×ÒÒÖÒ¸ÏÙÒÍÒÚÖ×ØÝÓÌÒÓÐÓݸÏÙÒ¿¼¼¼

ÓÑØÖÝÅÓÐÓÖÌÓÖØÙÓ×ØÝÓÐÓÛÈØÒÈÓÖÓÙ×ÅÍÓ¹ÅÒ´¥ ¤µ££¸ÄÁÂÒ¹ÀÙ´£¢¡µ½¾¿

ÎÓк¾½¸ÆÓº´¾¼¼µ½£

×ÔÖÓÔÓ××ÓÒØ××ÙÑÔØÓÒØØ×ÑÔÐÓÑØÖÝÑÓÐÓÖØÓÖØÙÓ×ØÝÓ­ÓÛÔØÒÔÓÖÓÙ×Ñ×ÓÑÔÖØÐ×ÒÔÓÖÓÙ×ÑÙÑÖÙÒÖ×ØÖØÐÝÓÚÖÐÔÔÒØÓØÖ×ÖÒÓغÌÔÖÓÔÓ×ÑÓÐ×ÜÔÖ×××ÙÒØÓÒÓÔÓÖÓ×ØÝÒØÖ×ÒÓÑÔÖÐÓÒ×ØÒØÒØ×ÑÓкÌÑÓÐÔÖØÓÒ×ÖÓÑÔÖÛØØÓ×ÖÓÑÚÐÐÓÖÖÐØÓÒ×ÓØÒÒÙÑÖÐÐÝÒÜÔÖÑÒØÐÐݸÓØÓÛÖÒÖÑÒØÛØÓØÖºÌÔÖ×ÒØÑÓÐÒÐ×ÓÚØØÓÖØÙÓ×ØÝÛØÓÓÔÔÖÓÜÑØÓÒÒÖØÔÖÓÐØÓÒØÖ×ÓкÌÚÐØÝÓØÔÖ×ÒØØÓÖØÙÓ×ØÝÑÓÐ×ØÙ×ÚÖ¬ºÈ˺ºÅ¸º½º Ü¸ºº Ø

´Ê

Ú¾

ÔÖо¼¼µ

ÌÖØÖ×Ø×ÓÑØÖÐØÖÒ×ÔÓÖØÒÔÓÖÓÙ×Ѹ×Ù×ØÝÖÙÐÔÖÑÐØÝÓÖÐØÖÐÓÒÙØÚØݸÚÖÚÑÙØØÒØÓÒ½ ½¾ÙØÓÑÒÝÙÒÖ×ÓÐÚÔÖÓÐÑ×Ò×ÒÒÒÒÖ¹ÒÔÔÐØÓÒ׺Ì×ÑÖÓ×ÓÔØÖÒ×ÔÓÖØÔÖѹØÖ×´ººØÝÖÙÐÔÖÑÐØÝÓÖÐØÖÐÓÒ¹ÙØÚØݵÖÙ×ÙÐÐÝÖÐØØÓØØÓÖØÙÓ×ØÝÓØÓÖ¹ØÙÓÙ×ÔØÓÐÐÓÛÝØÖÒ×ÔÓÖØÑØÖÐ׺ÀÓÛ¹ÚÖ¸Ø×ÒÓÛÒØØØØÓÖØÙÓÙ×ÔØØÖÒ×ÔÓÖØÑØÖÐÓÐÐÓÛ××ÑÖÓ×ÓÔÐÐÝÚÖÝÓÑÔÐغÌÖÓÖ¸ØØÓÖØÙÓ×ØÝÓÖ­ÓÛÔØÒÔÓÖÓÙ×ѹ×ÓÒÚÒØÓÒÐÐÝØÖÑÒÒÜÔÖÑÒØ×½¿½ÒØÜÔÖÑÒØÐØÖØÒÓÖÖÐØ×ÓÖ¹ÖÐØÓÒ×ÛØÓÒÓÖÑÓÖÑÔÖÐÓÒ×ØÒØ׺ÁÒØÓÒ¸ØØÓÖØÙÓ×ØÝÓÖ­ÓÛÔØÒÔÓÖÓÙ×ѹÒÐ×ÓØÖÑÒÝÔÔÐÝÒØÐØØ״ĵÐÐÙÐÖÙØÓÑØÓÒÑØÓº¿ÀÓÛÚÖ¸ÒÒ¹ÐÝØÐ×ÓÐÙØÓÒÓÖØÓÖØÙÓ×ØÝÓ­ÓÛÔØÒÔÓÖÓÙ×Ñ×ÙÖÖÒØÐÝÒÓØÚÐÐØÓÓÙÖÒÓÛк̬ÒØÓÒÓØÓÖØÙÓ×ØÝ×ÓØÒÚÒݽ¾ÄÄ´½µÛÖÄÒÄÖØØÙÐÐÒØÓ­ÓÛÔØÒØ×ØÖØÐÒØÓÖØÒ××Ó×ÑÔлÙÒØÐÐÐ

ÓÒØÑÖÓ×ÓÔÔÖ××ÙÖÖÒظÖ×ÔØÚÐݺËÓÑÖ×ÖÖ׬ÒØÓÖØÙÓ×ØÝ×´Äĵ¾º½¾ËÓÑÓØÖÖ×ÖÖ×½¬ÒØØÓÖØÙÓ×ØÝ×´Äĵ¾ÒÓÙÒØÚÐÙ×Ó´Äĵ¾¼ºÖ¹ÑÒ¬Ò×ØØÓÖØÙÓ×ØÝ×ÄĸÒÓÙÒØÑÔÖÐÚÐÙÄļ½¸½ÒÓØÖÚÐÙ×ÖÔÓÖØÒØÐØÖØÙÖÓÖÄÄÚÖÝÒØÖÒÓ¼ºß¼ºº½ÁÒØ×ÛÓÖ¸Õº´½µ×ÔÔÐÓÖجÒØÓÒÓØÓÖØÙÓ×ØݺÃÓÔÓÒÒØк¿ÔÔÐØÄÑØÓØÓ×ÓÐÚÒÙÑÖÐÐÝÖÔÒ­ÓÛÓÆÛØÓÒÒÒÓÑÔÖ×׹ЭÙÒØÛÓ¹ÑÒ×ÓÒÐÔÓÖÓÙ××Ù×ØÒÓÒ¹£

×ØÖÙØÝÖÒÓÑÐÝÔÐÖØÒÐ×ÓÕÙÐ×ÞÒÛØÙÒÖ×ØÖØÓÚÖÐÔºÌÝÓØÒÓÖ¹ÖÐØÓÒØÛÒØÚÖØÓÖØÙÓ×ØÝÓ­ÓÛÔØÒØÔÓÖÓ×ØÝ×¼´½ µ·½´¾µÁÒØÖÐØÖÛÓÖ¸ÃÓÔÓÒÒØкÓÒ×ÖØÔÖÓÐØÓÒØÖ×ÓдÓÙÒØÓ¼º¿¿ÒØÖ×Ý×ØѵÒÒÔÔÐØÄÑØÓØÓ×ÓÐÚØ­ÓÛÓÆÛØÓÒÒÒÓÑÔÖ××ЭÙÒØÛÓ¹ÑÒ×ÓÒÐÔÓÖÓÙ××Ù×ØÒÓÒ×ØÖÙØÝÖÒ¹ÓÑÐÝÔÐÖØÒÐ×ÓÕÙÐ×ÞÒÛØÙÒÖ¹×ØÖØÓÚÖÐÔºÌÖÄ×ÑÙÐØÓÒ×ÛÖÖÖÓÙØØÔÓÖÓ×Ø×¼º¼ß¼º¼ÓÖØÓÖØÙÓ×ØÝÒÒÙÑÖ¹ÐÖ×ÙÐØ×ÛÖ¬ØØÝØÓÐÐÓÛÒÓÖÖÐØÓÒ´¿µ½·´´½ µµ ÛÖ¸´¼µÒÑ´¼½µÖجØØÒÔÖÑØÖ׺ÓÖÖÐØÓÒÓØÓÖѽ·ÈÐÒ´½µ´µÛ×ÓØÒÝØÜÔÖÑÒØ×ÓÒ­ÓÛØÖÓÙ×ÔÛØÙ׸½ÒÈ´¼¿µ×ØÑÔֹл¬ØØÒÓÒ×ØÒØÓØÒݬØØÒØÜÔÖÑÒ¹ØÐغÕÙØÓÒ×´¾µß´µÐÐ×Ø×ÝØÓÒØÓÒ½ÓÖ½¸Ø××ÓÒ××ØÒØÛØØÔÝ×Ð×ØÙØÓÒºÀÓÛÚÖ¸ØÝÐÐÚÓÒÓÖÑÓÖѹÔÖÐÓÒ×ØÒØ×ÓØÒÝÑØÒØÒÙÑÖÐÖ×ÙÐØ×ÓÖÜÔÖÑÒØÐغÌ×ÛÓÖÓÙ××ÓÒØÖÚØÓÒÓ×ÑÔÐÒÔÔÖÓÜÑØÜÔÖ××ÓÒÓÖØÓÖØÙÓ×ØÝÓ­ÓÛÔØÒÔÓÖÓÙ×ѺÌÖ×ÙÐØ×ÔÖØÖÓÑØÔÖÓ¹ÔÓ×ÑÓÐÖÓÑÔÖÛØØÓ×ÖÓÑØÚйÐÓÖÖÐØÓÒ×Õ׺´¾µß´µºÑ

ËÙÔÔÓÖØÝØÆØÓÒÐÆØÙÖÐËÒÓÙÒØÓÒÓ££ÑÐÝÙ¿¿ÔÙкۺºÒ­¾¼¼Ò×ÈÝ×ÐËÓØÝÒÁÇÈÈÙÐ×ÒÄØ

ÒÙÒÖ

ÖÒØÆÓ½¼¾¾¼¾º

A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity a

½¼

ÍÓ¹ÅÒ

Øк

ÎÓк¾½

ÙÖ½×ÔÐÝ×ØØÛÓÔÓ××ÐÓÒ¬ÙÖØÓÒ×ÓÖ­ÓÛØÖÓÙÔÓÖÓÙ×ÑÓØÛÓ¹ÑÒ×ÓÒÐ×ÕÙÖÔÖ

ØÐ׺ÓÖÓÒ¬ÙÖØÓҸ׺½´µ¸ÛÚØØÓØÐÚÓÐÙÑÎÓØÙÒØÐÐ×ÓÛÒ×Ø××ÕÙÖ×δ·µ¾´µÛÖÒÖØÔÖØÐ×ÞÒÔ×Þ¹ØÛÒÔÖØÐ׸Ö×ÔØÚÐݺÌØÓØÐÔÓÖÚÓÐÙÑÒØÙÒØÐÐ×´µÎ´µ¾·¾¢ÌÙ׸ØÔÓÖÓ×ØÝ×ØØÔ

½ ÖÓÑÕº´µ¸ÛÓØÒ

·

¾

´µ

Ô½½  ½´µÕÙØÓÒ´µÒØ×ØØÛÒ¼¸¼¸ÒÛÒ½¸½ºÌ××ÜÔØÙ×ÛÒ¼¸ØÔ×ÞØÛÒÔÖØÐ×ØÒ×ØÓÞÖÓ¸ÒÛÒ½¸ÒÓÔÖØÐ×ÒØÑÙѸÓÖÖ×ÔÓÒÒØÓØÔÒÒ¬Òغ

ÖÓÑÛØÐÒØÓ×ØÖÑÐÒÒÓ¹ØÒÝ×¾Ô½½  ½·½´½¼µÕÙØÓÒ´½¼µ×ÓÛ×ØØÛÒ¼¸ØÐÒؾ¸ÒÛÒ½¸ØÐÒØØÒ×ØÓÒ¬ÒغÌ××ÜÔØÙ×ÛÒ¼¸ØÔ×ÞØÛÒÔÖØÐ×ØÒ×ØÓÞÖÓ¸Ö×ÙÐØÒÒØÒÒØÓÕÙÐØÓ¾´º½´µµºÏÒ½¸ÒÓÔÖØÐ×ÒØÑÙѸØÐÒØØÙ×ØÒ×ØÓÒ¬ÒغËÒØÔÖØÐ×ÒØÙÐÔÓÖÓÙ×ÑÖÖÒ¹ÓÑÐÝ×ØÖÙظØ×ÑÒ×ØØ×ÓÑÔÖØÐ×ÓÚÖÐÔÓØÖ¸ÛÐØÓØÖ×ÓÒÓغÃÓÔÓÒÒØк¸¿ÒØÖÒÙÑÖÐ×ÑÙÐØÓÒ׸ÓÒ×ØÖÙØØÛÓ¹ÑÒ×ÓÒÐÔÓÖÓÙ××Ù×ØÒÝÖÒÓÑÐÝÔÐÖØÒÐ×ÓÕÙÐ×ÞÒÛØÙÒÖ×ØÖØÓÚÖÐÔºÌÖÓÖ¸ÒØÔÖ×ÒØÑÓиثØÓÙÒÖ¹×ØÖØÓÚÖÐÔ³×Ð×ÓØÒÒØÓÓÙÒغÓÖØ×ÔÙÖÔÓ׸ÛÖÙØØ×Ò×ÓÑÔÖØÐ×ÖÒÓÑÐÝÓÚÖÐÔÓØÖÒÖÐÔÓÖÓÙ×ѸØÔÖÓÓ×ØÖÑÐÒ×ÑÝÒÓØØ×Ñ×ØØ×ÓÛÒÒØ×ÐÓÔÓÖ×ÞÒº½´µÒØÑÝ´µºÌÖÓÖ¸ÓÖÒØÓجÒØÓÒÕº´½µ¸ÛÚØØÓÖØÙÓ×ØÝÓÖ­ÓÛØÖÓÙÙÒÖ×ØÖØÐÝÓÚÖÐÔÔÔÖØÐ×´ÖÖÖÒØÓÓÒ¬ÙÖØÓÒµ×Ö¾Ô½½  ½·½ÔÔ´½½µ½ ½ ½ ÓÖÔÓÖÓÙ×ÑÙÑÛØÙÒ¹ÓÚÖÐÔÔÔÖعÐ׸Û××ÙÑØØØ­ÓÛÔØÓÐÐÓÛ×ØйÞÔØÛÝ××ÓÛÒÒº½´µ¸ÓÒ¬ÙÖØÓÒºËÒØ×ØÖÑÐÒ×ÔÖÔÒÙÐÖØÓØÓÖ¹ÞÓÒØÐÖØÓÒ¸ÛØØÛÓÐÐÒØÓ×ØÖѹÐÒßßßØÓÐÙÐØØØÓÖØÙÓ×ØÝÒØÙÒØÐкÓÖÒØÓجÒØÓÒÓÕº´½µ¸ÛÓØÒØØÓÖØÙÓ×ØÝÓÖÓÒ¬ÙÖØÓÒ×··½··´½Ô½¾  ½µ·Ô´½¾µ½·½½ ¾Û־׺½´µºÌÖÐØÓÖØÙÓ×ØÝÒÓØÒÝÚÖ¹ÒÓÚÖÐÐÔÓ××ÐÓÒ¬ÙÖØÓÒ×ÓÖ­ÓÛÔØÒÔÓÖÓÙ×ѺÓÖ×ÑÔÐØݸØ×Û

ÓÖÖÓÙÐÝÓÒ¹×Ö×ØÛÓÐÞÓÒ¬ÙÖØÓÒ׸ºº×ÓÑÔÖØÐ×ÖÓÚÖÐÔÔÒØÓØÖ×ÖÒÓغÌÚÖØÓÖØÙÓ×ØÝ×ØÙ×ÚÒÝÔ½Ô½´·µ¾¾½·¾½ ·½ Ö¾Ô½½  ½·½Ô´½¿µ¡½ ½ Ú

º½ºÌÛÓÐÞÓÒ¬ÙÖØÓÒ×Ó×ØÖÑÐÒ×ÓÖÖÔÒ­ÓÛÒÔÓÖÓÙ×Ѻ

¬×

ÖÓÑ´

º½´µ¸ØÐÒØÓ×ØÖÑÐÒµ¾¾

×Ø×¹´µ

Ô½½  ½·¾

¾

A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity a

ÆÓº

ÍÓ¹ÅÒ

Øк

½½

ÕÙØÓÒ´½¿µÔÖ×ÒØ××ÑÔÐÒÔÔÖÓÜÑØÑÓÐÓÖØÓÖØÙÓ×ØÝÓ­ÓÛÔØÒÔÓÖÓÙ×ѺÌÖ×ÒÓÑÔÖÐÓÒ×ØÒØÒØ×ÑÓкÁØ×ÚÒØØØÕº´½¿µ×ÙÒØÓÒÓÔÓÖÓ×ØÝÓÒÐݺÁÒº¾´µ¸ØÔÖ×ÒØÑÓÐÔÖØÓÒ×ÖÓÑÔÖÛØØÓ×ÖÓÑÕ׺´¾µß´µºÁØ××ÓÛÒØØØÔÖ×ÒØ×ÑÔÐÑÓÐÔÖ×ÒØ×ÓÓÖ¹ÑÒØ´ÛÐÐÛØÒØÖÖÓÖÖ׿ÝÄ×ÑÙйØÓÒ×µÛØÓØÖÓÖÖÐØÓÒ׺ÆÓØØØÕ׺´¾µÒ´¿µÖÓØÒÖÓÑØÄ×ÑÙÐØÓÒ׸ÒÕº´µ×ÓÖÖÐØݬØØÒØÜÔÖÑÒØÐغÌÓܹÑÒØÚÓÙÖÓØÔÖ×ÒØÑÓÐÒÖØÔÖ¹ÓÐØÓÒØÖ×Óи¼¿¿¸ÛÓÑÔÖØÔÖ×ÒØÑÓÐÔÖØÓÒ×ÛØÕº´¿µÒÖØÔÖÓÐØÓÒØÖ×Óм¿¿¸××ÓÛÒÒº¾´µºÁØÒ×ÒØØØÔÖ×ÒØ×ÑÔÐÑÓÐÚ×ØØÓÖØÙ¹Ó×ØÝÐÓÛÖÓÙرØÒØØÔÖØÝÕº´¿µÒÖØÔÖÓÐØÓÒØÖ×Óм¿¿º

ÒØÚÐØÝÓØÔÖ×ÒØ×ÑÔÐÑÓÐ×ÙÖØÖÚÖ¬ºËÒÕ׺´¾µÒ´µÓÒÓØÐÛØØØÓÖØÙÓ×ØÝÒÖØÔÖÓÐØÓÒØÖ×ÓиØ×ÛÓÖ×ÓÑÔÖÐÓÒÐÝÛØÕº´¿µÒÖØÔÖÓÐØÓÒØÖ×ÓкÁÒ×ÙÑÑÖݸÛÚ×ÓÛÒ×ÑÔÐÓÑØÖÝÑÓÐÓÖØÓÖØÙÓ×ØÝÓ­ÓÛÔØÒÔÓÖÓÙ×ѺÌ×ÑÓÐ×ÜÔÖ×××ÙÒØÓÒÓÔÓÖÓ×ØÝÒØÖ×ÒÓÑÔÖÐÓÒ×ØÒغÌÑÓÐÔÖØÓÒ×ÖÓÑÔÖÛØØÓ×ÖÓÑÚÐÐÓÖÖÐØÓÒ×ÓØÒÝÓØØÄ×ÑÙÐØÓÒ×ÒÜÔÖÑÒ¹ØÐغÌÔÖ×ÒØÑÓÐÔÖØÓÒ×ÖÒÓÓÖÑÒØÛØØÓ×ÖÓÑØÚÐÐÓÖÖÐØÓÒ׺ÁÒØÓÒ¸ØÔÖ×ÒØÑÓÐÒÐ×ÓÚØØÓÖ¹ØÙÓ×ØÝÛØÓÓÔÔÖÓÜÑØÓÒÒÖØÔÖÓÐØÓÒØÖ×ÓкÌÚÐØÝÓØÔÖÓÔÓ×ÑÓÐ×ØÙ×ÚÖ¬ºÀÓÛÚÖ¸Ø×ÛÓÖØÔÓÒØÒÓÙØØØÐØÓÙØ××ÑÔÐÓÑØÖÝÑÓÐÒÔÖÓÚØØÓÖØÙÓ×¹ØÝÚÓÙÖÓÚØÔÖÓÐØÓÒØÖ×ÓиØÒÒÓØÔÖ×Ò

ØØÔÖÓÐØÓÒØÖ×ÓкÁÓÒ×Ð×ÓÒØÖ×ØÒØÐ×ÐÒÔÖÓÔÖØ×ÒÖØØÖ×ÓиÐÓÖØÑÔÐÓØÛØÑÓÖØÒÓÒÓÖÖÓÑÒØÙÒÚÖØÓÒÒÖØØÖ×ÓÐÑØ×ÖкÓÖØ×ÔÙÖÔÓ׸ØÅÓÒØÖÐÓÓÖÄ×ÑÙÐØÓÒ×ÓÖÒÐÝØÐÛÓÖ×ÓÒÔÖÓÐØÓÒØÓÖÝ×ÓÙÐÔÖÓÖѸÒØ×ÑØÓÙÖÒÜØÛÓÖº

ÊÖÒ×Ö½¾ÝÒÑ×ÓÐÙ×ÒÈÓÖÓÙ×Å´ÆÛÓÖÐ×ÚÖµ¾ÙÐÐÒĽÈÓÖÓÙןÐÙÌÖÒ×ÔÓÖØÒÈÓÖËØÖÙØÙÖ´ËÒÓѵ¿ÃÓÔÓÒÒ¸ÃØÅÒÌÑÓÒÒ½ÈÝ׺ÊÚº¼ÃÓÔÓÒÒ¸ÃØÅÒÌÑÓÒÒ½ÈÝ׺ÊÚº¿¿½Ò˸ÊÒÊÒ¾¼¼¾ÒºÈÝ׺ÄØغ½ËÒÏÙž¼¼¾ÒºÈÝ׺ÄØغ½½¿Ï¸ÒËϸÏÒÀ¸ÏÒËÂÒÀÒÀ¾¼¼¾ÒºÈÝ׺ÄØغ½½½¿ÌÒÂÈÒÓÃľ¼¼¿ÒºÈÝ׺ÄØغ¾¼¿ÄÙ¸ÏÒÀ¸ÅÓÈÒÏÙÉ˾¼¼¿ÒºÈÝ׺ÄØغ¾¼½½¼ÌÒÂÈÒÓÃľ¼¼¿ÒºÈÝ׺ÄØغ¾¼¾¿½½ÒĸÒÒÀ¾¼¼¿ÒºÈÝ׺ÄØغٽ¾ÙÅÒÄÂÀ¾¼¼ÒºÈÝ׺ÄØغ¾½½½½¿ÏÝÐÐÅÊÂÒÖÓÖÝʽÁÒºÒÒºÈÖÓ××׺ں½¿½ÓÑØÂÒÊÒÙŽѺÒҺ˺½

ÌÖÓÖ¸ØÔÖ×ÒØÑÓÐÒÐ×ÓÚÓÓÔÔÖÓÜÑØØÓÖØÙÓ×ØÝÒÖØÔÖÓÐØÓÒØÖ×Óи

º¾º´µÓÑÔÖ×ÓÒØÛÒØÔÖ×ÒØÑÓÐÔÖ¹ØÓÒ×ÒÓØÖÑÓÐ׸ҴµÓÑÔÖ×ÓÒØÛÒØÔÖ×ÒØÖ×ÙÐØÒØÑÓÐÔÖ×ÒØÝÃÓÔÓÒÒØкÒÖØÔÖÓÐØÓÒØÖ×Óм¿¿º

¾¼

Ѻ

½¿

本文来源：https://www.bwwdw.com/article/uh94.html