
granular metteeriyal

kanikakal edapazhakumpozhellaam oorjjam nashtappedunna savisheshathayulla vyathirikthamaya khara, macroscopic kanangalude samyojanamaanu granular metteeriyal (daanyangal koottiyidikkumbol gharshanam aayirikkum ettavum saadhaaranamaaya udaaharanam). granular metteeriyal roopappeduthunna gadakangal taapa chalana ettakkurachilukalkku vidheyamaakaathathra valuthaanu. athinaal, granular metteeriyalile daanyangalude kuranja valippa paridhi ekadesham 1 micrometeraanu. uyarnna valippa paridhiyil, granular vasthukkalude bhauthikashaasthram vyakthigatha daanyangal manjumalakalaaya aise flocalilum vyakthigatha daanyangal chinnagrahangalaaya sourayoodhathinte chhinnagraha belttukalilum prayogikkaam.
manju, andipparippu, kalkari, manal, arrie, kaappi, daanyangal, valam, bairing bolukal ennivayaanu granular vasthukkalude chila udaaharanagal. granular metteeriyalukalekkurichu gaveshanam nerittu baadhakamaan, kuranjathu chaals-augustin dii coolombilekku pookunnu, avarude gharshana niyamam yadhaarthathil granular meteeriyalukalkkaayi prasthaavichirunnu. aushadha vyavasaayam, krishi, oorjja uthppaadanam thudangiya vaividhyamaarnna prayogangalil granular metteeriyalukal vaanijyaparamaayi pradhaanamaan.
podikal avayude cheria kanangalude valippam kaaranam oru prathyeka tharam granular meteeriyalaanu, ithu avaye kooduthal yojipikkukayum vaathakathil eluppathil thookkiyidukayum cheiyunnu.
sainikan/bhauthikashaasthranjan brigadier ralph algar bagnold granular dravyathinte bhauthikashaasthrathinte aadyakaala thudakkakkaaranaayirunnu, addehathinte "dhii physics oof fload manal aandu desert duns" enna pusthakam eee divasathe oru pradhana paraamarshamaayi thudarunnu. metteeriyal shaasthranjanaaya patrick richaardinte abhipraayathil, "granular metteeriyalukal sarvavyaapiyaanu, vyavasaayathile randaamathe ettavum krithrimamaaya meteeriyalaanu (aadyathethu jalamaan)".
oru tharatthil paranjaal, granular metteeriyalukal dravyathinte orotta gattamalla, marichu oru dhaanyathinte sharashari oorjjathe aashrayich kharapadaarthangal, draavakangal allengil vaathakangal ennivaye anusmarippikkunna savisheshathakalundu. ennirunnaalum, eee oro avasthayilum, granular vasthukkal savisheshamaaya gunangalum prakadippikkunnu.
granular metteeriyalukal aaveshabharithamaakumbol (udha.jii. vibrate cheiyukayo ozhukaan anuvadikkukayo cheyyuka). atharam granular metteeriyalukal aaveshathinte keezhil oru sankeernna samvidaanathinte udaaharanamaayi kanakkakkaam. avaa draavakam adisthaanamaakkiyulla asthirathakalum magnus ephakt polulla prathibhaasangalum pradarshippikkunnu.
nirvachanangal.
niravadhi macroscopic kanikakal chernna oru samvidaanamaanu granular dravyam. microscopic kanangale (attangal \molecialukal) sisttathinte ellah dofukalum vivarikkunnu (classical mechanicsil). oro kanikayudeyum chalanathe oru karkkashamaaya pindamayi maathrame macroscopic kanangale vivarikkukayulloo. oro kanikayilum dhaaraalam aantharika doff undu. rund kanikakal thammilulla asthiramaaya koottiyidi pariganikkuka-vegathayil ninnulla oorjjam karkkashamaaya vasthuvayi microscopic aantharika doffilake kaimaattam cheyyappedunnu. namukk "decypation"-maattaanaavaatha taapa uthppaadanam labhikkunnu. baahya driving illaathe, oduvil ellah kanangalum neengunnathu nirtthum ennathaanu phalam. macroscopic kanangalil thaapaparamaaya ettakkurachilukal aprasakthamaan.
oru dravyam nertthathum chalanathmakavum (nayikkappedunna) aayirikkumbol athine granular vaathakam ennum disipeshan prathibhasam aadhipathyam pulartthunnu ennum vilikkunnu.
oru dravyam saandravum sthiravumaayirikkumbol, athine granular soolid ennum jamming prathibhasam aadhipathyam pulartthunnu ennum vilikkunnu.
saandrata idatharam aayirikkumbol athine granular liqvid ennu vilikkunnu.
sthiramaaya perumattangal.
coolumb gharshana niyamam.
granular kanikakal thammilulla aantharika shakthikale oru gharshana prakriyayayi coolomb kanakkaakkukayum kharakanangalude gharshanashakthi avaa thammilulla saadhaarana marddathinu aanupaathikamaanennum staatik gharshana gunakam gathikorshana gunakathekkaal valuthaanennum gharshana niyamam nirddeshikkukayum cheythu. manalthottukalude thakarchayekkurichu addeham padikkukayum anubhavaparamayi rund nirnaayaka konukal kandethukayum cheythu paramavadhi sthirathayulla angle formula _ 1 umm repose formulayude ettavum kuranja angle _ 2 umm. manalthottikkullile charivu paramavadhi sthirathayulla koniletthumbol, koombaaratthinte uparithalathile manal kanikakal veezhaan thudangunnu. uparithala charivu koonn vishrama koninu thulyamaakumbol prakriya nirtthunnu. eee rund konukalum thammilulla vyathyasam, formula _ 3, bagnold konaanu, ithu granular metteeriyalukalude histerisisinte alavaanu. eee prathibhasam fozhsu cheyinukal moolamaanu oru granular solidile stress orupole vitharanam cheyyappedunnilla, marichu parasparam vishramikkunna daanyangalude shringalayaaya fozhsu cheyinukal ennu vilikkappedunnavayiloode ithu kondupookunnu. eee shringalakalkkidayil kuranja sammarddamulla pradeshangalundu, avayude daanyangal mukalilulla daanyangalude falangalkkaayi volting kamaanavum upayogichu samrakshikkunnu. shear stress oru nischitha moolyathil athumbol, fozhsu cheyinukal thakarukayum uparithalathile cheyinukalude avasaanathilulla kanikakal slide cheyyaan thudangukayum cheyyum. thudarnnu, shear stress critical moolyathekkaal kuravaayirikkunnathuvare puthiya fozhsu cheyinukal roopappedunnu, athinaal sandpile sthiramaaya vishramakon nilanirthunnu.
jansen prabhavam.
1895ll echu. eiii. steevin niyamam pinthudarunna neutonian draavakangalil ninnu vyathyasthamayi, kanikakal niranja oru lamba silindaril, silindarinte adithattil alakkunna marddam fillinginte uyarathe aashrayichirikkillenna jansen kandethi. thaazhepparayunna anumaanangalulla oru lalithamaaya maathruka jansen nirddeshichu
1) lamba marddam, formula _ 4, thirashcheena thalatthil sthiramaanu;
2) thirashcheena marddam, formula 5, lamba mardha formula 4 nuu aanupaathikamaanu, ivide formula 7 bahiraakaashath sthiramaanu;
3) mathil gharshana staatik coffificient formula _ 8 mathilumaayulla sanbarkkathil lambamaya looad nilanirthunnu;
4) ellah aazhangalilum vasthuvinte saandrata sthiramaanu.
granular metteeriyalile marddam pinneedu mattoru niyamathil vivarikkunnu, athu saachureshane kanakkaakkunnu formula _ 9, ivide formula _ 10 umm formula _ 11 umm silindarinte aaram, sailo formula _ 12 nte mukalil.
thannirikkunna mardha samavaakyam kanikayude valupavum sailoyude aaram thammilulla anupatham polulla athirthi vyavasthakalkku kaaranamakunnilla. vasthuvinte aantharika sammarddam alakkaan kazhiyaathathinal, jaansante oohaapohangal nerittulla oru pareekshanatthiloodeyum sthireekarichittilla.
roow stress-dailaattansi bandham.
1960 kalude thudakkathil, shoar testtukalil shoar shakthiyil dailaattansi prabhavam roow padikkukayum avaa thammil oru bandham nirddeshikkukayum cheythu.
2d-ll mono-dispersed kanangalude asambliyude mechanical propertykal prathinidheekarikkunna praadhamika voliyathe adisthaanamaakki vishakalanam cheyyaan kazhiyum, saadhaarana neelamulla formula _ 13, yathaakramam lambavum thirascheenavumaaya dishakalilaanu. sisttathinte jyaamitheeya savisheshathakal formula _ 14, variable formula _ 15 ennivayaal vivarikkunnu, ithu kondaakt pooyintukal sliding prakriya aarambhikkumbol konine vivarikkunnu. pradhana pradhana sammarddathinte dishayaaya lamba dishayaaya formula 16, cheria pradhana sammarddathinte dishayaaya thirashcheena disha enna formula 17 ennivayaal soochippikkuka.
appol athirthiyile sammarddam vyakthigatha kanikakal vahikkunna kendreekritha shakthiyaayi prakadippikkaam. ekeekritha stress formula _ 18 ulla bioxial loadinginu keezhil, athinaal formula _ 19.
santhulithaavasthayil
soothravaakyam _ 20
ivide formula _ 21, gharshana koonn, kondaakt fozhsum kondaakt normal dishayum thammilulla konaanu.
22 enna soothravaakyam, sparsana balam gharshana koninullil vannal kanikakal ippozhum sthirathayode thudarumenna konine vivarikkunnu. ithu nirnnayikkunnath gharshana soothravaakyam _ 23-nte gunakam kondaanu, athinaal soothravaakyam _ 24. sisttathil sammarddam prayogichukazhinjaal soothravaakyam _ 21 kramena vardhikkukayum soothravaakyam _ 26 maattamillathe thudarukayum cheiyunnu. formula _ 27 aayirikkumbol kanikakal slide cheyyaan thudangum, athinte falamaayi sisttathinte ghadana maarukayum puthiya fozhsu cheyinukal srishtikkukayum cheyyum. formula _ 28, thirascheenavum lambavumaaya sthaanachalanangal yathaakramam thripthippeduthunnu
soothravaakyam _ 29
granular vaathakangal.
daanyangal thammilulla sanbarkkam valare apoorvamaakunna tharatthil granular metteeriyal kooduthal kadinamaayi oodikkukayaanengil, metteeriyal vathaka avasthayilekku praveshikkunnu. athinanusarichu, thermodynamic thaapanilaykk samanamaaya dhaanya vegathayile ettakkurachilukalude root sharashari squarinu thulyamaaya oru granular thaapanila nirvachikkaan kazhiyum.
parambaraagatha vaathakangalil ninnu vyathyasthamayi, daanyangal thammilulla koottiyidikku kaaranamakunna disipative swabhaavam kaaranam granular vasthukkal koottamaayi koottimuttukayum koottimuttukayum cheyyum. eee clusteringinu rasakaramaaya chila prathyaaghaathangalundu. udaaharanathinu, bhaagikamaayi vibhajicha granular vasthukkalude petti shakthamayi ilakkiyaal, kaalakramena daanyangal oru parambaraagatha vaathakathil sambhavikkunnathupole rund paarteeshanukalilekkum thulyamaayi vyapikkunnathinupakaram oru partitionilekku shekharikkappedum. granular maiks wells demon ennariyappedunna eee prabhavam, eee prakriyayil sisttathil ninnu oorjjam nirantharam nashtappedunnathinaal thermodynamics thathwangalonnum lamghikkunnilla.
umm model.
oorjja soothravaakyam _ 30 kanikakal, oorjja soothravaakyam _ 32 ulla kanika soothravaakyam _ 31 pariganikkuka. yoonit samayathil chila sthiramaaya nirakkil, oorjja soothravaakyam _ 34 ulla rund kanangalude soothravaakyam _ 33 kramarahithamayi thiranjedukkuka, koodaathe koottuka soothravaakyam _ 35 kanakkaakkuka. ippol, kramarahithamayi rund kanikakalkkidayilulla motham oorjjam vitharanam cheyyuka kramarahithamayi soothravaakyam _ 36 thiranjedukkuka, angane koottiyidikku sesham aadyathe kanathinu oorjja soothravaakyam _ 37 umm randaamathe soothravaakyam _ 38 umm undaakum.
yaadruchika parinaama samavaakyam formula 39, ivide formula 40 koottiyidi nirakkaanu, formula 41 kramarahithamayi formula 42 (unifom distribution) ll ninnu thiranjedukkunnu, koodaathe jeey kramarahithamayi oru ekeekritha vitharanathil ninnu thiranjedukkunna soochikayaanu. oru kanikayude sharashari oorjjam soothravaakyam _ 43
randaamathe nimisham
formula _ 44
ippol randaamathe nimishatthinte samayathinte vyulppannam
formula _ 45
sthiramaaya avasthayil
formula _ 46
randaamathe nimishathe deferential samavaakyam pariharikkuka
soothravaakyam _ 47
ennirunnaalum, nimishangale savisheshathappeduthunnathu, oorjja vitharanam vishakalanaparamayi pariharikkan namukk kazhiyum, moment generating function muthal. laplace parivartthanam pariganikkuka formula _ 48.
ivide formula _ 49, formula _ 50
n derivativa
soothravaakyam _ 51
ippol
soothravaakyam _ 52
soothravaakyam _ 53
formula _ 54
formula _ 55-nuu parihaaramaayi formula _ 56 enna variable maattathode
soothravaakyam _ 57
laplace parivartthanam eduthu ulppaadana pravartthanam kanakkakkikkondu nammal aaa formula _ 58 (boltsman vitharanam) kanikkum
formula _ 59
jamming transition.
granular sisttangal jamming pradarshippikkukayum jamming avasthayilekkulla thermodynamic ghatta parivarthanamaayi kanakkaakkappedunna jamming parivarthanatthinu vidheyamaakukayum cheiyunnu.
draavakam polulla ghattathil ninnu khararoopathilulla ghattathilekkulla parivartthanatthe thaapanila, formula _ 60, vooliyam fraction, formula _ 61, shear stress, formula _ 62 ennivayaal niyanthrikkunnu. glass parivartthanatthinte saadhaarana ghatta rekhaachithram formula _ 63 thalathilaanu, ithu oru jammed stettu mekhalayaayum transition line vazhi anjaamd liqvid avasthayaayum thirichirikkunnu. granular dravyathinte ghatta rekhaachithram 64 thalam enna soothravaakyathilaanu, critical stress karvu formula 65 avastha ghattathe yathaakramam granular solidukalkku anuyojyamaaya jammed anjammidu mekhalayaayi vibhajikkunnu. isotropicalaayi jaam cheytha granular systethinu, formula _ 61 oru nischitha pooyintinu chuttum kuraykkumbol, formula _ 67, bulk, shear moduli sameepanam 0. formula _ 67 pooyint critical vooliyam fraction formula _ 69-maayi poruthappedunnu. pooyint formula _ 67-lekkulla dooram nirvachikkuka, critical vooliyam fraction, formula _ 71. formula _ 67 pooyintinu sameepamulla granular sisttangalude swabhaavam randaam krama parivarthanavumaayi saamyamullathayi anubhavaparamayi kandethithi bulk modulus formula _ 73 ulla oru power loow scaling kaanikkunnu, koodaathe formula _ 73 poojyathe sameepikkumbol chila vyathyastha swabhaavasavisheshathakal undu. oru ananthamaaya systethinu formula _ 69 sthiramaanenkilum, oru parimithamaaya sisttam athirthi efakttukalkku chila shreniyil formula _ 69 nte vitharanathinu kaaranamaakunnu.
jaaminginte lubachevsky-stillinger algoritam oraale simulated jaam cheytha granular konfigareshanukal nirmmikkaan anuvadikkunnu.
paatten roopeekaranam.
uthejithamaaya granular dravyam oru sambannamaaya paatten roopeekarana samvidaanamaanu. granular metteeriyalukalil kaanapedunna paatten roopappeduthunna chila perumattangal ivayaanu
paatten roopappeduthunna chila perumattangal computer simuleshanukalil punarnirmikkaan saadhyamaan.
atharam simuleshanukalkku rund pradhana computational sameepanangalund, samayakramavum sambhava-niyanthrithavum, aadyathethu metteeriyalinte uyarnna saandrathaykkum kuranja theevrathayulla chalanangalkkum ettavum kaaryakshamamaan, randaamathethu metteeriyalinte kuranja saandrathaykkum uyarnna theevrathayulla chalanangalkkum.
shabdaparamaaya efakttukal.
anuyojyamaaya perilulla skeeki beach polulla chila beach manalukal nadakkumbol nilavilikkunnu. chila marubhoomiyile manalkkunnukal manjuveezhchayude samayatho allengil avayude uparithalathe thadassappeduthumbozho kuthichuyarunnathaayi ariyappedunnu. sailo horking ennariyappedunna prakriyayil sailosil ninnu purathuvidunna granular metteeriyalukal uchathilulla shabda udvamanam srishtikkunnu.
granulation.
praadhamika podi kanikakal "granuelukal" ennu vilikkunna valia, multy particle entittikal roopappeduthunnathinaayi bandhippikkunna pravartthanamo prakriyayo aanu granulation."
chrystalisation.
vellamo mattu draavakangalo vendathra pathukke thanuppikkumbol, kramarahithamayi sthaapichirikkunna thanmathrakal punakrameekarikkukayum khara paralukal uyarnnuvarikayum valarukayum cheiyunnu. kramarahithamayi paaykk cheytha granular metteeriyalukalil samanamaaya chrystalisation prakriya sambhavikkam. thanuppikkunnathiloode oorjjam neekkam cheiyunnathil ninnu vyathyasthamayi, granular metteeriyalile chrystalisation baahya drivingiloode nedaam. krameekarichatho granular vasthukkalude christalisationo idaykkide kashanagal vettiyathilum vibrated granular dravyathilum sambhavikkunnath nireekshikkappettundu. tanmatra samvidaanangalil ninnu vyathyasthamayi, vyakthigatha kanangalude sthaanangal pareekshanatthil tracuchaian kazhiyum. golaakrithiyilulla daanyangalude oru samvidaanathinaayulla computer simulationukal oru vooliyam fraction formula _ 77-ll ekeekritha chrystalisation uyarnnuvarunnathayi velippeduthunnu. computer simulationukal granular chrystalisation aavashyamaaya ettavum kuranja cheruvakal thirichariyunnu. prathyekichu, guruthwaakarshanavum gharshanavum aavasyamilla.
granular metteeriyalukalude computational modeling.
granular metteeriyalukalude modelinginu niravadhi reethikal labhyamaan. eee reethikalil bhooribhaagavum sthithivivarakkanakku reethikal ulkkollunnu, athiloode pooyint daattayil ninno chithratthil ninno uruthirinja vividha sthithivivarakkanakku gunangal verthirichedukkukayum granular maadhyamathinte stokkaastik modalukal srishtikkaan upayogikkukayum cheiyunnu. atharam reethikalekkurichulla sameepakaalavum samagravumaaya avalokanam tahmasebiyilum mattu (2017) bhaashakalilum labhyamaan. aduthide avatharippicha granular kanangalude oru paaykk nirmmikkunnathinulla mattoru badal level settu algorithathe adisthaanamaakkiyullathaanu, athiloode kanangalude roopaghadanaykkaayi verthirichedutha sthithivivarakkanakkukali kanathinte yadhaartha aakruthi pidichedukkaanum punarnirmmikkaanum kazhiyum.

