Capillarity
Chiitiko checapillarity
Kana tikanyudza chubhu yegirazi yakatetepa mumudziyo une mvura yakanyarara isina kuyerera, mvura iri muchubhu inokwira kusvika paurefu hk pamusoro pechiyero N mumudziyo, uye pamusoro pemvura muchubhu uchaumba meniski m (fig. 1_a_). Kana chubhu iri nhete zvikuru, kukwirira kwekukwira kwekapirari kwemvura hk kunowedzera.
Kukwira kwemvura nekapilari kunonzi kunokonzerwa nesimba rinosimudza remeniscus m, uye kunotsanangurwa nemasimba ekukwezvana pakati pemamorekuru emvura negirazi pamwe nekumanikidzana kwepamusoro pakati pemadziro epepi nhete nepamusoro pemvura.
Panzvimbo yekusangana pakati pemadziro echubhu regirazi nepamusoro pemvura panoshanda simba recalipari R munzira inofambirana netangenti yepamusoro pe meniscus m, iro rinoratidzwa muchiyero chehuremu pachikamu chehurefu, mu p/cm. Nokupatsanura simba R kuita chikamu J chinofambirana nepamusoro pemadziro uye chikamu P chakanangana nemadziro, tinowana simba rinokwidziridza meniscus (fig. 1_a_): J = R cosα.
Kona α inoumbwa nesimba R nepamusoro pemadziro inonzi kona yekapilariti uye kukosha kwayo kuri pakati pe 0 ne 90O. Kana mvura iri mutubhu yekapilari nemadziro ayo zvakachena chose, ipapo α=0, pamusoro pemeniscus hunenge huri hwehafu yedenderedzwa, simba rinosimudza J = R riri guru zvikuru (fig. 1_b_). Kana mvura iine mafuta kana maorganic acids kana kana madziro aine mafuta, ipapo α = 90°, meniscus haumboumbwi, uye hapana kukwira kwemvura nekapilariti.
Muf. 1. Kukwira kwemvura kwekapilari nekushanda kwemasimba ekapilari
Simba rinokwidziridza J = R cos α tinoriwana kubva pamamiriro ekuenzana, maererano nawo simba rose rinokwidziridza J panzvimbo yese ye meniscus, kureva kapirari rine radius r, rinobata mbiru yemvura iri muchubhu pakureba h__ₖ:
R cos α · 2π_r_ = π_r_² h__ₖ γ__w
apo γ__w huremu hwevhoriyamu hwemvura.
Kubva paequation yapfuura tinowana simba recapillary rinokwidziridza:
R cos α = (r · h__ₖ · γ__w) / 2
kureva kureba kwekusimuka kwecapillary:
h__ₖ = (2_R_) / (r · γ__w) · cos α [cm].
Mvura inopisa yekapilari inokwira mutubhu yekapilari kusvika pakakwirira kupfuura inotonhora nekuda kwekuve neviscosity yakakura. Nokudaro, kune hurefu humwe chete hwekukwira kwekapilari h__ₖ simba R cos α rinenge diki pamvura inopisa yekapilari kupfuura pamvura inotonhora. Maererano nemiedzo yakaitwa pamitambo yakasiyana-siyana yetembiricha yemvura t pasi pemamiriro akafanana chose, kukosha kunotevera kwesimba rekusimudza R cos α kwakawanikwa:
t =
0°
10°
20°
40°
R cos α =
0,0756
0,0742
0,0727
0,0695 p/cm
Mvura iri muchubhu yekapilari iri pasi pekusanduka pakudhonzerwa, nokuti simba R cos α rinoisimudza kumusoro, ukuwo simba regiravhiti richiridhonza pasi. Zvisinei, madziro echubhu yekapilari ari pasi pekumanikidzwa pasi pechiito chesimba rekepilari R.
Kapilariti muvhu
Kapilarity inowanikwawo muvhu, uko machubhu ekapilari anoumba maporesi, ayo akabatana pamwe chete kumativi ose. Kana ivhu riri diki-diki muzvimedu, maporesi anowedzera kuva madiki uye kukwirira kwekukwira kwekapilari kunowedzera. Kukwirira uku kunobvawo pachimiro chevhu. Zvisinei, maporesi ari muvhu anogona kuva ehukuru hwakasiyana, uye ipapo kukwirira kwekukwira kwekapilari kunosiyanawo. Kana mvura yekapilari pakukwira kwayo yasvika pa“nzvimbo dzakafara”, kureva pane pore hombe kupfuura rinowirirana nesimba rekukwidza pahupamhi hwepore rakamanikana pakukwirira kwasvikwa, ipapo kukwira kwekapilari mberi kunobva pahukuru hweporo ihwohwo hukuru. Muchiitiko ichi tine kukwirira kwekapilari kunoshanda h__ₖₐ kunobva pama pores makuru zvikuru. Ukuwo, kana pakudzikira kwechiyero chemvura yepasi mvura yekapilari ichidzika kubva pamusoro ichienda pasi yasangana ne“nzvimbo dzakatetepa”, icharamba iri pakudzika ikoko uye haichazodziki mberi. Muchiitiko ichocho tine kukwirira kwekapilari kunongoita pasina kushanda h__ₖₚ, kunobva pama pores maduku zvikuru.
Zvichienderana neporosity uye chimiro cheivhu, panosiyaniswa mvura yekapilari yakavharwa uye mvura yekapilari yakazaruka.
Mvura yekapirari yakavharwa ine chekuita negirazi remvura yepasi pevhu uye pakusimuka inosundira mhepo iri pamberi payo kuenda kumusoro kwevhu. Nekuda kweizvozvo huwandu hwemhepo hunowedzera munzvimbo yepamusoro, uye pamwe nazvo kumanikidzwa kwemhepo mumapori enzvimbo iyoyo. Kumanikidzwa kwemhepo kwakadaro kunopikisana nekukwira kwekapirari, saka kukwirira kwekukwira kwekapirari kunova kudiki. Nyaya iyi inoitika muzvikamu zvevhu zviri pasi, zviri pamusoro chaipo pechiyero chemvura yepasi pevhu, apo mapori ari madiki uye pakukwira kwekapirari mvura inozadza mapori ese zvizere.
Mvura yecapillary yakazaruka inobatanidzwawo negirazi remvura yepasi pevhu, asi inowanikwa pedyo nemaporo akazara nemhepo. Mamiriro aya anoitika muchikamu chepamusoro chevhu apo maporo akasiyana saizi, zvekuti mvura inozadza zvizere maporo madiki chete, asi mumaporo makuru ari pedyo mune mhepo. Pakukwira kwecapillary, mvura inosundidzira mhepo kubva mumaporo madiki ichipinda mumaporo makuru ari pedyo, zvekuti munzvimbo yepamusoro pamusoro pembiru yemvura mucapillary hapagadzikwi kudzvinyirira kwemhepo, saka mvura yecapillary yakazaruka inokwira pakureba kukuru kupfuura yakavharika.
Nzvimbo mune iri mvura yekapilariti yakavharika kana yakazaruka inotsanangurwa zvichienderana nehuwandu hwemvura w muvhu.
Kana mvura ye capillary yakavharwa, maporesi ose anenge azadzwa nemvura, zvinoreva kuti huwandu hwemvura muvhu w = wZ, kureva kuti dhigirii rekuzara S__ᵣ = 1,0.
Pakati pemvura yecapillary yakavhurika, maburi madiki anozadzwa chose nemvura, asi maburi makuru anozadzwa chikamu nemvura, uye izvi zvichisanganisira firimu remvura rinofukidza zvidimbu zvakasimba nemvura yemakona (muf. 2) panzvimbo dzinobatanidza zvidimbu zvakasimba, uye chikamu nemhepo, saka munyaya iyi w < wZ, kureva kuti S__ᵣ < 1,0.
Kukwirira kwekukwira kwekapilari h__ₖ kumarudzi akasiyana evhu kunotariswa nekuedzwa kwelabhoritari. Avhareji yekukwirira h__ₖ kumarudzi akasiyana evhu inowanikwa mumiganhu inotevera:
Rudzi rwevhu
h****ₖ
jecha rakatsetseka
hₖ = 0,05 – 0,5 m
guruva
hₖ = 0,5 – 5,0 m
ivhu rine udongo
hₖ = 5,0 – 15,0 m
ivhu revhu
hₖ = 15,0 – 50,0 m uye kupfuura
Muf. 2. Bhande remvura nekunyorova kwemvura pakona
Muvhu, simba rekapirari R rinoita nekudzvanya pazvimedu zvakasimba nenzira yokuti pakati pazvo panoumbwa kunonzi kumedzerwa kunoonekwa, kunoshanda sechimwe chisungo pakati pezvimedu zvakasimba. Zvisinei, kumedzerwa kunoonekwa kunongovapo bedzi kana kuchikwanisika kukwira kwemvura nenzira yekapirari mumaporesi evhu. Kana ivhu rikanyudzwa mumvura, maporesi anozara nemvura uye kumedzerwa kunoonekwa kunopera kuvapo.
Kohesheni inoonekwa inotsanangura chiitiko chekuti jecha rakanaka, iro riri mushwere rakaoma rakasununguka, muhunyorova rinowana kuonana kunobatanidza zvokuti rinogona kuumbwa, chimwe chinhu chisingagoneki nejecha rakaoma.
Zvinozivikanwa kuti jecha (kana risiri silt kana guruva) pamhenderekedzo dzegungwa rinonyoroveswa nemafungu rine simba rakadaro rekutakura mutoro zvekuti bhasikoro kana motokari zvinogona kufambiswa pamusoro paro, asi kure zvishoma, uko mafungu asingasviki, jecha rimwe chetero riri rakaoma uye mavhiri anonyura mariri, zvichiita kuti kufamba kupi nokupi kusakwanise.
KUPFUURIRA
Kuyerera kwemvura kuburikidza nechinhu chinobvumira kupfuura
Ngatitarisei midziyo yakabatana A, B, C, D, uye E (muf. 3), umo chikamu chimwe kubva a kusvika b chehurefu L chakazadzwa nezvinhu zvinopfuura mvura, semuenzaniso jecha. Kana tikadurura mvura kune imwe mugumo wemidziyo yakabatana kusvika pachiyero N₁, ipapo chiyero chemvura mumidziyo yakabatana chichasiyana, kureva kuti chichadzikira maererano nehurefu hwenzira inofambwa nemvura.
Sl. 3. Kuyerera kwemvura kuburikidza nechinhu chinopindika
Panguva iyo kureba kwechikamu chemvura h₁ kwasvika pamberi pefilter, shure pefilter kuchava h₂. Musiyano pakati pemazinga N₁ ne N₂ panguva iyoyo ndiwo:
h = h₁ − h₂
Musiyano h unomirira kudzvinyirirwa kwehydrostatic kwakanga kwarasika, kwakashandiswa kukunda kuramba kwekuyerera kwemvura kuburikidza nesefa. Chiitiko ichi chakatsanangurwa nenyanzvi yechiFrench Darcy kare muna 1856. gore. Panguva iyoyo akaisawo fomura inotevera yekuverenga kumhanya kwekuyerera kwemvura kuburikidza nemuviri unopinda mvura:
V = k × (dh/dL) = ki
kupi:
- V = kumhanya kwekuyerera kwemvura kuburikidza nemutumbi unopindika, [cm/sec],
- k = coefficient yekupindika inoenderana nehunhu hwevhu [cm/sec],
- dh = kureba kunowanikwa kana urefu h hukakamurwa kuita nhamba huru yezvikamu zvitete [cm],
- dL = kureba kunowanikwa kana kureba L kukamurwa kuva nhamba imwe chete yekureba sezvakaita kukwirira h, [cm].
Chiyero dh/dL = i chiyero chekureba kwarasika mukunyura kana zvichienzaniswa nenzira yakafambwa nemvura uye chinonzi kuwira kwehydraulic, gradient yehydraulic kana zvakare kudzikira kwepiezometer. Iri zita rekupedzisira rinobva kumapombi B, C uye D, anonzi piezometric pipes. Muenzaniso uri mberi unonzi mutemo waDarcy wekuyerera kwemvura kuburikidza nefilter.
Huwandu hwese hwemvura q, hunopfuura nepasefa rine nzvimbo yekuchekwa A munguva yakatarwa t huri
q = kAti,
kwazvinobva
k = q / (Ati), kureva k = qL / Ath,
apo i = h / L = kuderera kwehydraulic pakureba L (kana kuri kwakatwasuka).
Koefficienti k inoratidza kupinda kwemvura muvhu patembiricha 10°C.
k = V / i [cm/sec]
Kumhanya kwekuyerera kwemvura kuburikidza nevhu kunowanikwa kubva mufomura
V = q / A [cm/sec],
apo q = huwandu hwemvura inoyerera nepavhu mu cm³ pasekondi, patembiricha ye10°C, A = nzvimbo yechikamu chemuchinjiko chevhu, iyo mvura inoyerera nayo, [cm²].
Mutemo waDarcy unoshanda pakufamba kwemvura kwelaminar, kureva kufamba kwakadzikama, kusina madenderedzwa uye pakumhanya kudiki.
Kumhanya kwefilter V ndiko kumhanya kwepakati pekufamba kwemvura kuburikidza nevhu uye hakufanani nekumhanya kwechokwadi kwekuyerera kwemvura, uko kwakakura. Pakuyerera kwemvura kuburikidza nefilter, zvikamu zvakaenzana zvekupinza dh zvinowanzoshandiswa pamarefu asina kufanana enzira yemvura dL, saka hydraulic gradient inoshanduka kubva pane imwe poindi yevhu kuenda pane imwe.
Kupindika kwevhu kunoenderana nehukuru hwemapore ari mariri. Kana tikaisa mutoro pavhu, mapore anoderera uye kupindika kunoderera. Saka, pavhu rimwe chete, koefishenti yekupindika k inonyatsoenderana zvakananga nehukuru hweporosity, kana kuti nekoefishenti yaro yeporosity e. Zvisinei, pamhando dzakasiyana dzevhu, porosity inoratidzwa nekoefishenti yeporosity e haigoni kuva muyero wekupindika, nokuti kupindika uku hakutsamiri zvakanyanya pa total porosity yevhu asi pahukuru hwemapore ari mariri. Saka semuenzaniso jecha rine matombo tudiki rine porosity e = 0,25, rine kupindika kukuru kwazvo, k = 2–3 cm/sec, asi ivhu rakapfava, rine porosity 60%, koefishenti ye porosity e = 1,50, rine kupindika kudiki, k = 10_⁻⁶ kusvika 10⁻_¹¹ cm/sec.
Coefficient yekupinda k inogona kutsanangurwa nenzira yekuverenga, nemiedzo yerabhoritari uye yemumunda.
Kutsunga kwekoefishenti nenzira dzekuverenga kunobva pakuumbwa kwegranulometric kwevhu. Pakutsunga koefishenti k inotorwa fungidziro yokuti zvidimbu zvakasimba zvevhu zvine chimiro chesero, izvo zvisingaenderani nechokwadi, kunyanya pavhu rakabatana. Nokuda kweizvozvo, kukosha kwekoefishenti k kwakatsanangurwa nenzira iyi hakugamuchirwi sekwechokwadi.
Kuongorora coefficient k nemiedzo yerabhoritari ndiko kwakapararira zvikuru uye kunoitwa pamasampuli evhu asina kukanganisika. Zvisinei, kunyatsojeka kwecoefficient k yakatarwa nenzira iyi kunoenderana nezvinhu zvakawanda zvakadai sekuti sampuli iri kuedzwa inomiririra here uye kusvika papi rukoko runofambiswa mvura muvhu, zvino kubva pamamiriro ekusakanganisika kwesampuli mumudziyo wekuedzera uye kubva panzira yekuitwa kwebvunzo. Nekuedza huwandu hwakakwana hwemasampuli anomiririra ivhu rakapiwa, nekutora sampuli panzvimbo mumacylinder emuchina chaiwo wekuedzera uye nenzira yakafanira yekuitwa kwebvunzo, zvinokwanisika kuwana kukosha kunoswedera pedyo kwecoefficient k kunogona kushandiswa sechinogutsa.
Kuona coefficient k nemuyedzo wemumunda kunopa mhedzisiro yakanyatsojeka, nokuti kunonyatsoenderana nekuumbwa nekutevedzana kwematanho evhu riri munzvimbo iyoyo. Zvisinei, nzira iyi yekuona coefficient k inoda nguva yakawanda nemari yakawanda, ndosaka ichiitwa kashoma uye chete muzviitiko apo kukosha kwayo kwakanyatsojeka kunonyatsodiwa.
Zvinoenderana nemitemo yedu yekumisikidza, ivhu rinofungidzirwa kuva iro rine coefficient yekupindika:
- k < 10_⁻_¹¹ cm/sec — inenge isingapfuuri
- k < 10_⁻_⁹ — inopindika zvishoma zvikuru
- k < 10_⁻_⁷ — rinopindika zvishoma
- k < 10_⁻_⁵ — chinopindika zviri pakati
- k < 10_⁻_³ — rinopindika zvakanyanya
- k > 10_⁻_³ — inopinda mvura zvikuru