Kukwera kwa kapilari
Zochitika za kapilarity
Tikamizamo chubu chaching’ono cha galasi m’chidebe chokhala ndi madzi bata osayenda, madzi a m’chubucho adzanyamuka kufika pa msinkhu hk pamwamba pa mulingo N m’chidebecho, ndipo pamwamba pa madzi m’chubucho adzapanga meniski m (chith. 1_a_). Chubucho chikakhala chocheperako, msinkhu wa kukwera kwa capillary wa madzi hk umakhala wokulirapo.
Kukwera kwa madzi mwa kapilari kumayikidwa pa mphamvu yokweza ya meniscus m, ndipo kumafotokozedwa ndi mphamvu zokopa za ma intermolecular pakati pa mamolekyu a madzi ndi galasi komanso ma tension a pamwamba pakati pa makoma a chubu chopyapyala ndi pamwamba pa madzi.
Pa malo olumikizana pakati pa khoma la chubu cha galasi ndi pamwamba pa madzi amagwira mphamvu ya capillary R m’njira ya tangent pa pamwamba pa meniscus m, yomwe imafotokozedwa ndi unit ya kulemera pa unit ya utali, mu p/cm. Pogawa mphamvu R kukhala gawo J lofanana ndi pamwamba pa khoma ndi gawo P loyima pa khoma, timapeza mphamvu yokweza ya meniscus (chith. 1_a_): J = R cosα.
Ngongole α imene mphamvu R imapanga ndi pamwamba pa khoma imatchedwa ngongole ya kapilariti ndipo mtengo wake umakhala pakati pa 0 ndi 90O. Ngati madzi ali mu chubu cha kapilari ndi makoma ake ali oyera kwathunthu, ndiye α=0, pamwamba pa meniscus ndi theka la bwalo, mphamvu yokweza J = R ndi yayikulu kwambiri (chith. 1_b_). Ngati madzi ali ndi mafuta kapena ma asidi a organic kapena ngati makomawo ali amafuta, ndiye α = 90°, palibe kupanga meniscus, choncho palibenso kukwera kwa madzi mwa kapilariti.
Sl. 1. Kukwera kwa madzi mwa capillary ndi kuchitapo kanthu kwa mphamvu za capillary
Mphamvu yokweza J = R cos α timaipeza kuchokera pa chifuniro cha mgwirizano, malinga ndi chomwe mphamvu yonse yokweza J pa mphepete wonse wa meniscus, ndiye kuti pa chubu cha capillary cha radius r, imagwira mzati wa madzi mu chubu wokhala ndi kutalika h__ₖ:
R cos α · 2π_r_ = π_r_² h__ₖ γ__w
kumene γ__w ndi kulemera kwa voliyumu ya madzi.
Kuchokera ku equation yapitayi timapeza mphamvu ya kapilari yokweza:
R cos α = (r · h__ₖ · γ__w) / 2
kapena kutalika kwa kukwera kwa capillary:
h__ₖ = (2_R_) / (r · γ__w) · cos α [cm].
Madzi ofunda a kapilara amakwerera m’chubu cha kapilara mpaka kutalika kwakukulu kuposa amadzi ozizira chifukwa cha kukhuthala kwakukulu. Chifukwa chake, pa kutalika kofanana kwa kukwera kwa kapilara h__ₖ mphamvu R cos α ndi yochepa kwa madzi ofunda a kapilara kuposa a ozizira. Malinga ndi mayesero omwe anachitika pa kutentha kosiyanasiyana kwa madzi t pa mikhalidwe yomweyi, ma values otsatirawa a mphamvu yokweza R cos α apezeka:
t =
0°
10°
20°
40°
R cos α =
0,0756
0,0742
0,0727
0,0695 p/cm
Madzi mu chubu cha kapilari amakhala pa tension ya kukokera chifukwa mphamvu R cos α imawakweza mmwamba, pamene mphamvu ya mphamvu yokoka imawakokera pansi. Komabe, makoma a chubu cha kapilari amakhala pa kukanikizidwa pansi pa mphamvu ya kapilari R.
Kapilarnosti mu nthaka
Capillarity ilipo komanso m’nthaka, kumene mapaipi a kapilari amapanga ma pore, omwe amalumikizana m’njira zonse. Nthaka ikakhala yofinyana kwambiri, ma pore amakhala ang’ono kwambiri ndipo kutalika kwa kukwera kwa kapilari kumakhala kwakukulu. Kutalika kumeneku kumadaliranso kapangidwe ka nthaka. Komabe, ma pore a m’nthaka angakhale a kukula kosiyanasiyana ndipo pamenepo kutalika kwa kukwera kwa kapilari kumakhalanso kosiyanasiyana. Ngati madzi a kapilari pakukwera afika pa “malo otakata,” ndiye kuti pa pore lalikulu kuposa lomwe limagwirizana ndi mphamvu yokweza ya m’lifupi mwa pore yopapatiza pa kutalika komwe kwafikidwako, ndiye kuti kukwera kwa kapilari kwina kumadalira kukula kwa pore lalikulolo. Pamenepa tili ndi kutalika kogwira ntchito kwa kukwera kwa kapilari h__ₖₐ komwe kumadalira ma pore akulu kwambiri. Mosiyana ndi pamenepo, pamene madzi a kapilari akatsika kuchokera pamwamba kupita pansi ndipo mlingo wa madzi apansi ukatsika, akakumana ndi “malo opapatiza” adzakhala pa kuya komweko ndipo sadzatsikanso kupitirira. Pamenepa tili ndi kutalika koipa kwa kapilari h__ₖₚ, komwe kumadalira ma pore ang’ono kwambiri.
Malinga ndi porosity ndi kapangidwe ka nthaka, amasiyanitsa madzi a capillary otsekedwa ndi otseguka.
Madzi a kapilale otsekedwa ali pa ubale ndi galasi la madzi apansi panthaka ndipo pamene akukwera amakankha mpweya patsogolo pake kulowa m’gawo la pamwamba la nthaka. Chifukwa chake kuchuluka kwa mpweya m’gawo lapamwamba kumawonjezeka, motero kupanikizika kwa mpweya m’mitundu ya mpata wa deralo. Kupanikizika kwa mpweya kotereku kumatsutsana ndi kukwera kwa kapilale, choncho kutalika kwa kukwera kwa kapilale kumakhala kochepa. Mlandu uwu umachitika m’magawo otsika a nthaka, pafupi kwambiri pamwamba pa madzi apansi panthaka, kumene ma pores ndi ang’ono ndipo pakukwera kwa kapilale madzi amadzaza mipata yonse kwathunthu.
Madzi a kapilari otseguka alinso okhudzana ndi mulingo wa madzi apansi panthaka, koma amakhala pafupi ndi mabowo odzaza ndi mpweya. Izi zimachitika m’gawo lapamwamba la nthaka pamene mabowo ali a kukula kosiyanasiyana moti madzi amadzaza kwathunthu mabowo ang’onoang’ono okha, pamene m’mabowo aakulu oyandikana nawo muli mpweya. Pa kukwera kwa kapilari, madzi amakankhira mpweya kuchokera m’mabowo ang’onoang’ono kupita m’mabowo aakulu oyandikana nawo, kotero kuti m’gawo lapamwamba pamwamba pa mzati wa madzi mu kapilari sipangike kuthamanga kwa mpweya, motero madzi a kapilari otseguka amakweza kwambiri kuposa otsekeka.
Dera limene kuli madzi a kapilari otsekedwa kapena otseguka limadziwika potengera kuchuluka kwa madzi w m’nthaka.
Pa madzi a capillary otsekedwa, ma pores onse amadzazidwa ndi madzi, zomwe zikutanthauza kuti kuchuluka kwa madzi m’nthaka w = wZ, ndiye kuti kuchuluka kwa kukhuta S__ᵣ = 1,0.
Pa madzi a capillary otseguka, mabowo ang’onoang’ono amadzazidwa kwathunthu ndi madzi, pamene mabowo akuluakulu amadzazidwa pang’ono ndi madzi ndipo ndi filimu ya madzi yomwe imaphimba tinthu tolimba ndi madzi a ngodya (sl. 2) pa malo olumikizana pakati pa tinthu tolimba, komanso pang’ono ndi mpweya, motero pa nkhaniyi w < wZ, ndiye S__ᵣ < 1,0.
Kutalika kwa kukwera kwa kapilara h__ₖ kwa mitundu yosiyanasiyana ya nthaka kumatsimikiziridwa ndi mayeso a labotale. Kutalika kwa pakati h__ₖ kwa mitundu yosiyanasiyana ya nthaka kuli m’malire awa:
Mtundu wa nthaka
h****ₖ
mchenga wabwino
hₖ = 0,05 – 0,5 m
fumbi
hₖ = 0,5 – 5,0 m
nthaka yaudongo
hₖ = 5,0 – 15,0 m
dongo
hₖ = 15,0 – 50,0 m ndi kuposerapo
Chith. 2. Filimu yamadzi ndi madzi a pamwamba a ngodya
M’nthaka mphamvu ya kapilare R imachitira pa tinthu tating’ono tolimba ndi kukakamiza kotero kuti pakati pawo pamapangika chimene chimatchedwa kumamatira konyenga, chomwe chimagwira ngati kulumikizana kwina pakati pa tinthu tolimba. Komabe kumamatira konyenga kulipo kokha pamene madzi akukwera mwa kapilare m’ma pore a nthaka. Nthaka ikamizidwa m’madzi, ma pore amadzazidwa ndi madzi ndipo kumamatira konyenga kumasiya kukhala kulipo.
Kukhazikika kooneka ngati mgwirizano kumafotokoza chochitika chakuti mchenga wosalala, womwe ukauma umakhala wotayirira, ukakhala wanyowa umakhala ndi kulumikizana kwina moti ungametedwe, zomwe sizingatheke ndi mchenga wouma.
Zimadziwika kuti mchenga (ngati si matope kapena fumbi) pa magombe a nyanja akanyowetsedwa ndi mafunde ali ndi mphamvu yabwino kwambiri yonyamula, moti pa iwo munthu angayendetse njinga kapena galimoto, pamene pang’ono patali, kumene mafunde safika, mchenga womwewo uli wouma ndipo mawilo amamiziramo, moti kuyendetsa kulikonse sikungatheke.
KUDUTSA
Kudutsa kwa madzi kudzera mu unyinji wodutsa
Tiyeni tiwone ziwiya zolumikizidwa A, B, C, D, ndi E (chith. 3), mmene gawo limodzi kuyambira a kufika b la utali L ladzazidwa ndi zinthu zololeza madzi, mwachitsanzo mchenga. Tikatsanulira madzi kumapeto kumodzi kwa ziwiya zolumikizidwazi kufika pa mlingo N₁, ndiye kuti mlingo wa madzi m’ziwiya zolumikizidwazi udzakhala wosiyana, ndiko kuti, udzatsika pamene kutalika kwa njira imene madzi adutsa kukuwonjezeka.
Chith. 3. Kuyenda kwa madzi kudzera mu misa yolowera
Nthawi imene kutalika kwa ndodo ya madzi h₁ kwafika patsogolo pa fyuluta, kumbuyo kwa fyuluta padzakhala h₂. Kusiyana pakati pa milingo N₁ ndi N₂ pa nthawiyo ndi:
h = h₁ − h₂
The difference h represents the lost hydrostatic pressure, which was used to overcome the resistance to the flow of water through the filter. This phenomenon was established by the French scientist Darcy as early as 1856. He then also set out the following formula for calculating the velocity of water flow through a permeable mass:
V = k × (dh/dL) = ki
kuti:
- V = liwiro la kuyenda kwa madzi kudzera mu misa yololeka kudutsa, [cm/sec],
- k = coefficient ya permeability yomwe imadalira makhalidwe a nthaka [cm/sec],
- dh = kutalika komwe kumapezeka pamene kutalika h kugawidwa mu zigawo zambiri zopyapyala [cm],
- dL = kutalika komwe kumapezeka pamene kutalika L kugawidwa pa chiwerengero chomwecho cha utali monga kutalika h, [cm].
Chiŵerengero dh/dL = i ndi chiŵerengero cha kutalika komwe kwatayika pa kulowera pansi poyerekeza ndi mtunda womwe madzi aenda ndipo chimatchedwa kutsika kwa madzi kwa hayidroliki, gradient ya hayidroliki kapena kugudubuka kwa piezometer. Dzina lotsiriza limachokera ku mapaipi B, C ndi D, omwe amatchedwa mapaipi a piezometer. Fomula yakutsogolo imatchedwa lamulo la Darcyev la kayendedwe ka madzi kudzera mu sefa.
Kuchuluka konse kwa madzi q, komwe mu nthawi inayake t kumadutsa kudzera mu fyuluta yokhala ndi malo odutsira A ndi
q = kAti,
kumene
k = q / (Ati), kapena k = qL / Ath,
kumene i = h / L = kugwa kwa hydraulic pa kutalika L (ngati kuli kowongoka).
Chiyerekezo k chikuwonetsa kuthekera kwa nthaka kulola madzi kudutsa pa kutentha 10°C.
k = V / i [cm/sec]
Liwiro la kuyenda kwa madzi kudzera mu nthaka limapezeka kuchokera ku fomula
V = q / A [cm/sec],
pomwe q = kuchuluka kwa madzi omwe amadutsa m’nthaka mu cm³ pa sekondi, pa kutentha kwa 10°C, A = malo a gawo lodulidwa la nthaka, limene madzi amadutsa, [cm²].
Lamulo la Darcyev limagwira ntchito pa kayendedwe ka laminar ka madzi, ndiko kuti kayendedwe kachetechete, kopanda ma vortices ndipo pa liwiro lochepa.
Liwiro la fyuluta V ndi liwiro lapakati la kuyenda kwa madzi kudzera m’nthaka ndipo siligwirizana ndi liwiro lenileni la kuyenda kwa madzi, lomwe ndi lalikulu kuposa ilo. Pamene madzi akudutsa mu fyuluta, magawo ofanana a kutayika kwa mutu dh kaŵirikaŵiri amagwiritsidwa ntchito pa utali wosiyana wa njira ya madzi dL, choncho gradient ya hayidroliki imasintha kuchokera pa malo amodzi a nthaka kupita pa ena.
Kudutsa kwa nthaka kumadalira kukula kwa mabowo ake. Tikayika nthaka pa katundu, mabowo amachepa ndipo kudutsa kumacheperanso. Choncho, pa nthaka imodzi yomweyo, chiyerekezo cha kudutsa k chimakhala molingana ndendende ndi kukula kwa porosity, kapena ndi chiyerekezo chake cha porosity e. Komabe, pa mitundu yosiyanasiyana ya nthaka, porosity yoimiridwa ndi chiyerekezo cha porosity e siingagwiritsidwe ntchito ngati muyezo wa kudutsa, chifukwa kudutsa kumadalira osati kuchuluka konse kwa porosity ya nthaka, koma kukula kwa mabowo ake. Choncho, mwachitsanzo mchenga wa miyala woterewuyowo womwe porosity yake ndi e = 0,25, uli ndi kudutsa kwakukulu kwambiri, k = 2–3 cm/sec, pamene dongo lofewa, lomwe porosity yake ndi 60%, chiyerekezo cha porosity e = 1,50, lili ndi kudutsa kochepa, k = 10_⁻⁶ mpaka 10⁻_¹¹ cm/sec.
Koefficients wa kupititsa k angadziwike mwa njira ya mawerengedwe, mayeso a labotale ndi mayeso a m’munda.
Kudziwa koyefishienti pogwiritsa ntchito mawerengedwe kumadalira kapangidwe ka granulometri ya nthaka. Pofuna kudziwa koyefishienti k timavomereza lingaliro lakuti tinthu touluka ta nthaka ndi ta mawonekedwe a mpira, zomwe sizikugwirizana ndi zenizeni makamaka pa nthaka yolumikizana. Chifukwa chake, mfundo za koyefishienti k zotsimikizidwa mwanjira imeneyi sizivomerezedwa ngati zolondola.
Kudziwira coefficient k ndi mayeso a labotale ndi njira yomwe yafalikira kwambiri ndipo imachitika pa zitsanzo za nthaka zosasokonezedwa. Komabe kulondola kwa coefficient k yodziwika motere kumadalira zinthu zingapo monga, ngati ndipo mpaka pati chitsanzo chomwe mayesowo akuchitikira chimaimira wosanjikiza wosadutsa bwino mu nthaka, kenako ndi mmene chitsanzocho chili chosakokedwa mu chipangizo chochitira mayesowo komanso njira yochitira mayesowo. Pofufuza chiwerengero chokwanira cha zitsanzo zomwe zimaimira nthaka inayake, potenga zitsanzo kumunda m’masilinda a chipangizo chomwecho chochitira mayeso komanso ndi njira yoyenera yochitira mayesowo, tingapeze mtengo pafupifupi wolondola wa coefficient k womwe ungagwiritsidwe ntchito ngati wokwanira.
Kudziwitsa koefishienti k kudzera mu mayeso a m’munda kumapereka zotsatira zolondola kwambiri, chifukwa chimagwirizana kwathunthu ndi kapangidwe ndi masanjidwe a nthaka yomwe ili. Komabe njira imeneyi yodziwira koefishienti k imafuna nthawi yochuluka ndi ndalama zazikulu, chifukwa chake sichimachitika kawirikawiri ndipo chimangochitika pokhapokha ngati mtengo wake wolondola kwenikweni ukufunika kwambiri.
Malinga ndi malamulo athu a maziko, nthaka imawerengedwa kuti ndi yomwe coefficient yake ya kuloweka ndi:
- k < 10_⁻_¹¹ cm/sec — pafupifupi osaloleka kudutsa
- k < 10_⁻_⁹ — lowolowa madzi kwambiri pang’ono
- k < 10_⁻_⁷ — chimadutsa pang’ono
- k < 10_⁻_⁵ — chimadutsa pang’ono
- k < 10_⁻_³ — zimalola madzi kudutsa kwambiri
- k > 10_⁻_³ — imalola madzi kwambiri