Ayyukan kewayar ruwa da ƙarfin wucewar ƙasa

Capillarity

Bayyanar kapilari

Idan muka nutsar da ƙaramar bututun gilashi a cikin kwantena mai ruwa mai natsuwa ba tare da gudana ba, ruwan da ke cikin bututun zai tashi zuwa tsayin hk sama da matakin N a cikin kwantenar, sannan saman ruwan a cikin bututun zai samar da menisk m (sl. 1_a_). Gwargwadon yadda bututun ya fi ƙanƙanta, haka tsayin hawan kapilari na ruwa hk zai fi yawa.

Ɗaga ruwan ta hanyar capillary ana danganta shi ga ƙarfin ɗaga na meniskus m, kuma ana bayyana shi da ƙarfin ja tsakanin ƙwayoyin ruwa da gilashi, da kuma matsin saman da ke tsakanin bangon ƙunƙuntar bututu da saman ruwan.

A wurin da bangon bututun gilashi da saman ruwa suka haɗu, ƙarfin capillary R yana aiki a kan tangenti ga saman meniscus m, wanda ake bayyana shi da nauyi a kowace tsawon, a p/cm. Ta raba ƙarfin R zuwa ɓangaren J mai layi da saman bangon da kuma ɓangaren P na tsaye ga bangon, muna samun ƙarfin ɗaga meniscus (hoto 1_a_):  J = R cosα.

Matsin α da ƙarfin R ke yi da saman bango ana kiransa matsin kapilari, kuma ƙimarsa tana tsakanin 0 da 90O. Idan ruwan da ke cikin bututun kapilari da bangon sa sun kasance tsaf ƙwarai, to α=0, saman meniscus zai zama rabin zagaye, ƙarfin ɗagawa J = R zai kasance mafi girma (sl. 1_b_). Idan ruwa na ɗauke da mai ko acid na halitta ko kuma bangon suna da mai, to α = 90°, ba a samar da meniscus, don haka ba a samun hawan ruwa ta kapilari.

Sl. 1. Tashin ruwan kapila da aikin ƙarfafan kapila

Ana samun ƙarfin ɗagawa J = R cos α daga yanayin daidaito, wanda bisa ga shi jimillar ƙarfin ɗagawa J a duk zagayen meniscus, wato a cikin bututun capillary mai radius r, ke riƙe ginshikin ruwa a cikin bututun a tsayin h__ₖ:

R cos α · 2π_r_ = π_r_² h__ₖ γ__w

inda γ__w shi ne nauyin ƙara na ruwa.

Daga ƙa’idar da ke gaba muna samun ƙarfin capillary ɗin da ke ɗaga ruwa:

R cos α = (r · h__ₖ · γ__w) / 2

wato tsayin hawan capillary:

h__ₖ = (2_R_) / (r · γ__w) · cos α  [cm].

Ruwan capillary mai ɗumi yana tashi a cikin bututun capillary zuwa mafi girma fiye da mai sanyi saboda mafi girman danko. Saboda haka, domin daidai tsayin tashi ta capillary h__ₖ, ƙarfan R cos α ya fi ƙanƙanta ga ruwan capillary mai ɗumi fiye da na mai sanyi. Bisa gwaje-gwajen da aka yi ga yanayin zafin ruwa daban-daban t a cikin daidaitattun sharuɗɗa guda ɗaya, an samu ƙimomin ƙarfin ɗagawa R cos α masu zuwa:

Ruwa a cikin bututun kapilari yana ƙarƙashin matsin ja, domin ƙarfi R cos α yana ɗaga shi sama, alhali ƙarfin nauyi yana ja shi ƙasa. Amma bangon bututun kapilari suna ƙarƙashin matsin lamba saboda ƙarfin kapilari R.

Kapilarity a cikin ƙasa

Akwai kapilariti a cikin ƙasa ma, inda bututun kapilari suke samar da ƙofofi, waɗanda ke da alaƙa da juna a dukkan hanyoyi. Duk yadda ƙasar ta fi ƙanƙanta ƙwaya, haka ƙofofin suke ƙanƙanta kuma tsayin hawar kapilari ya fi yawa. Wannan tsayi kuma yana dogara da tsarin ƙasar. Sai dai ƙofofin cikin ƙasa na iya bambanta da girma, a wannan yanayin kuma tsayin hawar kapilari yana bambanta. Idan ruwan kapilari yayin hawarsa ya kai ga „wurare masu faɗi“, wato zuwa babban ƙofa fiye da abin da ƙarfin ɗagawa ya dace da diamitan ƙunƙuntar ƙofa a tsayin da aka kai, to ci gaban hawar kapilari yana dogara da girman waccan babbar ƙofar. A wannan hali muna da tsayin hawar kapilari mai aiki h__ₖₐ wanda ke dogara da manyan ƙofofi. Akasin haka, idan a lokacin saukar matakin ruwan ƙasa ruwan kapilari, yayin da yake saukowa daga sama zuwa ƙasa, ya ci karo da „wurare masu ƙunci“, sai ya tsaya a wannan zurfin kuma ba zai ci gaba da sauka ba. A wannan hali muna da tsayin kapilariti mai passiv h__ₖₚ, wanda ke dogara da ƙananan ƙofofi.

Bisa ga porosity da tsarin ƙasa, ana bambanta ruwan kapilar mai rufe da ruwan kapilar mai buɗe.

Rufaffiyar ruwan capillary yana da alaƙa da matakin ruwan karkashin ƙasa kuma yayin hawa yana tura iska gaban sa zuwa yankin sama na ƙasa. Saboda haka yawan iska a yankin sama yana ƙaruwa, haka nan kuma matsin iska a cikin ramukan yankin. Matsin iska da aka samu ta haka yana ƙalubalantar hawan capillary, don haka tsayin hawan capillary ya ragu. Wannan yanayin yana faruwa a ƙananan yaduddukan ƙasa, kai tsaye sama da matakin ruwan karkashin ƙasa, inda ramuka suke ƙanana kuma a lokacin hawan capillary ruwan yana cike dukan ramukan gaba ɗaya.

Ruwan kapilari na buɗe shi ma yana da alaƙa da matakin ruwan ƙasa, amma yana kusa da ramuka da aka cika da iska. Wannan yanayin yana faruwa ne a ɓangaren sama na ƙasa inda ramuka suke da girma dabam-dabam, don haka ruwa yana cika ƙananan ramuka kawai gaba ɗaya, yayin da a cikin manyan ramukan da ke kusa akwai iska. A lokacin hawan kapilari, ruwa yana tura iska daga ƙananan ramuka zuwa manyan ramukan da ke kusa, don haka a saman yankin da ke sama da ginshiƙin ruwa a cikin kapilari ba a samu matsin iska, kuma ruwan kapilari na buɗe yana tashi zuwa mafi girma fiye da na rufe.

Yankin da akwai rufaffiyar ko buɗaɗɗiyar ruwa ta kapilari ana ƙayyade shi ne bisa adadin ruwa w a cikin ƙasa.

A cikin rufaffiyar ruwan capillary, dukkan ramuka suna cike da ruwa, wanda ke nufin cewa yawan ruwan da ke cikin ƙasa w = wZ, wato matakin cika S__ᵣ = 1,0.

A cikin ruwa na kapilar mai buɗe wa, ƙananan ramuka suna cike gaba ɗaya da ruwa, yayin da manyan ramuka suke cike da ruwa a ɓangare ne, wato da fim ɗin ruwa da ke rufe ƙwayoyin ƙarfi da ruwan kusurwa (siff. 2) a wuraren da ƙwayoyin ƙarfi suke taɓa juna, sannan wani ɓangare kuma da iska, don haka a wannan yanayin w < wZ, wato S__ᵣ < 1,0.

Tsayin hawan capillary h__ₖ na nau’o’in ƙasa daban-daban ana ƙayyade su ta hanyar gwajin dakin gwaje-gwaje. Matsakaicin tsayin h__ₖ na nau’o’in ƙasa daban-daban suna cikin waɗannan iyakoki:

Sl. 2. Fim ɗin ruwa da ruwan saman kusurwa

A cikin ƙasa ƙarfin capillary R yana aiki ta matsa wa ƙananan ƙwayoyin ƙarfi yadda ake samar da abin da ake kira kamar haɗin kai, wanda ke aiki a matsayin wata irin haɗe tsakanin ƙwayoyin ƙarfi. Duk da haka, haɗin kai na kama yana wanzuwa ne kawai muddin akwai hawan ruwa ta capillary a cikin ramukan ƙasa. Ta hanyar nutsar da ƙasa cikin ruwa, ramukan suna cika da ruwa kuma haɗin kai na kama yana daina wanzuwa.

Ta hanyar haɗin kai na bayyanawa ake bayyana abin da ya sa yashi ƙanƙani, wanda a busasshen yanayi yake watsewa, a cikin yanayin ɗumi yana samun wani ɗan haɗewa ta yadda za a iya masa siffa, abin da ba zai yiwu ba da yashi busasshe.

An san cewa yashi (muddin ba laka ko ƙura ba) a rairayin bakin teku na teku da raƙuman ruwa ke jika shi yana da irin wannan ƙarfin ɗauka mai kyau, har za a iya hawan keke ko mota a kansa, alhali kuwa kaɗan gaba, inda raƙuman ruwa ba sa kaiwa, wannan yashin a busasshiyar yanayi ƙafafun suna nitsewa a cikinsa, saboda haka kowace tuƙi ba ta yiwuwa.

WATSAWA

Gudun ruwa ta cikin taro mai iya wucewa ruwa

Mu duba kwantenoni masu haɗi A, B, C, D, da E (fig. 3), inda wani ɓangare daga a zuwa b mai tsawon L aka cika da abu mai wuce ruwa, misali yashi. Idan muka zuba ruwa a ɗaya ƙarshen kwantenonin masu haɗi har zuwa matakin N₁, to matakin ruwa a cikin kwantenonin masu haɗi zai bambanta, wato zai ragu gwargwadon tsawon hanyar da ruwa ya bi.

Sl. 3. Gudun ruwa ta cikin abu mai ratsa ruwa

A lokacin da tsayin ginshikin ruwa h₁ ya kai a gaban filter, a bayan filter zai kasance h₂. Bambanci tsakanin matakan N₁ da N₂ a wannan lokaci shi ne:

h = h₁ − h₂

Bambancin h yana nufin asarar matsin lamba na hydrostatic, wanda aka kashe wajen shawo kan juriya ga gudanawar ruwa ta cikin matattara. Masanin kimiyyar Faransa Darcy ne ya gano wannan al’amari tun a shekarar 1856. A wancan lokaci kuma ya kafa wannan ƙa’ida don ƙididdige saurin gudanawar ruwa ta cikin abu mai iya shigar ruwa:

V = k × (dh/dL) = ki

ina:

• V = saurin gudanawar ruwa ta cikin abin da yake da iyawar wucewa, [cm/sec],
• k = ƙimar iyawar wucewa wadda ke dogara da halayen ƙasa [cm/sec],
• dh = tsayin da ake samu lokacin da aka raba tsawon h zuwa yawan manyan laushi na sirara [cm],
• dL = tsawon da ake samu idan aka raba tsawon L zuwa yawan tsawon daidai da na h, [cm].

Dangantakar dh/dL = i ita ce dangantakar tsayin da aka rasa a nutsewa da hanyar da ruwa ya bi, kuma ana kiranta faɗuwar hydraulic, gradient na hydraulic ko kuma gangaren piezometer. Wannan suna na ƙarshe ya samo asali ne daga bututun B, C da D, waɗanda ake kira bututun piezometer. Tsarin da ke gaba ana kiransa dokar Darcy ta motsin ruwa ta cikin matattara.

Jimillar adadin ruwa q, wanda a cikin wani lokaci t ya bi ta cikin matatar mai fadin yanki A shi ne

q = kAti,

inda kuma

k = q / (Ati),  wato k = qL / Ath,

inda i = h / L = gangaren hydraulic a tsawon L (idan yana madaidaicin layi ne).

Matsayin k yana bayyana yawaitar shigar ruwa cikin ƙasa a zafin 10°C.

k = V / i  [cm/sec]

Saurin gudanawar ruwa ta cikin ƙasa ana samu daga dabara

V = q / A  [cm/sec],

inda q = adadin ruwan da yake gudana ta cikin ƙasa a cm³ a cikin sakan ɗaya, a zafin 10°C, A = yankin sassan ƙasa, ta inda ruwan ke gudana, [cm²].

Dokar Darcy tana aiki ne ga motsin ruwa na lamina, wato motsi mai natsuwa, ba tare da guguwar juyawa ba kuma a ƙananan gudu.

Gudun tacewa V ita ce matsakaiciyar gudun motsin ruwa ta cikin ƙasa, kuma ba ta dace da ainihin gudun kwararan ruwa ba, wadda ta fi girma. A yayin da ruwa ke wucewa ta cikin matattara, daidaitattun sassan shigar ruwa dh sau da yawa ana cinye su ne a kan wurare marasa daidaito na hanyar ruwa dL, don haka gangaren hydraulics yana sauyawa daga wani wuri na ƙasa zuwa wani.

Yawan shiga ruwa a ƙasa ya danganta da girman ramukanta. Idan muka ɗora nauyi a kan ƙasa, ramukan suna raguwa kuma yawan shiga ruwa yana ƙasa. Saboda haka, ga ƙasa ɗaya daidai, alamar yawan shiga ruwa k tana daidai gwargwado da girman porosity, wato da ma’aunin porosity ɗinta e. Sai dai ga nau’o’in ƙasa daban-daban, porosity da aka bayyana da ma’aunin porosity e ba zai iya zama mizani na yawan shiga ruwa ba, domin wannan yawan shiga ruwa ba ya dogara sosai da jimillar porosity na ƙasa, sai dai da girman ramukan da ke cikinta. Misali, yashi mai ƙananan tsakuwa wanda porosity ɗinsa yake e = 0,25, yana da matuƙar yawan shiga ruwa, k = 2–3 cm/sec, yayin da laka mai laushi, wadda porosity ɗinta yake 60%, ma’aunin porosity e = 1,50, ke da ƙarancin yawan shiga ruwa, k = 10_⁻⁶ zuwa 10⁻_¹¹ cm/sec.

Za a iya ƙayyade ƙimar wucewa k ta hanyar lissafi, ta gwaje-gwajen dakin gwaje-gwaje da na fili.

Ƙayyade maƙasudin ta hanyar lissafi yana dogara ne da tsarin granilometrik na ƙasa. Domin ƙayyade maƙasudin k ana ɗaukar zato cewa ƙwayoyin ƙasa masu ƙarfi suna da siffar ƙwallo, abin da ba ya dace da gaskiya musamman a ƙasa mai haɗuwa. Saboda haka, ƙimomin maƙasudin k da aka ƙayyade ta wannan hanya ba a ɗauke su a matsayin daidai ba.

Ƙayyade ma’aunin k ta gwaje-gwajen ɗakin gwaje-gwaje shi ne mafi yawan yaɗuwa kuma ana yin sa ne a kan samfuran ƙasa marasa lalacewa. Sai dai daidaiton ma’aunin k da aka ƙayyade ta wannan hanyar yana dogara da abubuwa da dama kamar ko kuma gwargwadon yadda samfurin da ake gwajin ke wakiltar layin da ruwa ke ratsawa a cikin ƙasa, sannan kuma daga yanayin rashin lalacewar samfurin a cikin na’urar gwaji da kuma daga hanyar aiwatar da gwajin. Ta hanyar gwada isasshen adadin samfura da za su wakilci ƙasar da aka ba, ta ɗaukar samfurin a filin a cikin silindar na’urar gwaji kanta da kuma hanyar aiwatar da gwajin da ta dace, ana iya samun kimanin madaidaitan ƙimomi na ma’aunin k waɗanda za a iya amfani da su a matsayin masu gamsarwa.

Tantance ma’aunin k ta gwajin fili yana ba da mafi daidaitattun ƙimomi, domin ya yi daidai ƙwarai da tsarin da kuma layayyen tsarin ƙasar da take cikinsa. Sai dai wannan hanyar tantance ma’aunin k tana buƙatar lokaci mai yawa da kuma kuɗi masu yawa, saboda haka ba kasafai ake yin ta ba, kuma sai a lokutan da ake buƙatar sahihin ƙimarta gaba ɗaya.

A cewar ka’idojinmu na kafuwar tushe ana ɗaukar cewa ƙasashen da ma’aunin shigarsu ya kasance:

• k < 10_⁻_¹¹ cm/sec — kusan ba ya wucewa
• k < 10_⁻_⁹        — ƙwarai ƙanana mai wucewa ruwa
• k < 10_⁻_⁷        — mara ɗan shigar ruwa
• k < 10_⁻_⁵        — matsakaici mai iya wuce ruwa
• k < 10_⁻_³        — mafi yawan wuce ruwa
• k > 10_⁻_³        — mai matuƙar yawo