hydrogel中..含水量與DK關係之推導.. - 隱形眼鏡

※ [本文轉錄自 optical 看板]

作者: kramnik (progressive) 看板: optical
標題: [心得] hydrogel中..含水量與DK關係之推導..
時間: Sat Nov 7 20:52:01 2009

含水量與Dk值之關係

縱軸為DK值[單位:10^(-11)*cm^2*mole O2*second^(-1)*ml^(-1)*mmhg^(-1)]

橫軸為water content[單位:%]

http://www.wretch.cc/album/show.php?i=kramnik1&b=30&f=1054551174&p=1



根據morgan的實驗，hydrogel中含水量與DK值間之關係為

Dk = 1.67*e^(0.0397*W)…….其中w為水的質量比例



資料出處：Morgan PB, Efron N. The oxygen performance of contemporary hydrogel

contact lenses. Contact Lens Ant Eye. 1997;21:3-6.


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物理模型推導:

the Maxwell-blotzmann distribution
http://www.wretch.cc/blog/kramnik1/13700353

fisk's law 推導 (對於理想氣體)
http://www.wretch.cc/blog/kramnik1/13700363


fisk's law 推導 (對於理想液體..使用stoke's law..納入Einstein relation)
http://www.wretch.cc/blog/kramnik1/13700368


我們可以推導出fisk’s first law

設單位體積內濃度為Φ，單位截面單位時間濃度流出量為J，D是擴散參數

J = -D*▽Φ

for T = constant，D = constant

J單位為[mole*length^-2*time^(-1)]
Φ單位為[mole*length^(-3)]
D單位為[length^2*time^(-1)]

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如果要求取暫態解..我們會需要使用到fisk's second law

fisk's second law推導
http://www.wretch.cc/blog/kramnik1/13700372

mathematical tactic to slove diffusion equation
http://www.wretch.cc/blog/kramnik1/13700375

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我們已經解決了擴散係數..接下來要解決溶解係數..

熱力學三定律
http://www.wretch.cc/blog/kramnik1/13700378

clausius theorem
http://www.wretch.cc/blog/kramnik1/13700379

Arrhenius Equation
http://www.wretch.cc/blog/kramnik1/13700382

henry's law
http://www.wretch.cc/blog/kramnik1/13700384


我們可以得到 Henry’s law


等溫狀態下，設P為大氣中溶解物之分壓，溶液內單位體積內溶解物濃度為Φ，

K為溶解參數，則　K*P = Φ成立

P單位為[pressure]
Φ單位為[mole*length^(-3)]
K單位為[mole*length^(-3)*pressure^(-1)]

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Cohen and Turnbull liquid model
http://www.wretch.cc/blog/kramnik1/13719546

含水量與DK間之關係(morgan近似式)
http://www.wretch.cc/blog/kramnik1/13700390




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