Search or add a thesis

Advanced Search (Beta)
Home > Theoretical Investigation of Liquid Chromatography in Cylindrical Columns

Theoretical Investigation of Liquid Chromatography in Cylindrical Columns

Thesis Info

Access Option

External Link

Author

Khan, Farman Ullah

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2017

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/10506

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727602058

Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

Join our Whatsapp Channel to get regular updates.

Similar


Liquid chromatography is one of the most widely used separation and puri¯cation tech- niques utilizing cylindrical columns. Generally, one-dimensional chromatographic models are used to study concentration gradients along the column axis only, while gradients along the radial direction are ignored. However, consideration of radial concentration gradients are necessary when sample injection at inlet of the column is imperfect, that is when a radial pro¯le is inserted at the column entrance, and radial dispersion is rate limiting. In such a scenario, the two-dimensional (2D) models of chromatography have to be consid-ered. This work focuses on the derivation of analytical solutions and temporal moments of linear 2D models of liquid chromatography in cylindrical geometry. In liquid chromatogra-phy, the injected sample size is small and diluted, thus, the current assumptions of linear adsorption and reaction in the models are valid and practically applicable. The models are formed by convection-dominated partial di®erential equations coupled with some algebraic and di®erential equations. Both non-reactive and reactive chromatographic models, two sets of boundary conditions, as well as injections through inner and outer regions of the column inlet cross section are considered. The Laplace and Hankel transformations are successively applied to solve the model equations. To further analyze the process, tempo-ral moments up to the fourth order are derived from the Hankel and Laplace transformed solutions. The correctness of analytical results are veri¯ed by comparing them with the numerical solutions of a high resolution ¯nite volume scheme. Results of di®erent test prob-lems are presented and discussed covering wide ranges of kinetics in°uencing mass transfer and reaction rates. The developed analytical solutions and moments provide useful tools to quantify combined longitudinal and radial dispersion e®ects, to perform sensitivity anal-ysis, to analyze numerical algorithms, as well as to understand, design and optimize the process.
Loading...
Loading...

Similar Books

Loading...

Similar Chapters

Loading...

Similar News

Loading...

Similar Articles

Loading...

Similar Article Headings

Loading...

ہمیں معلومات سے زیادہ حکمت چاہیے

ہمیں معلومات سے زیادہ حکمت چاہیے
نحمدہ ونصلی علی رسولہ الکریم امّا بعد فاعوذ بااللہ من الشیطن الرجیم
بسم اللہ الرحمن الرحیم
معزز اساتذہ کرام اور میرے ہم مکتب ساتھیو!
آج مجھے جس موضوع پر لب کشائی کا موقع دیا گیا ہے وہ ہے:’’ہمیں معلومات سے زیادہ حکمت چاہیے‘‘
صدرِذی وقار!
علم ایک خزانہ ہے، ہر ایک اس خزانے سے اپنی تجوریوں کو بھرنا چاہتا ہے، علم جستجو سے حاصل ہوتا ہے ،علم کے حصول کے لیے محنت شاقہ کی ضرورت ہے، علم کی تگ و دو میں زندگیاں صرف ہو جاتی ہیں۔ معلومات حاصل کرتے کرتے ایّام زیست گزر جاتے ہیں۔ معلومات جیسی بھی ہوں جہالت کے گھٹا ٹوپ اندھیروں کا خاتمہ کر دیتی ہیں۔
جنابِ صدر!
معلومات کا خزانہ اس وقت متمتع اور کار آمد ثابت ہوتا ہے، جب اس خزانے کے صحیح مصارف معلوم ہوں، ان معلومات کے لیے صحیح استعمال سے آشنائی حاصل ہو، معلومات کے مطابق زندگی کے ڈھنگ ہر صاحب علم کی دسترس میں ہوں۔ دنیا بھر کی معلومات ہیں لیکن وہ صرف اپنی ذات کی حد تک محدود ہیں تو وہ نہ ہونے کے برابر ہیں۔
جنابِ صدر!
جب کسی کام میں حکمت شامل ہو جاتی ہے تو اس کے حسن کو دوبالا کر دیتی ہے، اس کی خوبصورتی میں اضافہ ہو جاتا ہے، اس کی دھنک کے رنگ نمایاں ہو جاتے ہیں، اس کی اہمیت دوبالا ہو جاتی ہے، اس کی شان نرالی ہو جاتی ہے۔ دانائی اور حکمت سے معمور کام انفرادیت کا حامل ہوتا ہے، اس علم صفت کے حامل طفلان خودمعا ملہ نہیں ہوتے بلکہ زیرک و فطین لوگ ہوتے ہیں۔
صدرِذی وقار!
حکمت کے پھول کاغذی پھول نہیں ہوتے، گلشن حکمت و دانائی میں چلنے والی ہوا حیات بخش جھونکوں سے معمور ہوتی ہے، جس جگہ پر حکمت ہوتی ہے...

Pengaruh Konsep Diri dan Disiplin Belajar terhadap Motivasi Belajar Peserta Didik di Sekolah Menengah Pertama Negeri 4 Palu Pada Mata Pelajaran Pendidikan Agama Islam

The purpose of this study is to find out the significant effect of self-concept on learning motivation of VII grade students in SMP Negeri 4 Palu on Islamic Religious Education subjects, (2) knowing the effect of learning discipline on learning motivation of VII grade students at SMP Negeri 4 Palu in the eyes of Islamic Religious Education subjects and (3) determine the effect of self-concept and learning discipline on learning motivation of grade VII students in SMP Negeri 4 Palu on Islamic Religious Education subjects. This study uses a quantitative approach. The population in this study were 220 class VII students of SMP Negeri 4 Palu. The sample was determined using proportional random sampling technique using a formula developed by Isaac and Michael, so that a sample of 135 students was obtained. Primary data were obtained using a questionnaire. Data analysis techniques include descriptive analysis, and regression tests using simple regression and multiple regression. The results showed that (1) There was a significant influence between self-concept on learning motivation of VII grade students in SMP Negeri 4 Palu on Islamic Religious Education subjects, with a significance level of 5%, the magnitude of the effect of self-concept variables on students' learning motivation was 0, 615 means having a high influence (2) There is a significant influence between learning discipline on learning motivation of VII grade students in SMP Negeri 4 Palu on Islamic Religious Education subjects, with a significance level of 5%, the magnitude of the effect of the discipline of learning variables on motivation student learning is 0, 565, (3) There is a significant influence between self-concept and learning discipline on learning motivation of grade VII students in SMP Negeri 4 Palu on Islamic Religious Education subjects, with a significance level of 5%, the high influence of concept variables self and discipline of learning towards learning motivation of VII grade students of SMP Nege ri 4 Palu in Islamic Religious Education subjects is 0, 615. The contribution of self-concept variables and learning discipline to learning motivation variables is R2 x 100% or 0, 6152 x 100% = 37.9%, the remaining 62.1% is determined by other variables outside of this study include the level of interest, talent, attention, parenting parents and others.

Enhancing Bioavailable Phosphorous in Soil Through Sulfur Oxidation by Thiobacillus

Phosphorus (P) fertilizer use efficiency is only 15 % in calcareous alkaline soils as in Pakistan. Sulfur oxidizing bacteria (SOB) especially Thiobacillus spp. solubilize the unavailable P in soil by synthesizing sulfuric acid. This study was performed in three steps: (i) screening of SOB from different microbial ecologies, (ii) use of different SOB with S levels for enhancing bio-available P, and (iii) effect of SOB along with P fertilizer and S on plant growth and yield. Sulfur oxidizing bacteria were isolated, screened, identified and the most efficient SOB were found as the genus Thiobacillus in sulfur based ecologies such as industrial wastewater, sewerage water and sulfur mud. These SOB isolates were IW1, SW2, SS1, IW13, IW14, IW16 and SM1 which reduced the pH of different media (thiosulphate, tricalcium phosphate and rock phosphate) in 07 to 40 days after inoculation. Four Thiobacillus isolates viz., IW16, SW2, IW1 and IW14 were inoculated in soil with three S levels 50, 37.5 and 25 mg kg-1. Thiobacillus spp. IW16 and SW2 reduced soil pH with 50 mg S kg-1 from 7.90 to 7.12 and 7.28 respectively. Similarly, Thiobacillus strain IW16 in combination with 50 mg S kg-1 reduced CaCO3 contents from 7.14 to 6.93 % and solubilized Ca8-P and Ca10- P. Increase in the concentration of sparingly soluble Ca2-P (20.33 mg kg-1) and xvii bioavailable P contents (net increase of 22.26 mg kg-1) were also recorded as a result of P solubilization phenomenon. Lastly field experiments were conducted on two permanent lay outs (plot size 3 m × 3 m) at two different places growing for rice-wheat and maize-maize crops. The best Thiobacillus isolates (IW16 and SW2) along with 100 kg S ha-1 were inoculated in combination with two doses of P fertilizer viz., 45 and 90 kg P2O5 ha . Significant increase in the concentration of bio-available P in soil was recorded through bacterial S oxidation in both experiments. Growth and yield parameters of the tested crops (rice, wheat and maize) exhibited positive significant correlation with P solubilization through S oxidation by Thiobacilli with the highest values by strain IW16 along with 100 kg S ha-1. Interaction between Thiobacillus spp. and S was highly significant in enhancing the growth and yield of crops. Treatment of soil with Thiobacilli and S was the best practice for enhancing bioavailability of P already present as fixed P in huge quantity.