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Analytical and Numerical Solutions of Dynamic Models for Liquid Chromatography Systems

Thesis Info

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Author

Noreen Akram

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/10791/1/Noreen%20Akram_Maths_2018_Comsats_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725496762

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This dissertation presents solutions of general rate models (GRMs) of non-reactive and reactive liquid chromatography with a focus on evaluating the effect of finite rates for the adsorption and desorption steps, typically considered to be in equilibrium. Such slow rates of adsorption-desorption steps influence the column efficiency and elution shapes. The model equations are partial differential equations accounting for convection, dispersion, mass transfer resistances, and/or reaction kinetics coupled with algebraic and ordinary differential equations for describing adsorption-desorption on the stationary phase. Mostly in liquid chromatography operations, the injected sample is diluted or of small volume, justifying the use of linear models for process simulation. In this study, the Laplace trans formation is applied for deriving analytical solutions of the linear model equations. To get back solutions in the original time domain, numerical Laplace inversion formula is applied. Analytical solutions are further used for deriving the Laplace domain expressions of the first four temporal moments. In some applications, mixture samples are concentrated and have large volumes, necessitating the use of nonlinear models which are not solvable analyt ically. A high resolution finite volume scheme is applied for the numerical approximation of nonlinear GRM considering core-shell particles. Several test problems are considered to compute influences of the rate constants for adsorption and desorption, axial dispersion, intraparticle diffusion resistance, film mass transfer resistance, core-radius fraction and in let boundary conditions on the elution profiles. The developed analytical and numerical solutions are helpful tools to predict dynamic behaviors inside the column and to evalu ate the influence of model parameters on the elution profiles, in particular the effects of finite rates of the intrinsic adsorption and desorption steps. They provide useful tools for sensitivity analysis, process optimization and for parameters estimation from experiments.
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مولانا شہاب الدین ندوی

مولانا شہاب الدین ندوی
قارئین معارف کو اس اطلاع سے نہایت رنج ہوگا کہ ان کے محبوب اور معارف کے خاص مضمون نگار مولانا شہاب الدین ندوی ۱۹؍ اپریل ۲۰۰۲؁ء کو سفرِ آخرت پر روانہ ہوگئے، اناﷲ وانا الیہ راجعون۔
وہ کئی برس سے موذی امراض میں مبتلا تھے اور چند ماہ سے موت و حیات کی کشمکش میں گرفتار تھے جس کی تفصیل مجھے ۳۱؍ دسمبر ۲۰۰۱؁ء کو اپنے والا نامہ میں اس طرح لکھی تھی۔
’’طبیعت بہت زیادہ خراب اور نڈھال رہتی ہے، کئی کئی دن بستر پر پڑا رہتا ہوں، علاج و معالجے سے کوئی فائدہ نہیں ہورہا ہے کئی قسم کے امراض میں مبتلا ہوں اور ڈاکٹر ان کی تشخیص نہیں کرپارہے ہیں، ایک بیماری ذرا دبتی ہے تو دوسری ابھر کر سامنے آجاتی ہے ان جان لیوا بیماریوں سے تنگ آچکا ہوں اور مزید طرفہ یہ کہ اب آنکھوں کی بینائی بھی مسلسل ضائع ہوتی جارہی ہے۔ داہنی آنکھ کا آپریشن ہوا مگر بینائی بڑھنے کے بجائے گھٹ رہی ہے، معلوم ہوتا ہے کہ اب میں صرف چند دن کا مہمان ہوں لیکن طبیعت جب کبھی ذرا سنبھلتی ہے تو جم کر لکھنے اور اپنے مسودات صاف کرنے بیٹھ جاتا ہوں‘‘۔
آخر وہی ہوا، خط لکھنے کے ساڑھے تین مہینے بعد وقت موعود آگیا اور مولانا کی ساری دینی، علمی اور تحقیقی سرگرمیاں ہمیشہ کے لیے بند ہوگئیں۔
مولانا کا وطن بنگلور تھا۔ میٹرک کی تعلیم یہیں ہوئی اور دینی تعلیم کی تکمیل دارالعلوم ندوۃالعلماء لکھنؤ میں کی۔ طالب علمی ہی کے زمانے سے ان کی طبیعت کا رجحان قرآنی علوم اور سائنس کی جانب ہوگیا تھا اور وہ ان میں تطبیق اور ہم آہنگی پیدا کرنا چاہتے تھے اسی لیے لکھنؤ کے بعض کالجوں کے سائنس کے اساتذہ سے ان کا ربط و ضبط ہوگیا تھا، دارالعلوم سے فراغت...

Demography and Pakistan

Demography, along with geography, has always figured in the making of nations and in inter-state relationships. But perhaps never so critically as in the case of Pakistan. Indeed, in all the annals of its proto-history and existential career, demography and Pakistan have been interminably entwined. This may sound incredible, even inexplicable.

Preparation and Evaluation of Controlled Release Matrix Formulations Using Cellulose Acetate Ether Derivatives As Release Controlling Agents

The present research work was conducted in two phases. The research work in first phase was carried out in Drug Delivery Research Laboratories of Faculty of Pharmacy, Gomal University D.I.Khan Pakistan and the second phase was carried out in the Laboratories of Centre of Pharmaceutical Engineering Science, School of Life Sciences, University of Bradford UK. The objective of the research work in first phase was to develop controlled release matrix tablets of analgesic drugs like Nimesulide and Tramadol HCl. Cellulose acetate ether derivatives were used as rate controlling agents and their effect on the drug release kinetics and mechanism was evaluated in comparison to various polymers. In this connection first preformulation studies were carried out for identification and solubility of the selected drugs and determination of any incompatibility between drugs and polymers. FTIR and DSC studies proved that there was no incompatibility between the drugs and polymer. A set of formulations were developed using Ethocel® polymer of various grades [Ethocel® Standard 7 Premium (P), Standard 7 Fine Particle (FP) Premium, Standard 10P, Standard 10FP Premium, Standard 100P and Standard 100FP Premium], Carbopols [Cabopol 974P and 934P] and Eudragit [Eudragit RS-100] in various drug to polymer ratios. Some formulations of the drugs were prepared by partial replacement of the filler (lactose) with co.excipients like CMC, Starch and HPMC KM-100 to evaluate the effect of these co.excipients on the release of drugs from the matrix tablets. The micromeritic studies of the pure drugs and physical mixtures of the formulations were carried out following official procedures which suggested that pure drugs had a poor flow properties but when different ingredients of formulations were mixed together (physical mixtures), the flow properties were enhanced which was considered to be important in tablet preparation. Matrix tablets were prepared from all formulations by following direct compression method for Nimesulide tablets and dry granulation method for Tramadol HCl. Physicochemical characterization of prepared matrix tablets was carried out by performing hardness, weight variation, dimensional, friability and content uniformity tests according to the established procedures. All these physical and quality control parameters were well within the acceptable ranges. Matrix tablets that were prepared with the fine particle (FP) premium grades of Ethocel® were harder and thinner as compared to those with conventional granular grades. The matrix tablets were then evaluated for in vitro drug release by performing in vitro dissolution tests. Dissolution tests were performed by USP method I (rotating basket method) using Monobasic potassium phosphate buffer (pH 7.4) as dissolution medium. Tablets that contain Ethocel® 7FP premium grades extended the release of the drug more efficiently than other grades of Ethocel® polymer. Viscosity grades, particle size and drug to polymer ratio were the main factors that affect the drug release rates and kinetics from matrix tablets of Ethocel® polymers. Carbopol 974P and 934P both proved to be effective in controlling the release of Nimesulide upto 24 hours depending upon the quantity of polymer used, however in case of the water soluble drug (Tramadol HCl), these two polymers fails to extend the release upto 24 hours. An extended release of drugs was demonstrated from matrices prepared with Eudragit RS 100. Co.excipients like starch, CMC and HPMC enhanced the release of the selected drugs from matrix tablets and the all of the drug was released in just 3-5 hours from these matrix tablets. Different Kinetic models were applied on the release data of the matrix tablets. Coefficient of determination (R2) values in the kinetic models showed a linear relation with drug release from matrix tablets containing Ethocel® and Carbopols without co.excipients. The diffusional exponent (n) in the Korsmeyer Peppas Kinetics showed that the release from matrix tablets without co.excipients followed anomalous non fickain release mechanism. The dissolution profiles of matrix tablets and conventional immediate release formulations were compared by determination of similarity factor (f1) and difference factor (f2). The results of in vitro dissolution studies and data from the kinetic models concluded in selection of an optimised test formulation for both the drugs. Nimesulide matrix tablets that contain Ethocel® 7FP premium in drug to polymer ratio of 10:2 and in case of Tramadol HCl matrix tablets of Ethocel® 7FP premium in a drug to polymer ratio of 10:4 were considered as the optimised test formulation for both of the drugs. A batch of each optimised test formulations was prepared with wet granulation method to determine the effect of method of preparation of matrix tablets. In case of matrix tablets of Nimesulide, Wet granulation method proved to be more effective in retarding the release rate of drug when compared with the direct compression method but while considering the release of Tramadol HCl matrix tablets, there was no significant difference in the release of drug from matrix tablets prepared by dry granulation or wet granulation. The optimised test tablets were evaluated for stability testing in short term accelerated conditions. Both the optimised formulations demonstrated good stability in accelerated conditions of temperature and humidity. Microcapsules of both the selected drugs were developed using Ethocel® 7FP as carrier in different drug to polymer ratios, with the objective of explaining the effect of change in dosage form on the release of the drugs. All batches of microcapsules demonstrated good physicochemical characteristics. The release of the drugs from microcapsules was on the basis of non fickian anomalous mechanism and was affected by quantity of the polymer. In vivo studies were carried out on the optimised test formulations by comparing the effect of the optimised test formulation and conventional IR formulations on the in vivo absorption and pharmacokinetic parameters of the drugs in animals (rabbits). In vivo pharmacokinetic parameters of test formulations showed more extended release rates as compared to reference IR formulations of Nimesulide and Tramadol HCl. Moreover, the test formulations showed good linear relationship between In vitro drug release and In vivo drug absorption, and prolonged MRT0-t and t1/2 values as compared to reference formulations. In second phase, solid dispersions of a water insoluble model drug (Ibuprofen) and a carrier polymer hydroxypropylmethyl cellulose acetate succinate (HPMC-AS) was prepared using spray drying technique in order to enhance the solubility and ultimately the bioavailability of the drug. In this connection different batches of Ibuprofen solid dispersions were prepared by following a 32 factorial design of experiments. Effects of variables like drug to polymer ratio and inlet temperature on the percent yield and in vitro dissolution profile was studied. The physicochemical characterisation of the batches was carried out using SEM, TGA, DSC, PXRD, FTIR and RAMAN spectroscopic analysis. The results of the characterization analysis, in vitro dissolution studies and statistical application of ANOVA and response surface methodology concluded that drug to polymer ratio was the main factor responsible for the increased solubility of the model drug (Ibuprofen).