Study Of Nanoparticle Dispersion In Capillaries Using Power Law Nanofluid Model

AUTHOR(S)

Rekha Bali, Bhawini Prasad

DOI: https://doi.org/10.46647/ijetms.2023.v07i02.052

ABSTRACT
This paper investigates the aspects of dispersion of nanoparticles in blood capillaries linked to nanodrug delivery systems. Nanoparticles are injected intravenously in blood capillaries and the resultant fluid has been identified as nanofluid. The viscosity of nanofluid is modelled using the nanoparticle size dependent viscosity relation. The properties of blood are studied using power law fluid, owing to their physically close simulations. The dispersion model framed here has been solved applying the method used by Sankarsubramanian and Gill for deriving exchange coefficients. The study conducted gives an insight into temperature, velocity and three transport coefficients of nanoparticles dispersed in blood with respect to various parameters like heat source parameter, volume fraction, power law index, size of nanoparticles, Grashof number, Darcy number and slip parameter for small values of wall absorption parameter under steady state conditions. MATLAB software has been used to plot the graphs. The outcomes reveal that physical properties of nanoparticles like size chiefly govern their dispersion. Convergence analysis is also stated for the inhomogeneous Bessel differential equation obtained while solving the problem. The developed mathematical model has useful applications to understand the dispersion of nanodrugs in the treatment of cardio vascular diseases.
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References:

G Taylor. “Dispersion Of Soluble Matter In Solvent Flowing Slowly Through A Tube”. Proceedings of The Royal Society London A 219, pp 186-203, 1953 DOI:10.1098/rspa.1953.0139

R Aris. “On The Dispersion Of A Solute In A Fluid Flowing Through A Tube”. Proceedings of The Royal Society London A 235, pp 67-77, 1956 DOI:10.1098/rspa.1956.0065

W N Gill and R Sankarsubramanian. “Exact Analysis Of Unsteady Convective Diffusion.” Proceedings of The Royal Society London A 316, pp 341-350, 1970 DOI:10.1098/rspa.1971.0083

R Sankarsubramanian and W N Gill. “Dispersion Of Non-Uniform Slug In Time-Dependent Flow” Proceedings of The Royal Society London A 322, pp 101-117, 1971 DOI:10.1098/rspa.1971.0057

R Sankarsubramanian and W N Gill. “Dispersion From A Prescribed Concentration In Time Variable Flow.” Proceedings of The Royal Society London 329, pp 479-492, 1972 DOI:10.1098/rspa.1972.0125

R Sankarsubramanian and W N Gill. “Unsteady Convective Diffusion With Interphase Mass Transfer.” Proceedings of The Royal Society London A 833, pp 115-132, 1973 DOI:10.1098/rspa.1973.0051

R Sankarsubramanian and W N Gill. “Corrections to ‘Unsteady convective diffusion with interphase mass transfer’ ”. Proceedings of The Royal Society London A 341, pp 407-408, 1974 DOI:10.1098/rspa.1974.0195

P Decuzzi, F Causa, M Ferrari and A P Netti. “The Effective Dispersion Of Nanovectors Within The Tumour Microvasculature.” Annals of Biomedical Engineering 32, pp 798-802, 2006

F Gentile, M Ferrari and P Decuzzi. “The Transport Of Nanoparticles In Blood Vessels: The Effect Of Vessel Permeability And Blood Rheology.” Annals of Biomedical Engineering 36, pp 254-261, 2008

F Gentile and P Decuzzi. “Time Dependent Dispersion Of Nanoparticles In Blood Vessels.” Journal of Biomedical Science and Engineering 3, pp 517-524, 2010 DOI:10.4236/jbise.2010.35072

S Shaw, S Ganguly, P Sibanda and S Chakraborty. “Dispersion Characteristics Of Blood During Nanoparticle Assisted Drug Delivery Process Through A Permeable Micro Vessel.” Microvascular Research 92 pp 25-33, 2014 DOI:10.1016/j.mvr.2013.12.007

R Bali, N Gupta and S Mishra. “Dispersion Characteristics Of Non-Newtonian Fluid During Transportation Of Nanoparticles In Permeable Capillary.” Applications and Applied Mathematics Vol 11, Issue 2, pp 632-645, 2016

J V R Reddy, D Srikanth and S K Das. “Modelling And Simulation Of Temperature And Concentration Dispersion In A Couple Stress Nanofluid Flow Through Stenotic Tapered Artery.” The European Physical Journal Plus 132:365 , 2017 DOI: 10.1140/epjp/i2017-11643-1

R Bali and N Gupta. “Study Of Transport Of Nanoparticles With K-L Model Through A Stenosed Micro Vessels.” Applications and Applied Mathematics Vol 13, Issue 2, pp 1157-1170, 2018

K M Surabhi, J V R Reddy and D Srikanth. “Impact Of Temperature And Concentration Dispersion On The Physiology Of Blood Nanofluid: Links To Atherosclerosis.” Indian Academy of Sciences, Sadhana 43:210, 2018 DOI:10.1007/812406-018-0986-8

J V R Reddy and D Srikanth. “Impact Of Blood Vessel Wall Flexibility On The Temperature And Concentration Dispersion.” Journal of Applied and Computational Mechanics. Vol 6, Issue 3, pp 564-581, 2020 DOI:10.22055/JACM.2019.29023.1542

S Rathore and D Srikanth. “Mathematical Study Of Transport Phenomena Of Blood Nanofluid In A Diseased Artery Subject To Catheterization.” Indian Journal of Physics, 2021 DOI:10.1007/s12648-021-02166-2

S U S Choi and J A Eastman. “Enhancing Thermal Conductivity Of Fluids With Nanoparticle In Developments And Applications Of Non-Newtonian Flows.” International mechanical engineering congress and exhibition, San Francisco , U S, Conference, 1995

J Buongiorno. “Convective Transport In Nanofluids.” Journal of Heat Transfer, Vol 128, Issue 3, pp 240-250, 2006 DOI:10.1115/1.21150834

A Einstein. “Eine neue bestimmumng der molekuldimensionen.” Ann Phys 19,pp 289-306, 1906 DOI:10.1002/andp.19063240204

A Santra, S Sen and N Chakraborty. “Study Of Heat Transfer Due To Laminar Flow Of Copper Water Nanofluid Through Two Isothermally Heated Parallel Plates.” International Journal of Thermal Sciences 48, pp 391-400, 2009

T Hayat, M Hussain, S A Shehzad and A Alsaedi. “Flow Of A Power Law Nanofluid Past A Vertical Stretching Sheet With A Convective Boundary Condition” Journal of Applied Mechanical and Technical Physics 57, pp 173-179, 2016

M Khan and W A Khan. “MHD Boundary Layer Flow Of A Power Law Nanofluid With New Flux Condition.” AIP Advances 6, pp 2119-2126, 2016

S Hussain, A Aziz, C M Khalique and T Aziz. “Numerical Investigation Of Magnetohydrodynamic Slip Flow Of Power-Law Nanofluid With Temperature Dependent Viscosity And Thermal Conductivity Over A Permeable Surface.” De Gruyter Open 15, pp 867-876, 2017 DOI:10.1515/phys-2017-0104

Usman, A Ghaffari, I Mustafa, J Muhammad and Y Altaf. “Analysis Of Entropy Generation In A Power Law Nanofluid Flow Over A Stretchable Rotatory Porous Disk.” Case studies in thermal engineering, 2021 DOI:10.1016j.csite.2021.101370

El Mehdi Acchal, H Jabraoui, S Zeroual, H Loulijit, A Hasnaoui and S Ouaskit. “Modelling And Simulations Of Nanofluids Using Classical Molecular Dynamics: Particle Size And Temperature Effects On Thermal Conductivity.” Advanced powder technology, 2018 DOI:10.1016/j.apt2018.06.023

B Ankamwar. “Size And Shape Effect On Biomedical Applications Of Nanomaterials.” Biomedical Engineering- Technical Applications in Medicine pp 94-114, 2012 DOI:10.5772/46121

S Ganguly and S Chakraborty. “Effective Viscosity Of Nanoscale Colloidal Suspensions.” Journal of Applied Physics, 2009

L Pasol and F Feuillibois. “Effective Viscosity Of An Inhomogeneous Dilute Suspensions Flowing In A Wall.” XXI International Congress of Theoretical and Applied Mechanics, Warsaw Poland,2004

S Shaw. “Effective Shear Augmented Dispersion Of Solutes During Nanoparticle Ssisted Vdrug Delivery In A Micro Vessel.” The Japan society of fluid mechanics, Fluid Dynamics Research. ,2020 DOI:10.1088/1873-70051/ab6617

J C Maxwell. “A Treatise On Electricity And Magnetism”. Clarendon Press, Oxford, 1873

D A G Bruggeman. “Berichnung verschiedener physikalischer Konstantein von heterogenen substanzen I Dielektrizitatskonstanten und leiffahigkuten der mischkorpher aus isotropen substanzen.” Annals of Physics Vol 416, pp 636-664, 1935 DOI:10.1002/anap.193541560705

B C Pak and Y I Cho. “Hydrodynamics And Heat Transfer Study Of Dispersed Fluids With Submicron Metallic Oxide Particles.” Exp heat transfer 11, pp 151-170, 1980 DOI:10.1080/08916159808946559

Y Xuan and W Roetzel. “Conceptions For Heat Transfer Correlation Of Nanofluids.” International Journal of Heat Transfer 43, pp 3701-3707, 2000 DOI:10.1016/S0017-9310(99)00369-5

J R Philip. “Numerical Solution Of The Diffusion Type With Diffusivity Concentration Dependent.” Division of Plant Industry, CSIRO, Deniliquin, NSW, 1956

M G Scherberg. “The Degree Of Convergence Of A Series Of Bessel Functions.” University of Minnesota, Minneapolis. Minn, 1932

S Ijaz and S Nadeem. “Examination Of Nanoparticles As A Drug Carrier On Blood Flow Through Catheterized Composite Stenosed Artery With Permeable Walls.” Computer methods and programs in biomedicine, 133, pp 83-94, 2016 DOI:10.1016/j.cpmb.2016.05.004

J Tan, W Keller, S Sohrabi, J Yang and Y Liu. “Characterization Of Nanoparticle Dispersion In Red Blood Cell Suspension By The Lattice Boltzmann-Immersed Boundary Method.” Nanomaterials, 6, 30, 2016 DOI:10.3390/nano6020030

D Ramaya, R S Raju, A Rao and A J Chamkha. “Effects Of Velocity And Thermal Wall Slip On Magnetohydrodynamics Boundary Layer Viscous Flow And Heat Transfer Of A Nanofluid Over A Non-Linearly-Stretching Sheet: A Numerical Study.” Propulsion and power research. Volume 7, Issue 2, pp 182-195, 2018 DOI:10.1016/j.jppr.2018.04.003

B Ramana and G Sarojamma. “Unsteady Convective Diffusion In A Herschel-Bulkley Fluid In A Conduit With Interphase Mass Transfer.” International journal of Mathematical modelling and computations. Vol 2, No.3, pp- 159-179, 2012

J W Shreffler, J E Pullan, K M Dailey, S Mallik and A E Brooks. “Overcoming Hurdles In Nanoparticle Clinical Translation: The Influence Of Experimental Design And Surface Modification.” International journal of molecular sciences, 20, 6056, 2019 DOI:10.3390/ijms20236056

T Hupfeld, A Sommereyns and S Barickowski. “Analysis Of The Nanoparticle Dispersion And Its Effects On The Crystalline Microstructure In Carbon-Additivated PA12 Feedstock Material For Laser Powder Bed Fusion.” Materials, Multidisciplinary Digital Publishing Institute, 13(15):3312, 2020 DOI: 10.3390/ma13153312

A Mukherjee and B S Mazumder. “Buoyancy Effect On Dispersion Of A Solute In A Flow Through A Horizontal Channel.” Acta Mechanica 58, pp 137-152, 1986 DOI:10.007/BF01176596

P Bihari, M Vippola, S Schultes, M Praetner, A G Khandoga, C A Reichel, C Coester, T Tuomi, M Rehberg and F Krombach. “Optimized Dispersion Of Nanoparticles For Biological In Vitro And In Vivo Studies.” Particle and Fibre Toxicology, 5:14, 2008 DOI:10.1186/1743-8977-5-14

Shwetasaibal Samanta Sahoo; Mousime Xalxo; B G Mukunda. "A Study on Tourist Behaviour Towards Sustainable Tourism in Karnataka". International Research Journal on Advanced Science Hub, 2, 5, 2020, 27-33. doi: 10.47392/irjash.2020.28

Muniyandy Elangovan; Mohamed Yousuf; Mohamed Nauman; Mohammed Nayeem. "Design and Development of Delivery Robot for Commercial Purpose". International Research Journal on Advanced Science Hub, 4, 07, 2022, 192-197. doi: 10.47392/irjash.2022.047

Manikandan N; Swaminathan G; Dinesh J; Manish Kumar S; Kishore T; Vignesh R. "Significant Attention in Industry and Academia for Wire Arc Additive Manufacturing (WAAM) - A Review". International Research Journal on Advanced Science Hub, 4, 07, 2022, 198-204. doi: 10.47392/irjash.2022.048

Shoeb Ahmed Syed; Steve Ales; Rajesh Kumar Behera; Kamalakanta Muduli. "Challenges, Opportunities and Analysis of the Machining Characteristics in hybrid Aluminium Composites (Al6061-SiC-Al2O3 ) Produced by Stir Casting Method". International Research Journal on Advanced Science Hub, 4, 08, 2022, 205-216. doi: 10.47392/irjash.2022.051

Ashima Saxena; Preeti Chawla. "A Study on the Role of Demographic Variables on Online Payment in Delhi NCR". International Research Journal on Advanced Science Hub, 4, 08, 2022, 217-221. doi: 10.47392/irjash.2022.052

Vishnupriya S; Nirsandh Ganesan; Ms. Piriyanga; Kiruthiga Devi. "Introducing Fuzzy Logic for Software Reliability Admeasurement". International Research Journal on Advanced Science Hub, 4, 09, 2022, 222-226. doi: 10.47392/irjash.2022.056

GANESAN M; Mahesh G; Baskar N. "An user friendly Scheme of Numerical Representation for Music Chords". International Research Journal on Advanced Science Hub, 4, 09, 2022, 227-236. doi: 10.47392/irjash.2022.057

Nirsandh Ganesan; Nithya Sri Chandrasekar; Ms. Gokila; Ms. Varsha. "Decision Model Based Reliability Prediction Framework". International Research Journal on Advanced Science Hub, 4, 10, 2022, 236-242. doi: 10.47392/irjash.2022.061

Vishnupriya S; Nithya Sri Chandrasekar; Nirsandh Ganesan; Ms. Mithilaa; Ms. Jeyashree. "Comprehensive Analysis of Power and Handloom Market Failures and Potential Regrowth Options". International Research Journal on Advanced Science Hub, 4, 10, 2022, 243-250. doi: 10.47392/irjash.2022.062

Minh Duc Ly; Que Nguyen Kieu Viet. "Improvement Productivity and Quality by Using Lean Six Sigma: A Case Study in Mechanical Manufacturing". International Research Journal on Advanced Science Hub, 4, 11, 2022, 251-266. doi: 10.47392/irjash.2022.066

Ragunath A; Poonam Syal. "Net Zero Energy Buildings Initiatives - A Review". International Research Journal on Advanced Science Hub, 4, 11, 2022, 267-271. doi: 10.47392/irjash.2022.067

Suresh P; Justin Jayaraj K; Aravintha Prasad VC; Abishek Velavan; Mr Gokulnath. "Deep Learning for Covid-19 Identification: A Comparative Analysis". International Research Journal on Advanced Science Hub, 4, 11, 2022, 272-280. doi: 10.47392/irjash.2022.068

Chirag H B; Darshan M; Rakesh M D; Priyanka D S; Manjunath Aradya. "Prediction of Concrete Compressive Strength Using Artificial Neural Network". International Research Journal on Advanced Science Hub, 4, 11, 2022, 281-287. doi: 10.47392/irjash.2022.069

Minh Ly Duc; Que Nguyen Kieu Viet. "Analysis Affect Factors of Smart Meter A PLS-SEM Neural Network". International Research Journal on Advanced Science Hub, 4, 12, 2022, 288-301. doi: 10.47392/irjash.2022.071

Lely Novia; Muhammad Basri Wello. "Analysis of Interpersonal Skill Learning Outcomes in Business English Students Class". International Research Journal on Advanced Science Hub, 4, 12, 2022, 302-305. doi: 10.47392/irjash.2022.072

Ms. Nikita; Sandeep Kumar; Prabhakar Agarwal; Manisha Bharti. "Comparison of multi-class motor imagery classification methods for EEG signals". International Research Journal on Advanced Science Hub, 4, 12, 2022, 306-311. doi: 10.47392/irjash.2022.073

Aniket Manash; Ratan Kumar; Rakesh Kumar; Pandey S C; Saurabh Kumar. "Elastic properties of ferrite nanomaterials: A compilation and a review". International Research Journal on Advanced Science Hub, 4, 12, 2022, 312-317. doi: 10.47392/irjash.2022.074

Prabin Kumar; Rahul Kumar; Ragul Kumar; Vivek Rai; Aniket Manash. "A Review on coating of steel with nanocomposite for industrial applications". International Research Journal on Advanced Science Hub, 4, 12, 2022, 318-323. doi: 10.47392/irjash.2022.075

Twinkle Beniwal; Vidhu K. Mathur. "Cloud Kitchens and its impact on the restaurant industry". International Research Journal on Advanced Science Hub, 4, 12, 2022, 324-335. doi: 10.47392/irjash.2022.076

T. Pravin, C. Somu, R. Rajavel, M. Subramanian, P. Prince Reynold, Integrated Taguchi cum grey relational experimental analysis technique (GREAT) for optimization and material characterization of FSP surface composites on AA6061 aluminium alloys, Materials Today: Proceedings,Volume 33, Part 8, 2020, Pages 5156-5161, ISSN 2214-7853. doi.org/10.1016/j.matpr.2020.02.863.

R. Ranjith, C. Somu, G. Tharanitharan, Venkatajalapathi.T, Naveenkumar M, Integrated Taguchi cum Grey Relational Experimental Analysis (GREAT) for Optimization and Machining Characterization of Cryogenic Cooled AA6063 Aluminium Alloys, Materials Today: Proceedings, Volume 18, Part 7, 2019,Pages 3597- 605, https://doi.org/10.1016/j.matpr.2019.07. 291.

R. Devi Priya, R. Sivaraj, Ajith Abraham, T. Pravin, P. Sivasankar and N. Anitha. "Multi-Objective Particle Swarm Optimization Based Preprocessing of Multi-Class Extremely Imbalanced Datasets". International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems Vol. 30, No. 05, pp. 735-755 (2022). Doi: 10.1142/S0218488522500209

M. S. N. K. Nijamudeen, G. Muthuarasu, G. Gokulkumar, A. Nagarjunan, and T. Pravin, “Investigation on mechanical properties of aluminium with copper and silicon carbide using powder metallurgy technique,” Advances in Natural and Applied Sciences, vol. 11, no. 4, pp. 277–280, 2017.

Pravin T, M. Subramanian, R. Ranjith,Clarifying the phenomenon of Ultrasonic Assisted Electric discharge machining, “Journal of the Indian Chemical Society”, Volume 99, Issue 10, 2022, 100705, ISSN 0019-4522, Doi: 10.1016/j.jics.2022.100705

V.S. Rajashekhar; T. Pravin; K. Thiruppathi , “Control of a snake robot with 3R joint mechanism”, International Journal of Mechanisms and Robotic Systems (IJMRS), Vol. 4, No. 3, 2018. Doi: 10.1504/IJMRS.2018.10017186

T. Pravin, M. Sadhasivam, and S. Raghuraman, “Optimization of process parameters of Al-10% Cu compacts through powder metallurgy,” Applied Mechanics and Materials, vol. 813-814, pp. 603–607, 2010.

Rajashekhar, V., Pravin, T., Thiruppathi, K.: A review on droplet deposition manufacturing-a rapid prototyping technique. Int. J. Manuf. Technol. Manage. 33(5), 362–383 (2019) https://doi.org/10.1504/IJMTM.2019.103277

Rajashekhar V S, Pravin T, Thirupathi K, Raghuraman S.Modeling and Simulation of Gravity based Zig-zag Material Handling System for Transferring Materials in Multi Floor Industries. Indian Journal of Science and Technology.2015 Sep, 8(22), pp.1-6.

How to Cite This Article:
Rekha Bali, Bhawini Prasad . Study Of Nanoparticle Dispersion In Capillaries Using Power Law Nanofluid Model . ijetms;7(2):430-458. DOI: 10.46647/ijetms.2023.v07i02.052