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A novel two-indenter based micro-pump for lab-on-a-chip application: modeling and characterizing flows for a non-Newtonian fluid

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Abstract

Inspired by the feeding mechanisms of a nematode, a novel two-indenter (2I) micro-pump is analyzed theoretically for transport and mixing of a non-Newtonian fluid for the purpose of lab-on-a-chip applications. Considering that the viscous forces dominate the flows in microscopic regime, the concept lubrication theory was adopted to device the two-dimensional flow model of the problem. By approximating the movements of the indenter as a sinusoidal function, the details of the flow were investigated for variations in—frequency of contraction of the first value keeping the second valve at higher occlusion, and occlusion. The study indicates that occlusive nature of the second valve leads to the large pressure barrier which prevents the fluid to enter into the neighboring compartment. Transport occurs as the lumen opens to develop a suction pressure. Pressure barrier is found to be highest for dilatants followed by Newtonian and pseudo-plastics. Shear stress dependency on frequency the contraction of the first value is highest for lower values of flow behavior index. In conclusion, the study provides details connecting the flows resulting from the indentation of the front-end indenter to the frequency of indentation, geometry and rheology of the fluid, thus facilitating optimal design of the micro-pumps.

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Abbreviations

C. elegans :

Caenorhabditis elegans

MDDS:

Micro drug delivery system

µTAS:

Micro total analysis systems

POC:

Point of care

PCR:

Polymerase chain reaction

t:

Time

r:

Radial coordinate

θ:

Aximuthal coordinate

z:

Axial coordinate

c:

Velocity scale

f:

Frequency of closure/opening of the 1st valve

z0 :

Reference axial position of the 1st valve

z0’:

Reference axial position of the 2nd valve

a:

max. radius of the cylinder

λ:

Wavelength of the 1st valve

λ’:

Wavelength of the 2nd valve

R:

Shape function of cylinder indicating radius

pocc,max :

max. occlusion of the valves

pocc :

Occlusion of the 1st valve at time ‘t’

pocc’ :

Occlusion of the 2nd valve at time ‘t’

ur :

Radial velocity

uθ :

Velocity along th-direction

uz :

Axial velocity

Ur,B :

Radial velocity of the wall

m:

Flow consistency index

n:

Flow behavior index

µ:

Viscosity of the fluid

P:

Pressure

τ:

Wall shear stress

Q:

Flow rate

*:

Indicates dimensional variable

References

  1. Woias P (2005) Micropumps—past, progress and future prospects. Sens Actuators, B 105:28–38

    Article  Google Scholar 

  2. Laser DJ, Santiago JG (2004) A review of micropumps. J Micromech Microeng 14:R35–R64

    Article  Google Scholar 

  3. Au AK et al (2011) Microvalves and micropumps for BioMEMS. Micromachines 2(2):179–220

    Article  MathSciNet  Google Scholar 

  4. Figeys D, Pinto D (2000) Lab-on-a-chip: a revolution in biological and medical sciences. Anal Chem 72(9):330A–335A

    Article  Google Scholar 

  5. Haeberle S, Zengerle R (2007) Microfluidic platforms for lab-on-a-chip applications. Lab Chip 7(9):1094–1110

    Article  Google Scholar 

  6. Vilkner T, Janasek D, Manz A (2004) Micro total analysis systems. Recent developments. Anal Chem 76(12):3373–3385

    Article  Google Scholar 

  7. Jung W et al (2015) Point-of-care testing (POCT) diagnostic systems using microfluidic lab-on-a-chip technologies. Microelectron Eng 132:46–57

    Article  Google Scholar 

  8. Cui P, Wang S (2018) Application of microfluidic chip technology in pharmaceutical analysis: a review. J Pharm Anal 9:238–247

    Article  Google Scholar 

  9. Auroux PA et al (2002) Micro total analysis systems. 2. Analytical standard operations and applications. Anal Chem 74(12):2637–2652

    Article  Google Scholar 

  10. Reyes DR et al (2002) Micro total analysis systems. 1. Introduction, theory, and technology. Anal Chem 74(12):2623–2636

    Article  Google Scholar 

  11. Yu F, Choudhury D (2019) Microfluidic bioprinting for organ-on-a-chip models. Drug Discov Today 24(6):1248–1257

    Article  Google Scholar 

  12. Bein A et al (2018) Microfluidic organ-on-a-chip models of human intestine. Cell Mol Gastroenterol Hepatol 5(4):659–668

    Article  Google Scholar 

  13. Gerasimenko TN et al (2017) Modelling and characterization of a pneumatically actuated peristaltic micropump. Appl Math Model 52:590–602

    Article  MathSciNet  MATH  Google Scholar 

  14. ChanJeong O, Konishi S (2007) Fabrication and drive test of pneumatic PDMS micro pump. Sens Actuators, A 135(2):849–856

    Article  Google Scholar 

  15. Huang C-W, Huang S-B, Lee G-B (2006) Pneumatic micropumps with serially connected actuation chambers. J Micromech Microeng 16(11):2265–2272

    Article  Google Scholar 

  16. Lee I et al (2016) Four-electrode micropump with peristaltic motion. Sens Actuators, A 245(1):19–25

    Article  Google Scholar 

  17. Uhlig S et al (2018) Electrostatically driven in-plane silicon micropump for modular configuration. Micromachines 9(4):1–15

    Article  Google Scholar 

  18. Said MM et al (2017) Hybrid polymer composite membrane for an electromagnetic (EM) valveless micropump. J Micromech Microeng 27(7):1–8

    Google Scholar 

  19. Said MM et al (2018) The design, fabrication, and testing of an electromagnetic micropump with a matrix-patterned magnetic polymer composite actuator membrane. Micromachines 9(1):1–10

    Google Scholar 

  20. Chen S et al (2016) A normally-closed piezoelectric micro-valve with flexible stopper. AIP Adv 6:045112–045119

    Article  Google Scholar 

  21. Shabanian A et al (2016) A novel piezo actuated high stroke membrane for micropumps. Microelectron Eng 158(1):26–29

    Article  Google Scholar 

  22. Yamahata C et al (2005) A PMMA valveless micropump using electromagnetic actuation. Microfluid Nanofluidics 1(3):197–207

    Article  Google Scholar 

  23. Avvari RK (2019) Biomechanics of the small intestinal contractions. In: Qi DX (ed) Management of digestive disorders. Intech Open, London

    Google Scholar 

  24. Avvari RK (2019) Effect of local longitudinal shortening on the transport of luminal contents through small intestine. Acta Mech Sin 35(1):45–60

    Article  MathSciNet  Google Scholar 

  25. Avvari RK (2015) Bio-mechanics of the distal stomach and duodenum: an insight into mechanisms of duodenogastric reflux and duodenal mixing. In: Department of biological sciences and bioengineering. 2015, 48th Graduating Students Convocation, Indian Institute of Technology Kanpur

  26. Smits JG (1990) Piezoelectric micropump with three valves working peristaltically. Sens Actuators A Phys 21(1):203–206

    Article  MathSciNet  Google Scholar 

  27. Cao L, Mantell S, Polla D (2001) Design and simulation of an implantable medical drug delivery system using microelectromechanical systems technology. Sens Actuators A Phys 94(1):117–125

    Article  Google Scholar 

  28. Bu M et al (2003) Design and theoretical evaluation of a novel microfluidic device to be used for PCR. J Micromech Microeng 13(4):S125–S130

    Article  Google Scholar 

  29. Husband B et al (2004) Novel actuation of an integrated peristaltic micropump. Microelectron Eng 74(1):858–863

    Article  Google Scholar 

  30. Berg JM et al (2003) A two-stage discrete peristaltic micropump. Sens Actuators, A 104(1):6–10

    Article  Google Scholar 

  31. Shapiro AH, Jaffrin MY, Weinberg SL (1969) Peristaltic pumping with long wavelengths at low Reynolds number. J Fluid Mech 37(4):799–825

    Article  Google Scholar 

  32. Misra JC, Maiti S (2011) Peristaltic transport of a rheological fluid: model for movement of food bolus through esophagus. Appl Math Mech 33(3):315–332

    Article  MathSciNet  Google Scholar 

  33. Avvari RK (2020) Theoretical modeling of the resistance to gastric emptying and duodenogastric reflux due to pyloric motility alone, presuming antral and duodenal quiescence. J Theor Biol 508:1–16

    MathSciNet  Google Scholar 

  34. Avery L, You YJ (2012) C. elegans feeding. WormBook, Hoboken, pp 1–23

    Google Scholar 

  35. Fang-Yen C, Avery L, Samuel AD (2009) Two size-selective mechanisms specifically trap bacteria-sized food particles in Caenorhabditis elegans. Proc Natl Acad Sci 106(47):20093–20096

    Article  Google Scholar 

  36. Avery L, Shtonda BB (2003) Food transport in the C. elegans pharynx. J Exp Biol 206:2441–2457

    Article  Google Scholar 

  37. Kwiatek MA et al (2006) Quantification of distal antral contractile motility in healthy human stomach with magnetic resonance imaging. J Magn Reson Imaging 24(5):1101–1109

    Article  Google Scholar 

  38. Tanaka Y et al (2012) Mechanics of peristaltic locomotion and role of anchoring. J R Soc Interface 9(67):222–233

    Article  Google Scholar 

  39. Brackenbury J (1999) Fast locomotion in caterpillars. J Insect Physiol 45(6):525–533

    Article  Google Scholar 

  40. Li M, Brasseur JG (1993) Non-steady peristaltic transport in finite-length tubes. J Fluid Mech 248:129–151

    Article  MATH  Google Scholar 

  41. Pal A et al (2004) Gastric flow and mixing studied using computer simulation. Proc Biol Sci 271(1557):2587–2594

    Article  Google Scholar 

  42. Misra JC, Pandey SK (2001) A mathematical model for oesophageal swallowing of a food-bolus. Math Comput Model 33:997–1009

    Article  MathSciNet  MATH  Google Scholar 

  43. Misra JC, Maiti S (2012) Peristaltic transport of rheological fluid: model for movement of food bolus through esophagus. Appl Math Mech 33(3):315–332

    Article  MathSciNet  Google Scholar 

  44. Ravi Kant A, Pal A (2011) Intestinal transport and mixing analyzed using computer simulations. In: 1st Biennial meeting of Indian motility and functional diseases association (IMFDA). SGPGIMS, Lucknow

  45. Weinberg SL, Ecksein EC, Shapiro AH (1971) An experimental study of peristaltic pumping. J Fluid Mech 49:461–479

    Article  Google Scholar 

  46. Latham TW (1966) Fluid motions in a peristaltic pump. Massachusetts Institute of Technology, Cambridge

    Google Scholar 

  47. Suzuki Y et al (2019) Particle selectivity of filtering by C. elegans. Theor Appl Mech Lett 9(2):61–65

    Article  Google Scholar 

  48. Fueser H et al (2019) Ingestion of microplastics by nematodes depends on feeding strategy and buccal cavity size. Environ Pollut 255(Pt 2):113227

    Article  Google Scholar 

  49. Salafi T, Zeming KK, Zhang Y (2016) Advancements in microfluidics for nanoparticle separation. Lab Chip 17(1):11–33

    Article  Google Scholar 

  50. Fakour M et al (2015) Analytical study of micropolar fluid flow and heat transfer in a channel with permeable walls. J Mol Liq 204:198–204

    Article  Google Scholar 

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Acknowledgements

The author received no financial support for the research, and/or publication of this article. For the purpose of the study, author has used computational resources (with Matlab licence) at the institute facility.

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  1. Department of Biotechnology and Medical Engineering, NIT Rourkela, Rourkela, Odisha, 769008, India

    Ravi Kant Avvari

  2. Sasi Institute of Technology & Engineering, Tadepalligudem, West Godavari, Andhra Pradesh, 534101, India

    Ravi Kant Avvari

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Correspondence to Ravi Kant Avvari.

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Avvari, R.K. A novel two-indenter based micro-pump for lab-on-a-chip application: modeling and characterizing flows for a non-Newtonian fluid. Meccanica 56, 569–583 (2021). https://doi.org/10.1007/s11012-020-01303-1

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