Skip to main content
SpringerLink
Log in

Measurement and modeling of pulsatile flow in microchannel

  • Research Paper
  • Published:
Microfluidics and Nanofluidics Aims and scope Submit manuscript

Abstract

An experimental study of pulsatile flow in microchannel is reported in this paper. Such a study is important because time-varying flows are frequently encountered in microdevices. The hydraulic diameter of the microchannel is 144 μm and deionized water is the working fluid. The pressure drop across the microchannel as a function of time is recorded, from which the average and r.m.s. pressure drops are obtained. The experiments have been performed in the quasi-steady flow regime for a wide range of flow rate, frequency of pulsations, and duty cycle. The results suggest that the pressure with pulsations lies between the minimum and maximum steady state pressure values. The average pressure drop with pulsation is approximately linear with respect to the flow rate. The theoretical expression for pressure has also been derived wherever possible and the experimental data is found to lie below the corresponding theoretical values. The difference with respect to the theoretical value increases with an increase in frequency and a decrease in flow rate, with a maximum difference of 32.7%. This is attributed to the small size of the microchannel. An increase in frequency of square waveform leads to a larger reduction in pressure drop as compared to rectangular waveform, irrespective of the duty cycle. The results can be interpreted with the help of a first-order model proposed here; the model results are found to compare well against the experimental results. A correlation for friction factor in terms of the other non-dimensional governing parameters is also proposed. Experimental study of mass-driven pulsatile flow in microchannel is being conducted for the first time at these scales and the results are of both fundamental and practical importance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

Abbreviations

A :

Area of cross-section of channel (m2)

C :

Capacitance (F)

D h :

Hydraulic diameter of the channel (=4A/perimeter) (m)

f :

Average friction factor \( \left( {{{pD_{\text{h}} } \mathord{\left/ {\vphantom {{pD_{\text{h}} } {{\tfrac{1}{2}}\rho v^{2} L}}} \right. \kern-\nulldelimiterspace} {{\tfrac{1}{2}}\rho v^{2} L}}} \right) \)

f rms :

Friction factor r.m.s \( \left( {{{p_{\text{rms}} D_{\text{h}} } \mathord{\left/ {\vphantom {{p_{\text{rms}} D_{\text{h}} } {{\tfrac{1}{2}}\rho v^{2} L}}} \right. \kern-\nulldelimiterspace} {{\tfrac{1}{2}}\rho v^{2} L}}} \right) \)

F :

Dimensionless form of frequency \( \left( { = {\frac{{D_{\text{h}} }}{{(t_{\text{N}} + t_{\text{F}} )\alpha }}}} \right) \)

i :

Current (A)

L :

Length of the microchannel (m)

m F :

Minimum flow rate (kg/s)

m N :

Maximum flow rate (kg/s)

\( \tilde{p} \) :

Pressure (Pa)

p :

Time-averaged pressure drop (Pa)

p rms :

Root mean square value of the pressure drop (Pa)

Q :

Volumetric flow rate (m3/s)

R :

Resistance (ohm)

Re :

Reynolds number \( \left( { = {\frac{{vD_{\text{h}} }}{\alpha }}} \right) \)

Re N :

On-time Reynolds number \( \left( { = {\frac{{v_{\text{N}} D_{\text{h}} }}{\alpha }}} \right) \)

t :

Time (s)

t F :

Off-time. Time for which minimum flow (m F) occurs (s)

t N :

On time. Time for which maximum flow (m N) occurs (s)

T :

Duty cycle or ratio of on-time to off-time (t N/t F)

u :

Streamwise velocity (m/s)

v :

Time-averaged velocity of the flow over the cross-section (m/s), normalized voltage

V :

Voltage (V)

v F :

Average velocity over the cross-section, during the state of minimum flow (m/s)

v N :

Average velocity over the cross-section, during the state of maximum flow (m/s)

x :

Streamwise coordinate (m)

α:

Kinematic viscosity of the fluid (m2/s)

β:

Womersley parameter \( \left( { = D_{\text{h}} \sqrt {{\frac{\pi }{{2\alpha (t_{\text{N}} + t_{\text{F}} )}}}} } \right) \)

μ:

Dynamic viscosity of the fluid (Pa.s)

ω′:

Dimensionless form of frequency \( \left( { = {\frac{{D_{\text{h}} }}{{4(t_{\text{N}} + t_{\text{F}} )\alpha }}}} \right) \)

ρ:

Fluid density (kg/m3)

τF :

Time constant during the off-phase (s)

τN :

Time constant during the on-phase (s)

References

  • Abdullah M, Duwairi HM (2008a) Thermal and flow analysis of two-dimensional fully developed flow in an AC magneto-hydrodynamic micropump. Microsyst Technol 14(8):1117–1123

    Article  Google Scholar 

  • Abdullah M, Duwairi HM (2008b) Numerical computation of two-dimensional flow in an AC magneto hydrodynamic micropump. Can J Phys 86(11):1321–1325

    Article  Google Scholar 

  • Brereton GJ (2009) Approximate behavior of arbitrarily unsteady laminar flow in long, straight, flexible tubes. Phys Fluids 21:081902

    Article  Google Scholar 

  • Çarpinlioglu MO, Gündogdu MY (2001) A critical review on pulsatile pipe flow studies directing towards future research topics. Flow Meas Instrum 12:163–174

    Article  Google Scholar 

  • Chakraborty S, Bhalla APS (2007) Controlling microchannel gas flow rates through time-modulated pressure pulsation. J Appl Phys 102:114910

    Article  Google Scholar 

  • Chakraborty S, Das T, Chattoraj S (2007) A generalized model for probing frictional characteristics of pressure-driven liquid microflows. J Appl Phys 102:104907

    Article  Google Scholar 

  • Das D, Arakeri JH (2000) Unsteady laminar duct flow with a given volume flow rate variation. J Appl Mech 67:274–281

    Article  MATH  Google Scholar 

  • Duwairi HM, Abdullah M (2007) Thermal and flow analysis of a magneto-hydrodynamic micropump. Microsyst Technol 13(1):33–39

    Article  Google Scholar 

  • Duwairi HM, Abdullah M (2008) Numerical computation of fluid flow in a magnetohydrodynamic micropump. Turkish J Eng Env Sci 32:1–5

    Google Scholar 

  • Glasgow I, Aubry N (2003) Enhancement of microfluidic mixing using time pulsing. Lab Chip 3:114–120

    Article  Google Scholar 

  • Glasgow I, Lieber S, Aubry N (2004a) Parameters influencing pulsed flow mixing in microchannels. Anal Chem 76:4825–4832

    Article  Google Scholar 

  • Glasgow I, Batton J, Aubry N (2004b) Electroosmotic mixing in microchannels. Lab Chip 4:558–562

    Article  Google Scholar 

  • Gu W, Zhu X, Futal N, Cho BS, Takayama S (2004) Computerized microfluidic cell culture using elastomeric channels and Braille displays. PNAS 101:15861–15866

    Article  Google Scholar 

  • Haddad K, Ertunc O, Mishra M, Delgado A (2010) Pulsating laminar fully developed channel and pipe flows. Phys Rev E 81:013603

    Article  Google Scholar 

  • Havemann HA, Rao NNN (1954) Heat transfer in pulsating flow. Nature 174:41

    Article  Google Scholar 

  • He X, Ku DN (1994) Unsteady entrance flow development in a straight tube. J Biomech Eng 116(3):355–361

    Article  Google Scholar 

  • Ku DN (1997) Blood flow in arteries. Annu Rev Fluid Mech 29:399–434

    Article  MathSciNet  Google Scholar 

  • Lee S-Y, Wereley ST, Gui L, Qu W, Mudawar I (2002) Microchannel flow measurement using particle image velocimetry. In: Proceedings of IMECE, New Orleans, Louisiana, USA, 17–22 November

  • Lee S-Y, Jang J, Wereley ST (2008) Effects of planar inlet plenums on the hydrodynamically developing flows in rectangular microchannels of complementary aspect ratios. Microfluid Nanofluid 5:1–12

    Article  Google Scholar 

  • Morini GL (2004) Laminar liquid flow through silicon microchannels. J Fluid Eng 126:485–489

    Article  Google Scholar 

  • Morris CJ, Forster FK (2004) Oscillatory flow in microchannels: comparison of exact and approximate impedance models with experiments. Exp Fluids 36:928–937

    Article  Google Scholar 

  • Muta T, Nakane K (1980) Unsteady flow in circular tube (velocity distribution in pulsating flow). Bull JSME 123:1990–1996

    Google Scholar 

  • Nichols WW, O’Rourke MF (1990) McDonald’s blood flow in arteries, 3rd Ed edn. Edward Arnold, London

    Google Scholar 

  • Ohmi M, Iguchi M (1981) Flow pattern and frictional losses in pulsatile pipe flow. Part 6: frictional losses in a laminar flow. Bull JSME 24:1756–1763

    Google Scholar 

  • Ohmi M, Iguchi M, Usui T (1981) Flow pattern and frictional losses in pulsatile pipe flow. Part 5: wall shear stress and wall pattern in a laminar flow. Bull JSME 24:75–81

    Google Scholar 

  • Singh SG, Kulkarni A, Duttagupta SP, Puranik BP, Agrawal A (2008) Impact of aspect ratio on flow boiling of water in rectangular microchannels. Exp Thermal Fluid Sci 33:153–160

    Article  Google Scholar 

  • Singh SG, Bhide R, Duttagupta SP, Puranik BP, Agrawal A (2009) Two-phase flow pressure drop characteristics in trapezoidal silicon microchannels. IEEE Trans Compon Packag Technol 32:887–900

    Article  Google Scholar 

  • Steinke ME, Kandlikar SG (2004) Single phase heat transfer enhancement techniques in microchannel and minichannel flows. In: International conference on microchannels and minichannels, Rochester, New York, USA, 17–19 June

  • Stroock AD, Dertinger SK W, Ajdari A, Meziç I, Stone HA, Whitesides GM (2002) Chaotic mixer for microchannels. Science 295:647–651

    Article  Google Scholar 

  • Tang GH, Li Z, Wang JK, He YL, Tao WQ (2006) Electroosmotic flow and mixing in microchannels with lattice Boltzmann method. J Appl Phys 100:1–10

    Article  Google Scholar 

  • Uchida S (1956) The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a circular pipe. ZAMP 7:403–422

    Article  MATH  MathSciNet  Google Scholar 

  • Unger MA, Chou HP, Thorsen T, Scherer A, Quake SR (2000) Monolithic microfabricated valves and pumps by multilayer soft lithography. Science 288:113–116

    Article  Google Scholar 

  • Ünsal B, Ray S, Durst F, Ertunç Ö (2005) Pulsating laminar pipe flows with sinusoidal mass flux variations. Fluid Dyn Res 37(2005):317–333

    Article  MATH  Google Scholar 

  • Wu YH, Wiwatanapataphee B, Hu M (2008) Pressure-driven transient flows of Newtonian fluids through microtubes with slip boundary. Phys A 387:5979–5990

    Article  Google Scholar 

  • Yakhot A, Arad M, Ben-Dor G (1999) Numerical investigation of a laminar pulsating flow in a rectangular duct. Int J Numer Methods Fluids 29:935–950

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    Mukul Tikekar & Amit Agrawal

  2. Department of Electrical Engineering, Indian Institute of Technology Hyderabad, Ordnance Factory Estate, Yeddumailaram, 502205, Andhra Pradesh, India

    Shiv Govind Singh

Authors
  1. Mukul Tikekar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shiv Govind Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amit Agrawal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amit Agrawal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tikekar, M., Singh, S.G. & Agrawal, A. Measurement and modeling of pulsatile flow in microchannel. Microfluid Nanofluid 9, 1225–1240 (2010). https://doi.org/10.1007/s10404-010-0642-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10404-010-0642-z

Keywords

Search

Navigation