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Electroosmotic oscillatory flow of micropolar fluid in microchannels: application to dynamics of blood flow in microfluidic devices

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Abstract

The electroosmotic flow of a micropolar fluid in a microchannel bounded by two parallel porous plates undergoing periodic vibration is studied. The equations for conservation of linear and angular momentums and Gauss’s law of charge distribution are solved within the framework of the Debye-Hückel approximation. The fluid velocity and microrotation are assumed to depend linearly on the Reynolds number. The study shows that the amplitude of microrotation is highly sensitive to the changes in the magnitude of the suction velocity and the width of the microchannel. An increase in the micropolar parameter gives rise to a decrease in the amplitude of microrotation. Numerical estimates reveal that the microrotation of the suspended microelements in blood also plays an important role in controlling the electro-osmotically actuated flow dynamics in microbio-fluidic devices.

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Abbreviations

(x,y):

Cartesian coordinate

u :

velocity

u s :

amplitude of the velocity

V :

suction velocity

E x :

x-component of the electric field

p :

pressure

j :

microinertia density

k :

microrotation viscosity

N :

microrotation

N s :

amplitude of microrotation

ν :

kinematic viscosity of the fluid

ρ :

density of the fluid

E :

amplitude of the electric field

e :

charge of an electron

z :

absolute value of the ionic valance

K B :

Boltzmann constant

T :

temperature

n 0 :

ionic number concentration

t :

time

τ = ωt :

instantaneous phase of the wave

ω :

angular velocity

ψ :

induced potential in the transverse direction

ζ :

wall zeta potential

ρ e :

electric charge density

σ :

electrical conductivity

h λ :

non-dimensional Debye-Hückel parameter

β :

constant related to the electrical double layer (EDL)

ε :

dielectric constant

γ s :

spin gradient viscosity

μ :

dynamic viscosity

\(K = \tfrac{k} {\mu }\) :

micropolar parameter

U HS :

Helmholtz-Smoluchowski velocity

B :

amplitude of the pressure gradient

M :

mobility

h :

half-width of the channel

Re :

Reynolds number

S 0 :

ratio \(\tfrac{V} {{U_{HS} }}\)

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Authors and Affiliations

  1. Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar, 751030, India

    J. C. Misra

  2. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    S. Chandra, G. C. Shit & P. K. Kundu

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  1. J. C. Misra
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Misra, J.C., Chandra, S., Shit, G.C. et al. Electroosmotic oscillatory flow of micropolar fluid in microchannels: application to dynamics of blood flow in microfluidic devices. Appl. Math. Mech.-Engl. Ed. 35, 749–766 (2014). https://doi.org/10.1007/s10483-014-1827-6

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  • DOI: https://doi.org/10.1007/s10483-014-1827-6

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