# Debye-Hückel solution for steady electro-osmotic flow of micropolar fluid in cylindrical microcapillary

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...with respect to the following constitutive equations [21-22];...

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...We shall not survey the history here but we shall refer [2, 7, 10-11, 21-22] for the reader who has interest to know their history....

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...kBT . (18) Here, k1 couples the two viscosity coeﬃcients, k2 and k3 are normalized micropolar parameters, Re may be called the Reynolds number, Romay be called the microrotation Reynolds number [12], and αois the ionic-energy parameter [20]. The Gauss law (10) can now be written as ∇2ψ(r) = −ρe(r). (19) The general condition of radial symmetry implies that ∂/∂θ≡ 0. As the length of the microcapi...

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...osed on microrotation are: vθ(1) = βo dVz(ρ) dρ ρ=1 , vθ(0) = 0 (33) where βo ∈ [−1,0] is some constant. Although some researchers have ignored microrotation eﬀects near a solid wall by setting βo= 0 [12,21], others have held that that βo<0 because the existence of the boundary layer requires that the shear and couple stresses on a wall must be high in magnitude in comparison to locations elsewhere [2...

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...g eﬀects are small enough to be ignored; and (ix) Ris much greater than the Debye length λD. Under these conditions, our starting point comprises the following three equations of micropolar2 ﬂuid ﬂow [12]: ∇′ • V′(r′) = 0, (3) ∇′ • σ′(r′)+ρ′ e(r ′)E′ app= ρm[V ′(r′) • ∇′]V′(r′), (4) ∇′ • m′(r′) +I • × σ′(r′) = ρ mjo[V ′(r′) • ∇′]v′(r′). (5) Introducing Eqs. (1) and (2) in these three equations, we get...

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...troids [10,11]. Therefore, not only is stress asymmetric in micropolar ﬂuids but they also sustain body couples. Micropolar ﬂuids are exempliﬁed by colloidal suspensions, liquid crystals, and epoxies [12]. Blood too is micropolar [13,14], along with other body ﬂuids containing particulate materials. As body ﬂuids are subjected to electric ﬁelds in labs-on-a-chip [15], electro-osmotic ﬂows of micropola...

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