Concentration profiles of ions and particles under hydrodynamic focusing in Y-shaped square microchannel

Abstract

Three-dimensional ion and particle concentrations under hydrodynamic focusing in a Y-shaped square microchannel are numerically simulated to clarify the decrease of the ion concentration along the flow direction within the focused particle stream. The simulation model is theoretically governed by the laminar flow and advection-diffusion equations. The governing equations are solved by the finite volume method. The ion and particle concentration distributions at five cross sections after the confluence of the branch channels are analyzed in 30 cases in which the sheath to sample flow rate ratio Q_sh/Q_sam and the Reynolds number Re are varied as parameters. The results show that the decrease of the cross-sectional average ion concentration along the flow direction within the particle stream [Formula: see text] is described by the diffusion length during the residence time with a characteristic velocity scale. In addition, the deformation of the particle stream due to inertial effects is described by a scaled Reynolds number that is a function of the flow rate ratio. The simulated particle stream thicknesses are validated by theory and a simple experiment. This paper reveals the relationship between the ion and particle concentrations and the dimensionless parameters for hydrodynamic focusing in the Y-shaped square microchannel under typical conditions.

Figure 1

(a) Schematic of hydrodynamic focusing in a Y-shaped microchannel. (b) Model geometry corresponding to the electrode-multilayered microfluidic device developed by Yao et al.^,. The electrode surface boundaries are prepared at the five longitudinal positions x = x₁, x₂, x₃, x₄ and x₅ for future study of electric effects. (c) Isometric drawing and computational grid of the model. The insets show the grid resolutions in the confluence region (upper left) and at the cross sections where the ion and particle concentration distributions are evaluated (lower right). The total number of control volumes (CVs) is 866,698.

Figure 2

(a) Experimental setup. The particle suspension as the sample liquid and water as the sheath liquid were injected into the device by two syringe pumps with different flow rate ratios Q_sh/Q_sam. (b) Schematic of the particle stream observation method. A local coordinate system with the origin at the third cross section is defined in order to evaluate the particle stream thickness.

Figure 3

Normalized concentration distributions of ions and particles at the three cross sections in the main flow channel for the three Reynolds numbers.

Figure 4

Decrease of the ion concentration along the flow direction within the particle stream. (a) An example of the ion concentration contour at a cross section. The dash line shows the particle stream shape in which the average ion concentration is evaluated. (b) Change of the average ion concentration ${\overline{c}}_i$ along the dimensionless length x′ = [(x/W)/Pe]^1/2. The dotted lines are polynomial fits to show the connection of the data for each flow rate ratio.

Figure 5

Cross-sectional shape of the particle stream. (a) An example of the particle concentration distribution at a cross section and description of the symbols for each part of the thickness of the particle stream. The dash line indicates the theoretical particle stream shape assuming the flat immiscible interface. (b,c) Changes of the thicknesses at the center and on the side wall, a/W and b/W, with respect to the flow rate ratio Q_sh/Q_sam. The solid line is the theoretical particle stream thickness calculated by Eq. (8).

Figure 6

Comparison between experimental and simulated particle stream thicknesses. (a) Observation images for three cases of different sample and sheath flow rates. (b) ζ-direction distributions of the ξ-directional average gray value and its time variance of the images in (a). (c) Simulated particle concentration distributions at the third cross section under conditions corresponding to Case 2 (right) and Case 3 (left) in the experiment.

Figure 7

Scaling analyses of the ion concentration profile and particle stream deformation. (a) Relationship between the normalized concentration change c^* described by Eq. (11) and the rescaled dimensionless length x^* described by Eq. (12). (b,c) Concave depth (δ-a)/W and cusp height (b-δ)/W of the particle stream as functions of the scaled Reynolds number (1-Q_sam/Q_sh)Re.