Transitional pressure drop in a cavitied microchannel

Microchannels have become prevalent as an integrated part of microfluidic devices in biochemistry and electronics applications. In such devices, the small scale results in a characteristically low Reynolds number laminar flow. The small scale also results in an associated high flow resistance. A design concept has been developed that reduced the flow resistance by featuring geometrically modified microchannels with cavities. Compared to an unmodified microchannel, the modification reduces flow resistance at low Reynolds numbers but conversely leads to higher flow resistance at high Reynolds numbers: i.e., a reversal of flow resistance occurred. Thus far, plausible fluidic mechanisms underlying such reversal have remained largely unstipulated. Based upon detailed pressure and flow field measurements, we stipulate that flow progression from laminar flow slippage to rotational vortices in cavitied microchannels is the main mechanism causing the reversal. We further clarify that the earlier transition of initial laminar flow to turbulent flow is triggered by instabilities generated along shear layers, formed between the mainstream flow and rotational vortices in each cavity.

Figure 1

Microfluidics: (a) Microchannels in micro-electro-mechanical systems (MEMS) in biomedical and electronics cooling applications [3, 4, 5, 6, 7] and (b) reversal of flow resistance quantified by friction factor ratios ($f_{\mathrm{CS}}/f_{\mathrm{ref}}$) for microchannels without and with cavitied sidewalls [9, 10, 11].

Figure 2

Microchannel specimens: (a) Circular microchannels include (i) a reference circular microchannel, (ii) a 2D cavitied circular microchannel, (iii) a 3D cavitied circular microchannel, and (iv) photographs of a fabricated microchannel showing upper and lower substrates, and designed micropassage. (b) Rectangular microchannels include (i) a reference rectangular microchannel, (ii) a photograph of a fabricated microchannel showing cover plate, substrate, and designed micropassage, and (iii) a 2D cavitied rectangular microchannel.

Figure 3

Experimental setup for measuring pressure drop and local flow fields using a μPIV system.

Figure 4

Comparisons between unmodified (reference) and cavitied circular microchannels for (a) pressure drop per unit length and (b) friction factor.

Figure 5

Comparisons between an unmodified (reference) and a circular cavitied microchannel with a rectangular cross section featuring curved sidewalls for (a) pressure drop per unit length and (b) friction factor.

Figure 6

Flow resistance and flow field varying with mean flow velocity ($u_m$): (a) pressure drop difference (Δ) and (b) flow structure and velocity profile within a representative cavity cell measured with a μPIV system.

Figure 7

Shear stress (τ) distribution at six selected $u_m$ values: (I) at $u_m=0.88$ m/s, (II) at 2.00 m/s, (III) at 3.80 m/s, (IV) at 5.00 m/s, (V) at 6.58 m/s, and (VI) at 8.55 m/s. (a) In the fluid along the central cavity plane perpendicular to the nominal channel axis and (b) wall shear stress $\left(\right|{\tau }_w\left|\right)$.

Figure 8

Vorticity distribution inside the sidewall cavities at six selected Reynolds numbers where positive vorticity denotes a counterclockwise rotation: (I) $\mathrm{R}{\mathrm{e}}_{D_h}=100$, (II) $\mathrm{R}{\mathrm{e}}_{D_h}=230$, (III) $\mathrm{R}{\mathrm{e}}_{D_h}=438$, (IV) $\mathrm{R}{\mathrm{e}}_{D_h}=576$, (V) $\mathrm{R}{\mathrm{e}}_{D_h}=758$, and (VI) $\mathrm{R}{\mathrm{e}}_{D_h}=1000$.

Figure 9

Schematics of flow structure (in the x-y plane) and shear stress distribution along the cross section (in the y-z plane): (a) $100\le \mathrm{R}{\mathrm{e}}_{D_h}\le 438$, (b) $438<\mathrm{R}{\mathrm{e}}_{D_h}\le 758$, and (c) $\mathrm{R}{\mathrm{e}}_{D_h}>758$.