A Review of Pressure Drop and Mixing Characteristics in Passive Mixers Involving Miscible Liquids

Abstract

The present review focuses on the recent studies carried out in passive micromixers for understanding the hydrodynamics and transport phenomena of miscible liquid-liquid (LL) systems in terms of pressure drop and mixing indices. First, the passive micromixers have been categorized based on the type of complexity in shape, size, and configuration. It is observed that the use of different aspect ratios of the microchannel width, presence of obstructions, flow and operating conditions, and fluid properties majorly affect the mixing characteristics and pressure drop in passive micromixers. A regime map for the micromixer selection based on optimization of mixing index (MI) and pressure drop has been identified based on the literature data for the Reynolds number (Re) range (1 ≤ Re ≤ 100). The map comprehensively summarizes the favorable, moderately favorable, or non-operable regimes of a micromixer. Further, regions for special applications of complex micromixer shapes and micromixers operating at low Re have been identified. Similarly, the operable limits for a micromixer based on pressure drop for Re range 0.1 < Re < 100,000 have been identified. A comparison of measured pressure drop with fundamentally derived analytical expressions show that Category 3 and 4 micromixers mostly have higher pressure drops, except for a few efficient ones. An MI regime map comprising diffusion, chaotic advection, and mixed advection-dominated zones has also been devised. An empirical correlation for pressure drop as a function of Reynolds number has been developed and a corresponding friction factor has been obtained. Predictions on heat and mass transfer based on analogies in micromixers have also been proposed.

Keywords: computational fluid dynamics (CFD); design optimization; friction factor; mixing; mixing index; passive micromixers; pressure drop; regime map.

Figure 1

Closed streamlines in cross-section of each half cycle: (a) the mixer; (b) flow visualization in the cross-section (reproduced with permission from Wiggins and Ottino [20]).

Figure 2

Various Types of Category 1 Passive Micromixers: (i) T Junction Mixer (TJM); (ii) Y Junction Mixer (YJM); (iii) Cross Flow Junction Mixer (CFJM).

Figure 3

(A). Category 2 Micromixers: (i) LTFMS Micromixer Khaydarov et al. [70]; (ii) Sinusoidal, Trapezoidal, and Triangular Micromixer Chen et al. [65]; (iii) Sinusoidal micromixer, Parsa et al. [62]; (iv) Helical Coil Micromixer, Luo et al. [28]. (B). Category 3 Micromixers: (i) Primary and Secondary Minkowski Fractal Obstacle Micromixer, Chen and Chen [74]; (ii) Staggered Baffle Micromixer, Niu et al. [32]; (iii) T-type Fractal Obstacle Micromixer, Hou et al. [33]; (iv) ASZMM micromixer, Yuan et al. [87]; (v) Obstacle Serpentine Micromixer, Karthikeyan et al. [89]; (vi) T-type mixer with rectangular inserts, Rudyak and Minakov, [34]; (vii) Obstructed Grooved Micromixer, Rahmannezhad and Mirbozorgi, [31]; (viii) Primary and Secondary Koch Fractal Baffle Micromixer, Zhang et al. [35]. (C). Category 4 Micromixers: (i) Twisted Y-Junction mixer; (ii) Tangential T Junction, Fischer and Kockmann, [54]; (iii) Circular-shaped Fluid Overlapping Micromixer, Okuducu and Aral, [78]; (iv) Random mixers, Zhang et al. [37]; (v) Multi-laminational elongated flow mixer, Adeosun and Lawal [36]; (vi) Two-layer crossing microchannel micromixer, Amar et al. [77]; (vii) Helical, Baker, and Small Micromixers, Ruijin et al. [40]; (viii) SAR micromixer for blood mixing, Tran-Minh et al. [61]; (ix) HC Micromixer, Mahmud et al. [83]; (x) Sickle, venture, SZ-type micromixers, Plouffe et al. [38]; (xi) Pore Array Tube-in-Tube micromixer, Li et al. [13]; (xii) Tree Micromixer, Wang et al. [57]; (xiii) Corning Advanced Flow Reactor, Nieves-Remancha et al. [39].

Figure 3

(A). Category 2 Micromixers: (i) LTFMS Micromixer Khaydarov et al. [70]; (ii) Sinusoidal, Trapezoidal, and Triangular Micromixer Chen et al. [65]; (iii) Sinusoidal micromixer, Parsa et al. [62]; (iv) Helical Coil Micromixer, Luo et al. [28]. (B). Category 3 Micromixers: (i) Primary and Secondary Minkowski Fractal Obstacle Micromixer, Chen and Chen [74]; (ii) Staggered Baffle Micromixer, Niu et al. [32]; (iii) T-type Fractal Obstacle Micromixer, Hou et al. [33]; (iv) ASZMM micromixer, Yuan et al. [87]; (v) Obstacle Serpentine Micromixer, Karthikeyan et al. [89]; (vi) T-type mixer with rectangular inserts, Rudyak and Minakov, [34]; (vii) Obstructed Grooved Micromixer, Rahmannezhad and Mirbozorgi, [31]; (viii) Primary and Secondary Koch Fractal Baffle Micromixer, Zhang et al. [35]. (C). Category 4 Micromixers: (i) Twisted Y-Junction mixer; (ii) Tangential T Junction, Fischer and Kockmann, [54]; (iii) Circular-shaped Fluid Overlapping Micromixer, Okuducu and Aral, [78]; (iv) Random mixers, Zhang et al. [37]; (v) Multi-laminational elongated flow mixer, Adeosun and Lawal [36]; (vi) Two-layer crossing microchannel micromixer, Amar et al. [77]; (vii) Helical, Baker, and Small Micromixers, Ruijin et al. [40]; (viii) SAR micromixer for blood mixing, Tran-Minh et al. [61]; (ix) HC Micromixer, Mahmud et al. [83]; (x) Sickle, venture, SZ-type micromixers, Plouffe et al. [38]; (xi) Pore Array Tube-in-Tube micromixer, Li et al. [13]; (xii) Tree Micromixer, Wang et al. [57]; (xiii) Corning Advanced Flow Reactor, Nieves-Remancha et al. [39].

Figure 3

(A). Category 2 Micromixers: (i) LTFMS Micromixer Khaydarov et al. [70]; (ii) Sinusoidal, Trapezoidal, and Triangular Micromixer Chen et al. [65]; (iii) Sinusoidal micromixer, Parsa et al. [62]; (iv) Helical Coil Micromixer, Luo et al. [28]. (B). Category 3 Micromixers: (i) Primary and Secondary Minkowski Fractal Obstacle Micromixer, Chen and Chen [74]; (ii) Staggered Baffle Micromixer, Niu et al. [32]; (iii) T-type Fractal Obstacle Micromixer, Hou et al. [33]; (iv) ASZMM micromixer, Yuan et al. [87]; (v) Obstacle Serpentine Micromixer, Karthikeyan et al. [89]; (vi) T-type mixer with rectangular inserts, Rudyak and Minakov, [34]; (vii) Obstructed Grooved Micromixer, Rahmannezhad and Mirbozorgi, [31]; (viii) Primary and Secondary Koch Fractal Baffle Micromixer, Zhang et al. [35]. (C). Category 4 Micromixers: (i) Twisted Y-Junction mixer; (ii) Tangential T Junction, Fischer and Kockmann, [54]; (iii) Circular-shaped Fluid Overlapping Micromixer, Okuducu and Aral, [78]; (iv) Random mixers, Zhang et al. [37]; (v) Multi-laminational elongated flow mixer, Adeosun and Lawal [36]; (vi) Two-layer crossing microchannel micromixer, Amar et al. [77]; (vii) Helical, Baker, and Small Micromixers, Ruijin et al. [40]; (viii) SAR micromixer for blood mixing, Tran-Minh et al. [61]; (ix) HC Micromixer, Mahmud et al. [83]; (x) Sickle, venture, SZ-type micromixers, Plouffe et al. [38]; (xi) Pore Array Tube-in-Tube micromixer, Li et al. [13]; (xii) Tree Micromixer, Wang et al. [57]; (xiii) Corning Advanced Flow Reactor, Nieves-Remancha et al. [39].

Figure 4

Pressure drop variation with Re for different categories of micromixers Khaydarov et al. [70] (LTFMSM); Chen and Chen [74] (SMFOM); Chen and Chen [74] (PMFOM) Okuducu and Aral [41] (TLM); Okuducu and Aral [41] (CSCRM); Lotfiani and Razazadeh [81] (YJM); Lotfiani and Razazadeh [81] (TLM); Mahmud et al. [83] (HCM); Mahmud et al. [83] (YUM); Tripathi et al. [85] (SpiM); Tripathi et al. [85] (RsPM); Tripathi et al. [85] (SESpM); Niu et al. [32] (ESBM); Niu et al. [32] (CSBM); Niu et al. [32] (SBM); Yuan et al. [87] (ASZMMM); Hou et al. [33] (TSFOM).

Figure 5

Mixing index of micromixers available in the literature: (A) Experimental Investigations, Ansari et al. [69] (TJM); Raza et al. [25] (TLCCM); Yuan et al. [87] (ASZMMM); Silva Jr, et al. [72] (TJM); Viktorov et al. [103] (TJM); Cortes-Quiro et al. [104] (HCM); (B) Numerical Studies. Amar et al. [77] (TJM); Mahmud et al. [83] (YUM); Tripathi et al. [84] (YJM); Tripathi et al. [84] (SM); Tripathi et al. [84] (SpiM); Tripathi et al. [85] (SpiM); Tripathi et al. [85] (RsPM); Tripathi et al. [85] (SESpM); Yuan et al. [87] (ASZMMM); Hou et al. [33] (TSFOM); Okuducu and Aral [78] (TJM); Niu et al. [32] (ESBM); Niu et al. [32] (CSBM); Niu et al. [32] (SBM).

Figure 5

Mixing index of micromixers available in the literature: (A) Experimental Investigations, Ansari et al. [69] (TJM); Raza et al. [25] (TLCCM); Yuan et al. [87] (ASZMMM); Silva Jr, et al. [72] (TJM); Viktorov et al. [103] (TJM); Cortes-Quiro et al. [104] (HCM); (B) Numerical Studies. Amar et al. [77] (TJM); Mahmud et al. [83] (YUM); Tripathi et al. [84] (YJM); Tripathi et al. [84] (SM); Tripathi et al. [84] (SpiM); Tripathi et al. [85] (SpiM); Tripathi et al. [85] (RsPM); Tripathi et al. [85] (SESpM); Yuan et al. [87] (ASZMMM); Hou et al. [33] (TSFOM); Okuducu and Aral [78] (TJM); Niu et al. [32] (ESBM); Niu et al. [32] (CSBM); Niu et al. [32] (SBM).

Figure 6

Map for selection of micromixer based on pressure drop v/s mixing index for a Re range of 1 ≤ Re ≤ 100. Talebjedi et al. [80] (TJM); Tripathi et al. [84] (YJM); Tripathi et al. [84] (SM); Tripathi et al. [84] (SpiM); Tripathi et al. [85] (SpiM); Tripathi et al. [85] (RsPM) Tripathi et al. [85] (SESpM); Yuan et al. [87] (ASZMMM); Niu et al. [32] (ESBM); Niu et al. [32] (CSBM); Niu et al. [32] (SBM).

Figure 7

Parity plot of friction factor as per experiments and predicted by Equation (1).