Influence of surface tension-driven network parameters on backflow strength

Abstract

Surface tension-driven flow is widely used, owing to its spontaneous motion, in microfluidic devices with single channel structures. However, when multiple channels are used, unwanted backflow often occurs. This prevents precise and sophisticated solution flow, but has been rarely characterized. We hypothesize that, with an analytical model, the parameters that influence backflow can be systematically characterized to minimize the backflow. In a microfluidic network, inlet menisci and channels are modeled as variable pressure sources and fluidic conductors, respectively. Through the model and experiment, the influence of each network element on the backflow strength is studied. Backflow strength is affected by the interplay of multiple inlet-channel elements. With the decrease (increase) of the fluidic channel conductance (inlet size), the backflow pressure of the corresponding inlet decreases. On the other hand, backflow volume reaches its peak value during the radius change of the corresponding inlet. In networks consisting of five inlet-channel elements, backflow pressure decreases with increasing step number. Our results provide the foundations for microfluidic networks driven by the Laplace pressure of inlet menisci.

Fig. 1. Surface tension-driven network showing backflow. (a) Generation of fluidic motion by the pressure difference of inlet menisci. Inlets (In i, i = 1 to 3) are connected to each other through channels (Ch i) and the junction (JCT). The inset shows the cross-section of inlet 3 with inlet radius r₃ and meniscus height h₃. (b) Photographs showing backflow generation process. The process consists of three steps, and backflow occurs in step 3b. Cases 1 and 2 show strong and weak backflows, respectively. In step 3, the initial pressures of inlet i (P_Ii) were the same for both cases with P_Ii = 35, 35, and 100 Pa (i = 1 to 3). (c) Circuit diagram of the capillary network. P_i is the pressure of inlet i with radius r_i, and C_i is fluidic conductance of channel i. (d and e) Temporal change in inlet pressures in step 3. Lines and points are the theoretical and experimental values, respectively. Inlet i has pressure P_i in step 3. ΔP_B2 is the backflow pressure of inlet 2, and ΔV_B2 is the normalized backflow volume. In (d), r_i = 2, 1, and 1 mm (i = 1 to 3), and C_i = 9, 9, and 9 (×10⁻¹²) m⁵ N⁻¹ s⁻¹. In (e), r_i = 1.5, 1, and 1 mm, and C_i = 12, 9, and 9 (×10⁻¹²) m⁵ N⁻¹ s⁻¹.

Fig. 2. Influence of C_i on the backflow of inlet 2. When one fluidic conductance was changed, the others were fixed at 7 × 10⁻¹² m⁵ N⁻¹ s⁻¹. Here, r_i = 2, 1, and 1 mm (i = 1 to 3). In step 3, P_Ii = 35, 35, and 75 Pa. Variations of ΔP_B2 and ΔV_B2 by C₁ are shown in (a), by C₂ in (b), and by C₃ in (c). Lines and points are the theoretical and experimental (n = 3) values, respectively.

Fig. 3. Influence of inlet radius r_i on the backflow of inlet 2. Unless otherwise noted, r₁ = 2 mm, and r₂ = r₃ = 1 mm. In step 3, P_Ii = 35, 35, and 75 Pa (i = 1 to 3). ΔP_B2 and ΔV_B2 are shown in (a) and (b), respectively. Lines and points are the theoretical and experimental (n = 3) values, respectively.

Fig. 4. Effect of initial pressure (P_Ii) of inlet i in step 3 on the backflow of inlet 2. Lines and points are the theoretical and experimental (n = 3) values, respectively.

Fig. 5. Backflow in surface tension-driven networks with five inlets and five channels. (a) Circuit diagram of the surface tension-driven network. (b) Change of ΔP_Bi and ΔV_Bi at inlet i (i = 2 to 4). Symbols designate subsets: circles for case 1; triangles for case 2. In case 1, C_j = 5, 10, 9, 13, and 13 (×10⁻¹²) m⁵ N⁻¹ s⁻¹ (j = 1 to 5). In case 2, C_j = 5, 10, 9, 5, 4 (×10⁻¹²) m⁵ N⁻¹ s⁻¹. For both cases, r_j = 2, 1, 1, 1, and 1 mm. For ΔV_Bi < 1 (under the dashed line), the backflow of inlet i stays in channel i and does not go into other channels. The error bars were obtained from five experiments.