Highly pressurized partially miscible liquid-liquid flow in a micro-T-junction. I. Experimental observations

This is the first part of a two-part study on a partially miscible liquid-liquid flow (liquid carbon dioxide and deionized water) which is highly pressurized and confined in a microfluidic T-junction. Our main focuses are to understand the flow regimes as a result of varying flow conditions and investigate the characteristics of drop flow distinct from coflow, with a capillary number, $\mathrm{C}{\mathrm{a}}_c$, that is calculated based on the continuous liquid, ranging from ${10}^{-3}$ to ${10}^{-2}$ (${10}^{-4}$ for coflow). Here in part I, we present our experimental observation of drop formation cycle by tracking drop length, spacing, frequency, and after-generation speed using high-speed video and image analysis. The drop flow is chronologically composed of a stagnating and filling stage, an elongating and squeezing stage, and a truncating stage. The common “necking” time during the elongating and squeezing stage (with $\mathrm{C}{\mathrm{a}}_c\sim {10}^{-3}$) for the truncation of the dispersed liquid stream is extended, and the truncation point is subsequently shifted downstream from the T-junction corner. This temporal postponement effect modifies the scaling function reported in the literature for droplet formation with two immiscible fluids. Our experimental measurements also demonstrate the drop speed immediately following their generations can be approximated by the mean velocity from averaging the total flow rate over the channel cross section. Further justifications of the quantitative analysis by considering the mass transfer at the interface of the two partially miscible fluids are provided in part II.

Figure 1

Schematic of the experimental system.

Figure 2

Assembly of a nonpermanent connector and a microchip: (a) schematic of a nonpermanent connector including an upper part, a bottom part, a compression glass cuboid, and three O rings (not shown here) placed in the three grooves as well as between the microchip and the bottom part; (b) a photo of the assembly where the connection fittings and four screws is also shown.

Figure 3

A silicon-glass microchip featured by a micro-T-junction: (a) a top view of the micro-T-junction and (b) the channel bottom with a certain degree of roughness resulted from the deep reactive ion etching (DRIE). Scale bars: 100 μm.

Figure 4

An example of liquid $\mathrm{C}{\mathrm{O}}_2$ and water two-phase flow in a micro-T-junction where liquid $\mathrm{C}{\mathrm{O}}_2$ drops are being produced. (a) Schematic of a newly generated liquid $\mathrm{C}{\mathrm{O}}_2$ drop and a second one starts formation: solid lines and dash lines depict the drops at the $i\mathrm{th}$ and the $(i+1)$-th frame, respectively, during one period of drop generation. Parameters to be measured include (I) drop length $L$, (II) drop spacing $S$ between the emerging drop and the adjacent formed one within one period, and (III) drop speed $V$ determined by the drop displacement $\mathrm{\Delta }d$ (centroid to centroid) during one time interval $\mathrm{\Delta }t$ of the frames. (b) A sample of frame selected from the experiment video. The image below shows the identification of a formed drop and the measurements of drop length $L$ and drop spacing $S$ using the same frame in Matlab.

Figure 5

Flow regimes of liquid $\mathrm{C}{\mathrm{O}}_2$ and water two-phase flow at a T-junction as a function of flow rate ratio $Q_{{\mathrm{H}}_2\mathrm{O}}/Q_{L\mathrm{C}{\mathrm{O}}_2}$ and $\mathrm{C}{\mathrm{a}}_c$ number: liquid $\mathrm{C}{\mathrm{O}}_2$ enters from the side channel as the dispersed phase and water flows in the main channel as the continuous phase of the T-junction. (a) The flow rate ratio $Q_{{\mathrm{H}}_2\mathrm{O}}/Q_{L\mathrm{C}{\mathrm{O}}_2}$ and $\mathrm{C}{\mathrm{a}}_c$ number are decreased from 50/50 to 5/220 and $1.6\times {10}^{-3}$ to $1.6\times {10}^{-4}$, respectively. Cases 3 to 5 are all shown by two frames captured using a $10\times$ (left) and a $5\times$ objective (right). Case 8 is shown by an end-to-end combination of three frames from using the $5\times$ objective. (b) From case 13 to 21, $Q_{{\mathrm{H}}_2\mathrm{O}}/Q_{L\mathrm{C}{\mathrm{O}}_2}$ and $\mathrm{C}{\mathrm{a}}_c$ number are both increased due to the flow rate increase of water; from case 22 to 28, water flow accelerates from 100 to $500\mu \mathrm{l}/min$ while the liquid $\mathrm{C}{\mathrm{O}}_2$ is maintained as a constant flow. As $\mathrm{C}{\mathrm{a}}_c$ reaches $O\left({10}^{-2}\right)$, it leads to a dripping regime (cases 27 and 28) of the drop flow.

Figure 6

A quick overview of one period $(t_0=7.8\mathrm{ms})$ of liquid $\mathrm{C}{\mathrm{O}}_2$ drop generation during the flow condition where both $\mathrm{C}{\mathrm{O}}_2$ and water flow at $50\mu \mathrm{l}/min$. Note that the images are rotated ${90}^{\circ }$ clockwise as compared to Fig. 4 for ease of alignments. The period $t_0$ is generally divided into three stages: (a) a stagnating and filling stage $t_{sf}$, (b) an elongating and squeezing stage $t_{es}$, and (c) a truncating stage $t_{tr}$. And each stage is characterized by a specific time length. Here within one period $t_0=7.8\mathrm{ms}, t_{sf}, t_{es}$, and $t_{tr}$ are approximately 1.6 ms, $(6.6-1.6)=5\mathrm{ms}$ and $(7.8-6.6)=1.2\mathrm{ms}$, respectively.

Figure 7

Liquid $\mathrm{C}{\mathrm{O}}_2$ drop size as a function of flow rate ratio ($Q_{{\mathrm{H}}_2\mathrm{O}}/Q_{L\mathrm{C}{\mathrm{O}}_2}$): the drop length ($L$) is normalized by the width ($W=150\mu \mathrm{m}$) of the microchannel. (a) The total flow rate of liquid $\mathrm{C}{\mathrm{O}}_2$ and water is a constant ($Q_{{\mathrm{H}}_2\mathrm{O}}+Q_{L\mathrm{C}{\mathrm{O}}_2}=100\mu \mathrm{l}/min$); (b) the flow rate of liquid $\mathrm{C}{\mathrm{O}}_2$ is a constant ($Q_{L\mathrm{C}{\mathrm{O}}_2}=50\mu \mathrm{l}/min$), $\mathrm{C}{\mathrm{a}}_c$ steps towards $O\left({10}^{-2}\right)$ from $O\left({10}^{-3}\right)$ when $Q_{{\mathrm{H}}_2\mathrm{O}}/Q_{L\mathrm{C}{\mathrm{O}}_2}$ reaches 7. Error bar: the standard deviation ($s$) of the mean normalized drop length ($\overline{L}/W$).

Figure 8

Comparison of the speeds of the liquid $\mathrm{C}{\mathrm{O}}_2$ drops $V_{\mathrm{drop}}$ ($•$) after generation to the average flow velocities of water $V_{{\mathrm{H}}_2\mathrm{O},a}$ ($▾$) and liquid $\mathrm{C}{\mathrm{O}}_2{V}_{\mathrm{C}{\mathrm{O}}_2,a}$ ($▴$) as well as the averaged total velocity $V_{\mathrm{Total},a}$ ($\blacksquare$) of the two fluids under drop flow cases for (a) $Q_{{\mathrm{H}}_2\mathrm{O}}+Q_{L\mathrm{C}{\mathrm{O}}_2}=100\mu \mathrm{l}/min$ and (b) $Q_{L\mathrm{C}{\mathrm{O}}_2}=50\mu \mathrm{l}/min$, respectively. Average velocities are defined as $V_{{\mathrm{H}}_2\mathrm{O},a}=Q_{{\mathrm{H}}_2\mathrm{O}}/\left(DW\right), V_{\mathrm{C}{\mathrm{O}}_2,a}=Q_{\mathrm{C}{\mathrm{O}}_2}/\left(DW\right)$ and $V_{\mathrm{Total},a}=(Q_{{\mathrm{H}}_2\mathrm{O}}+Q_{L\mathrm{C}{\mathrm{O}}_2})/\left(DW\right)$. Error bar: the standard deviation $\left(s^{\prime }\right)$ of $V_{\mathrm{Drop}}$.

Figure 9

The development of spacing between the emerging drop and the adjacent formed one: (a) as observed under the drop flow case 5 ($\blacksquare$), case 14 ($•$), case 19 ($⧫$) and case 20 ($★$), respectively; (b) the detailed spacing development observed continuously from 86 pairs of those two drops under case 14 ($Q_{{\mathrm{H}}_2\mathrm{O}}=55\mu \mathrm{l}/min$ and $Q_{\mathrm{C}{\mathrm{O}}_2}=45\mu \mathrm{l}/min$). Each upright line (indicated by the arrow) in the same row depicts an elemental spacing development during one period of the (emerging) drop generation.

Figure 10

Averaged spacing within one period (8.4 ms) of drop generation under drop flow case 14. The experimental data herein are averaged from those in Fig. 9, and each error bar indicates two standard deviations from the averaged spacing upon the corresponding time moment. Dashed lines are the fitting lines from the averaged spacing.