Experimental Study on the Effect of Locally Convergent Configurations on the Flow Pattern in PMMA Microchips

The geometries of micro-channel play a key role in forming of digital droplets, and can be real-time or effective controlling methodologies. Local convergence regions are designed in the rectangular cross-section channels on PMMA microchips, in which two-phase coaxial jets are introduced by inserting a syringe needle. The two-phase flow (lubricating oil (continuous phase, flow rate Q c)/deionized water (dispersed phase, flow rate Q d)) is considered. Two geometric control variables, the relative position (needle displacement x) and tapering characteristics (convergence angle α), are naturally adopted to discribe such geometry configurations. The micro-flow under the change of these two parameters is mainly studied in this paper. Four kinds of characteristic flow patterns, namely, sausages, slug, dripping and jetting, are found in the experiment, and their occurring parameters and developing dynamic characteristics are discussed. The experiment shows that the increase of inner needle displacement x can produce higher frequency and finer droplets, which is in consistent with our previous results obtained in round tube experiments and simulations. While increasing the convergence angle α, contrarily, takes opposite effects.


Introduction
Microfluidic equipment can produce monodisperse sub-micron droplets, bubbles, emulsions and capsules in a continuous way by deforming, stretching and splitting certain substances in the fluids, which can be precipitated and solidified if necessary.
Microfluidic technology prepares droplets with controllable volume, controllable frequency, controllable composition or controllable movement, and large specific surface area with high consistency, and also realizes large-scale droplet productions. Moreover, it can contribute to wide areas such as rapid chemical reaction [1], drug delivery [2], cell capsule, digital PCR (polymerase chain reaction) system [3], protein crystallization [4], polymer microcapsule [5], or microreactor [6], and so on.

Experimental Set-ups and Materials
The co-flowing configuration used and experimental apparatus in this research are shown in figure 1. The materials used are 5W-20 lubricating oil (continuous phase, density ρ c =826 kg/m 3 , viscosity μ c =40.96 mPa· s, interfacial tension σ=20.08 mN/m) and deionized water (dispersed phase, density ρ d =986.2 kg/ m 3 , viscosity μ d =1.23 mPa· s, interfacial tension σ=20.08 mN/m) separately. The devices include microchip, micro-injection-pump (LSP02-2A, Lange), highspeed camera (Phantom V611-16G-M, AMETEK), microlens (AT-X M100 PRO-D, Tokina), light source and computer, as shown in figure 1(a). The material of microfluidic chip is polymethylmethacrylate (PMMA), and its total dimensions are 30 mm * 30 mm * 4 mm.  Both phases mix at the convergence area, whose length is X L = 2680 µm and convergence angle α. The syringe needle, whose inner diameter is d = 200 µm and outer diameter D = 400 µm , of dispersed phase is inserted into this tapering area to form two-phase flow (region 1). The downstream micro-channel is a straight tunnel (region 2), with rectangular cross-section of width W out = 400 µm and height h = 600 µm . L d is the axial size (length) of the droplet generated.
The two immiscible liquids, driven by a high-precision two-channel injection pump97 (LSP02-2A, Lange), are injected into a nested coaxial outer-inner annular micro-channel. The dispersed phase Many samples of PMMA microchips are prepared. The combinations of the two geometrical parameters, convergence angle α and needle displacement x, are shown in table 1, labeled as sample A3, B3, C3, D3, C1, C2, C4, C5 and E. The microchips of certain convergence angle α (0 • , 5 • , 11 • , 17 • and 29 • ) and needle displacement x (0, 620, 1170, 1620 and 2160 µm ) are designed to avoid redundant experimental work. Note 'A, B, C, and D' are symbols for convergence angle α at values of 5 • , 11 • , 17 • , and 29 • respectively. The numbers '1, 2, 3, 4 and 5' represent the needle displacement x at relative locations 0, 620, 1170, 1620, and 2160µm . The sample E, which is used to check the consistency and effectiveness of our experiments with the work of others, is a straight micro-channel without tapering configuration, which is a commonly used and well studied microchip structure.

Flow Patterns
Many flow patterns can be obtained. Their descriptions are often based on qualitative and sometimes subjective visual discriminations. For instance, in the sample C4 (α = 17 • , and x = 1620 µm ), four main flow patterns are observed: slug, dripping, jetting and sausages, seen in figure 2. The slug pinches off at the tip of the inner needle tip, and produces a large droplet whose length L d far exceeds the size of the channel width. The dripping droplets are gained the similar size to the channel width. These two flow patterns are periodic for generating monodisperse droplet. For the type of sausages, it seems a widening jet with bamboo waves at the interface, which never breaks up and brings any droplets. While the jetting droplets form faraway from the inner needle tip and at the downward inner jet end. The jetting mode may cause very tiny satellite droplets.
In such small scales of micro-channels, the gravity force is usually ignored. The countable transition of two-phase flow pattern is mainly determined by the competitions among three forces, namely, the viscous force of continuous phase, the interfacial tension of two phases and the inertial force of dispersed phase, and we define two non-dimensional parameters to depict their competitions.   The four flow regimes, namely, slug, dripping, jetting and sausage as pictures represented in figure  2, are identified in figure 3. Dashed lines for pattern transition separation are used to divide these flow regimes. As a general, the slug regime occurs at low Ca c with low We d region, the dripping regime occurs at higher Ca c with low We d region, the jetting regime occurs at highest Ca c with low We d region, and the sausages regime occurs at high We d region. The transitions among these regimes are highly correlated with the relative power superiority of interfacial tension force, inertial force and shear stress force. Apparently, the interfacial tension dominates the proceeding of slug forming, the inner inertial force maintains the wavy interface of sausages, the moderate outer shear force and low inner inertial force produce dripping process, and the high outer shear force causes thin jetting.

The Variations of Convergence Angle α and Needle Displacement x on Flow Charts
When the needle displacement x increases, the flow pattern map varies correspondingly. We draw collectively the flow pattern maps for samples C1, C2, C3, C4 and C5 in figure 4. Apparently the convergence angle α is a constant of 17•, and the needle displacement x increases from 0, 620, 1170, 1620 to 2160 µm.
As can be seen from figure 4, with the increase of x, the flow pattern transition boundaries between sausages and slug move downwards, and the area of slug shrinks. The flow pattern transition boundary between slug and dripping moves left-upwards and also suppresses the slug region, and the area of dripping increases. Jetting begins to appear into the scope of our experimental setting parameters from the right side only for samples C4 and C5.
The influence of the convergence angle α on flow patterns is also investigated for samples A3, B3, C3 and D3, as shown in figure 5 for the fixed needle displacement x = 1170 µm. The corresponding convergence angle α of each sample increases from 5•, 11•, 17• to 29• respectively.  It can be seen from figure 5 that with the decrease of convergence angle α, the flow pattern transition lines between slug and sausages move downwards and compress the area of slug regime. The slug-dripping transition lines move left-upwards and also suppress the slug regime, and the regime of dripping increases with α getting smaller. Jetting begins to appear from the right side only for sample A3 for the smallest α in the present parameter scope.
By comparing figure 5 with figure 4, it is intuitive to see a correlation between the effects of x and α on the occurrence of flow patterns. The increase of the needle displacement x and decrease of the convergence angle α almost have the same influence on flow pattern transitions.

Scaling up Droplet Formation in Slug and Dripping Regimes
Slug and dripping are idealized flow patterns in heat and mass transfer processes or bio-testing. The droplets formed have high consistency in size and specific surface area, and monodisperse droplets can be obtained efficiently. The size of droplet and the frequency generated are the focus for applications.
The droplet formation at the inner needle tip can be divided into two processes: growth and necking off. Figure 6 shows photographs of droplet growth stages (a)-(c) and necking-shedding stages (d)-(f) in the slug flow pattern, and photographs of droplet growth stages (g)-(i) and necking-shedding stages (j)-(l) in the dripping flow pattern.

Conclusion
The PMMA microchips are designed to take into account the convergence configurations on behaviors of oil/water two-phase coaxial flows in rectangular cross-section micro-channels. The influence of two geometric parameters, needle displacement x and convergence angle α on droplet forming characters is mainly investigated.
Slug, dripping, jetting and sausage modes occur in the present experimental observations. Although all the modes are periodical, the sausage waves never pinch off, and the jetting mode has very tiny satellite droplets evolved, only slug and dripping modes can produce perfect uniform droplets. The decrease of needle displacement x and increase of convergence angle α can both expand the slug and dripping regimes. It is proved that the needle displacement x and convergence angle α are essentially correlated variables, and can be degenerated into a single geometrical variable, which means the great improvement on controlling costs.