*Microfluidics for Time-Resolved Small-Angle X-Ray Scattering DOI: http://dx.doi.org/10.5772/intechopen.95059*

compression, or focusing, of the central flow, and decreases the mixing times significantly by reducing the diffusion length. There are two main categories for microfluidic devices with hydrodynamic focusing: coaxial tube and planar on-chip devices. The design can be defined depending on the use, with adapted geometries for fast mixing (**Figure 2A**), gradients (**Figure 2B**), specific nanoparticle growth reactions or self-assembly processes (**Figure 2C**) [15].

The simplest type of coaxial tube reactors is a device consisting of two concentric capillaries (**Figure 2D**), which are connected to a channel where a central flow is injected through the inner capillary, with sheath flow injected from the outer layer. Coaxial tube microreactors find various applications, but are typically used as the interface for droplet-based reactors, as the transition from flow to droplet generation, dripping and jetting is defined by the flowrate of the outer sheath flow. However, this approach is of limited utility in time resolved mixing applications, as it only offers limited mixing geometries. Further limitations abound in the fabrication process for coaxial designs, which requires multiple steps and precise alignment and assembly of the parts [15].

On-chip hydrodynamic focusing devices can be differentiated in twodimensional (2D) and three-dimensional (3D) devices. In two-dimensional hydrodynamic focusing devices, the central flow is focused in the horizontal plane. The simplest geometry for a 2D device is a Y- or T-shaped mixer (**Figure 2E**), where the cross-sectional diffusion is broadened at the channel walls in comparison to the centre. However, this design is highly limited regarding flow stability and focusing and susceptible to variation in these parameters in operation. To avoid this, cross-

#### **Figure 2.**

This understanding of this pressure-driven, steady-state flow in microfluidic

microfluidics, the channel cross-sections can be of various shapes, depending on the application and fabrication method. Eqs. (13) to (16) describe the velocity field and hydraulic resistance for spherical and rectangular cross-sections, which are the most common geometries used for the devices described in this chapter. The derivation of those values is exceedingly more complicated for arbitrary channel cross-section

The first design consideration is how the device will enable time-resolved measurement of phenomenon. This can be achieved in two different ways. The first, and conceptually simplest method, is a static experiment, where a sample is firstly mixed and then introduced into a monitoring chamber and measured repeatedly at defined time periods. The most common apparatus for this style of measurement this is a *stopped flow* device, where mixing is achieved rapidly, and then flow is stopped as soon as the homogenously mixed sample fills the monitoring chamber. The measurement is triggered as soon as the flow is stopped, and generally continues as rapidly as possible until the reaction reaches completion. The second method is to use a continuous flow system, where the mixed sample is introduced into a flow-through system, and temporal measurements are achieved by varying

the distance between the mixing point and the sampling point.

Both styles of devices have advantages and disadvantages, and the choice depends strongly on several experimental considerations, including the time domain of the reaction, mixing efficiency, sample volume constraints, and sample chemistry constraints (e.g. resistance to photobleaching, or radiation damage). Stopped flow measurements are favoured when there is a small volume of sample that is resistant to measurement induced damage (for example a flurophore that is resistant to photobleaching), where the reaction is not extremely fast, and where the experimental measurements are not slow. In stopped flow measurements the initial point in the measurement is always some degree of time post the start of the reaction (given the time it takes to fill the sample cell, stop the flow and take the first measurement), and the temporal resolution of the measurement is given by the speed at which the measurement can be taken. However, agglomeration of the reacting sample on the channel walls can influence the quality of measurements and, due to the ongoing reaction, leads to only a small window that can be detected before the experiment needs to be repeated. Alternatively, continuous flow measurements favour samples that are sensitive to the measurement, are very rapid, and require temporal resolution finer then the measurement speed of the instrument. Continuous flow measurements allow for measurement very close to the point of mixing, temporal resolution is given by the spatial resolution of the measurement, and the time taken to travel to the point of measurement. Further, the deadtime and temporal resolution is heavily influenced by flowrate, allowing for fine control across many temporal regions. As a result, the observation of the reaction can be precisely controlled. It needs to be considered that continuous flow measurements need more sample volume in comparison to stopped flow methods,

The basis of hydrodynamic focusing lies in a central solution that flows with a lower flowrate within an outer sheath fluid with a higher flowrate. This enables the

channels is the basis of liquid handling in lab-on-chip systems. Especially in

shapes.

*2.1.2 Continuous flow vs. stopped flow*

*Advances in Microfluidics and Nanofluids*

to provide a constant flow profile.

*2.1.3 Hydrodynamic focusing*

**18**

*Left: Scheme of microfluidic features for kinetic investigations in flow in a cross shaped mixer. (A) Hydrodynamically focused Centre stream for fast mixing experiments. (B) Mapping of concentration gradient across and along the channel through interdiffusion of different liquids from main and side channels. (C) Nucleation and growth of nanoparticles or self-assembly processes of nanomaterials as a function of time along the outlet channel. Schematic comparison of the provided time scales in continuous and stopped flow microfluidic devices. Right: Schematic illustration of microfluidic devices with various channel cross designs with the corresponding cross-sections through the outlet channel. (D) Coaxial tube reactor with two concentric channels/capillaries. (E) Y-shaped design, where mixing is solely based on diffusion. (F) Cross-shaped geometry at the inlets for hydrodynamic focusing. (G) Two-cross-section geometry, also known as double-focus device, where three different solutions can be introduced into the channels. Solutions introduced into the first sidechannel (SC1) act as an inert buffer between reactants in main channel (MC) and second side-channel (SC2). (H) and (J) multilayer designs of the geometries from (F) and (G), respectively, avoiding contact between the central stream and channel walls. (K) Hybrid device consisting of multilayer focusing device (J) and an inserted glass capillary as outlet channel.*

shaped geometries can be employed, where the central flow is focused from both incoming side channels (**Figure 2F**). This provides good control over the thickness of the central stream. Furthermore, it allows a well-defined sample composition that can be adapted by variation of the volume flow in each inlet individually. To adapt the device design to multi-step synthesis, several side channels can be added to introduce additional reactants (**Figure 2G**). Thus planar on-chip hydrodynamic focusing is more highly favoured for flexible mixing devices, and is used much more often in general microfluidic designs.

**Lithography.** One of the most powerful methods in microfabrication is lithography. It can be differentiated by the type of radiation used, e.g. photolithography, electron-beam lithography, or X-ray lithography. With these different lithography methods, structures with sizes between 0.2 and 500 μm in hard materials like glass, or between 0.5 and 500 μm in soft materials like polymers, can be achieved. In the most common form of lithographic fabrication, a UV blocking mask is generated from the CAD model, and adhered to a silicon wafer. The master model for fabrication is then generated by photolithography, where the masked wafer is coated in a photosensitive epoxy monomer solution, and UV-cured. In general these silicon masters are then used to generate working devices via soft lithographic replication.

The most common approach is to use the master chip as a mould, and poly

which part of the structure was UV-cured on the silicon master.

*Microfluidics for Time-Resolved Small-Angle X-Ray Scattering*

*DOI: http://dx.doi.org/10.5772/intechopen.95059*

time [19, 20].

wider channels [21, 22].

*2.2.2 Device materials*

**21**

(dimethylsiloxane) (PDMS) to form an imprinted device, which can be bonded to a glass-slide or a second PDMS part to form the final microfluidic device [16–18]. The replicated structure can be a positive or negative of the initial design, depending on

**Hot embossing and micromoulding.** Hot embossing is a micromoulding technique that uses thermoplastic polymers to imprint structures at elevated temperatures. It usually uses high-temperature polymers, e.g. PMMA, PC, PI, PE, PVC or PEEK, which are heated above their glass transition temperature (*Tg*) before being pressed into a mould with high pressure. The moulds have to withstand the applied pressure and high temperatures, and are often made of metal or silicon, fabricated via etching, lithography in combination with electroforming and moulding or CNC (Computerised Numerical Control)-machining. The accuracy of hot embossing is in the order of tens of nanometres, making it possible to obtain high aspect ratios of structure, while being a low cost and easy procedure. It is often used with a defined and tested device design as high throughput method with a very short fabrication

**3D printing.** Within the last decade, 3D printing technologies have advanced to

Based on the desired purpose of the microfluidic chip, device materials must fulfil specific criteria. The most important requirements which will be addressed in this chapter are solvent stability, ease of fabrication, and optical and X-ray transparency. **Solvent stability.** Microfluidics deals with the manipulation of liquids, which means that the device material has to be resistant and inert to the solvent. This becomes especially relevant when using organic solvents, as they often cause swelling or dissolution of standard polymeric device materials. Swelling leads to deformation, which can cause channel closure. A number of device materials have been tested with regard to resistance to some common solvents for nanoparticle synthesis and self-assembly processes (**Table 1**). It is clear from these results that careful

**Ease of fabrication.** While the solvent is important, it is also essential to con-

sider the difficulty of working with the various polymers, and the end

stereolithography (SLA) or selective laser sintering (SLS), have been developed for various materials like polymers, resins, ceramics or metals. It is possible with these techniques to produce a complete microfluidic device in one step. The device material and process can thereby be selected with regard to required mechanical and chemical properties of the device. A channel size resolution of few hundred micrometres can be achieved, making this approach preferred for devices with

astonishing precision, in size-regimes down to the micrometre scale. Additive

manufacturing technologies like fused deposition modelling (FDM),

selection of polymer is necessary for long term stability.

However, there are further considerations that need to be taken into account, particularly for chemical reactions or self-assembly processes. In coaxial and 2D channel geometries the interface of reacting solutions is in contact with the channel walls, and particles or macromolecules can stick and agglomerate on the channel surface and disturb the laminar flow conditions. Furthermore, this accumulation interferes with analytical investigations and, in the worst case, can cause complete blockage of the channel.

To avoid channel contact, three-dimensional channel geometries can be used. 3D hydrodynamic focusing requires both horizontal and vertical focusing of the central reactant stream, leading to a complete enclosure with liquid from all sides (**Figure 2H** and **J**). The device design can be optimised to reach homogeneous mixing without integrating specific mixing regions before the measurement part of the microfluidic chip. Additionally, these devices are simple to fabricate and have easily adjustable designs. The most common design to achieve 3D hydrodynamic focusing is through multi-layer on-chip devices, which require precise alignment as part of the fabrication process. Alternate methods are single layer devices or novel fluid manipulation technologies like "microfluidic drifting", which introduces lateral drifts or counter-rotating vortex forces to achieve vertical and horizontal flow focusing. These alternatives require less alignment in manufacturing and are thus much more user friendly in regards to fabrication.

All previously described device geometries can be used to produce droplets, liquid jets and sprays under the right flow conditions, including ultra-high flowrates. These devices are not limited to constrained flows inside channels, and for time-dependent studies the use of free liquid jets is preferred. Measurements of free jets have significant advantages in many optical measurements, as there is little to no background signal from surrounding material. When employing free jet devices, the parabolic flow profile from laminar flow within channels turns into a plug flow profile after passing the nozzle outlet. The liquid–solid interface of the noslip condition resulting in parabolic flow is replaced by the liquid–gas interface in air, which has lower friction with the fluid and can be accelerated in flow direction. Free jets, however, are also quite difficult to work with, and despite the advantages in background have not found widespread use in the field.

#### **2.2 Fabrication**

#### *2.2.1 Fabrication techniques*

Many different technologies exist for the production of microfluidic devices. In general, fabrication of microfluidic devices in hard materials is often very timeconsuming and cost-intensive, thus polymers are generally preferred, particularly when cost and ease of fabrication are considerations in the design process. In most cases, designs are started in silicon, with a Computer-Aided Design (CAD) model of the device. The device is then fabricated using any of a number of different technologies following a process of rapid prototyping. We focus here on some of the more common approaches.
