Shear-free mixing to achieve accurate temporospatial nanoscale kinetics through scanning-SAXS: ion-induced phase transition of dispersed cellulose nanocrystals†

Time-resolved in situ characterization of well-defined mixing processes using small-angle X-ray scattering (SAXS) is usually challenging, especially if the process involves changes of material viscoelasticity. In specific, it can be difficult to create a continuous mixing experiment without shearing the material of interest; a desirable situation since shear flow both affects nanoscale structures and flow stability as well as resulting in unreliable time-resolved data. Here, we demonstrate a flow-focusing mixing device for in situ nanostructural characterization using scanning-SAXS. Given the interfacial tension and viscosity ratio between core and sheath fluids, the core material confined by sheath flows is completely detached from the walls and forms a zero-shear plug flow at the channel center, allowing for a trivial conversion of spatial coordinates to mixing times. With this technique, the time-resolved gel formation of dispersed cellulose nanocrystals (CNCs) was studied by mixing with a sodium chloride solution. It is observed how locally ordered regions, so called tactoids, are disrupted when the added monovalent ions affect the electrostatic interactions, which in turn leads to a loss of CNC alignment through enhanced rotary diffusion. The demonstrated flow-focusing scanning-SAXS technique can be used to unveil important kinetics during structural formation of nanocellulosic materials. However, the same technique is also applicable in many soft matter systems to provide new insights into the nanoscale dynamics during mixing.

Window material, COC-film Channel plate is driven by three syringe pumps , where the sheath ow pumps have two 1 mL syringes each (one for each side channel) and the core ow naturally only needs one (1 mL) syringe. Two more syringe pumps holding larger 20 mL syringes are connected to the core and 2nd sheath ow respectively. These are primarily used to be able to push out small bubbles and ll up the tubing prior to the experiment and then kept turned o. For the 1st sheath ow with water, one syringe pump with two large 60 mL syringes are connected, each  Figure 2: Illustration of the uid distribution to the experiments. The main ow is driven by small 1 mL syringes to be able to run at low ow rates. Larger syringes are also connected to the system to be able to ush the ow cell with larger volumes and higher ow rates. A peristaltic pump is connected to maintain a constant level in the outlet container and a small motor is attached to the outlet to remove excess gel at the outlet. The pumps ow rates Q 1 , Q 2 , Q 2,barrier , Q 3 and Q drain can be controlled remotely.
with ow rate Q 2,barrier /2. Their primary usage is to be able to run the ow continuously with a thick diusion (barrier) layer between the salt solution and the CNC dispersion and thus avoid gelation in the channel while not measuring. They are also used to ush the channel with high ow rates to push out any accumulated gel inside the channel. For all larger pumps, manual shut-o valves are placed to increase the stiness of the system and avoid potential bubbles in the large syringes to store energy and act as springs in the uidic system if pressure would build up. Adding this was generally seen to lead to a more stable ow over a longer time period. During experiment all valves were shut, except for the valves to one of the 1st sheath ow pumps, in order to quickly ush the system.
Since the outlet container is constantly lled with the uids from the ow cell, it needs to be drained using a peristaltic pump with ow rate Q drain = 5Q + Q 2,barrier to keep the level stationary. As gel is accumulating at the outlet, a small 6V motor rotating at around 5 rpm is attached to the ow cell to slowly remove gel without disturbing the ow upstream.
During the scanning-SAXS experiments, the three pumps with the 1 mL syringes (ow rates Q 1 , Q 2 and Q 3 ) as well as the additional pump for the 1st sheath ow (ow rate Q 2,barrier ) and the peristaltic pump are controlled remotely from outside the experimental hutch.
In between each measurement, the ow rate of the 1st sheath is increased by setting Q 2,barrier /2 = 6.7 mL/h, to ensure no gelation in the channel. When measuring, Q 2,barrier is set to zero and the ow is allowed to stabilize with the desired rates for the experiment.
Directly after the measurement, to remove possible gel that might have accumulated, the channel is ushed with Q 2,barrier /2 = 5000 mL/h for 1 s.
The system is running continuously with given ow rates Q 1 , Q 2 and Q 3 (Q 2,barrier = 0), while data is collected from the dierent y-and z-locations in the ow.

Supporting POM experiments
Prior to the SAXS experiment, the ow was studied with polarized optical microscopy (POM) to ensure that we indeed have a gel forming at the given ow conditions as well as determining the true core ow radius R 1 and velocity V . Fig. 3 shows By running only water in the second sheath ow and thus not inducing any gelation, we can observe that CNCs remain non-isotropic throughout the visible region (see Fig. 3a).
As the CNC dispersion exits, we still observe the dispersion interface, but it is clearly not held together strongly and eventually diuse out to the surrounding water. With gelation (i.e. with the NaCl solution in the 2nd sheath) in Fig. 3b, we can clearly observe an ioninduced loss of alignment at z/h ≈ 5 and a gel thread exiting the channel and accumulating in the container. Running the system at a higher ow rate Q = 2.5 mL/h (instead of Q = 1 mL/h), we nd that the point of isotropy in the channel is pushed downstream. Even though gel is accumulating in the container, the disappearance of the interface of the gel thread indicates that the gel is actually formed on the bottom of the container rather than inside the ow cell.
Owing to small impurities in the dispersions, it is straightforward to conrm that the ow is indeed a plug ow (all impurities moving with a constant velocity) as well as to experimentally determine the core velocity V and the projected radius R 1,y . By knowing the core ow rate Q 1 , we can calculate the core radius in the viewing direction R 1,x through Q 1 = πR 1,x R 1,y V . An illustration of the procedure is included in the supplementary video.
Estimating the ion concentration distribution in ow-focusing mixing Predicting core radius and velocity In order to predict the concentration distribution without an experimental measurement of the core radius R 1,y or velocity V , these parameters can be estimated through the following procedure, which is also applied in the main manuscript for the prediction in Fig. 3.
The ow situation downstream of the focusing section in the double ow-focusing mixing cell can be estimated given three assumptions: 1. The ow with quadratic cross-section of h × h, can be approximated with a cylindrical geometry with equivalent radius R = h/ √ π. This ensures the same average velocity for a given ow rate.
2. The ow consists of a core ow with ow rate Q 1 and radius R 1 surrounded by an inner sheath ow with ow rate Q 2 and radius R 2 and outer sheath ow with ow rate Q 3 bounded by the outer walls with the equivalent radius R.
3. The ow in the core is constant, i.e. v(r ≤ R 1 ) = V . The ow outside of the core is described with a linear shear prole: Given these assumptions, the unknowns R 1 , R 2 and V can be calculated by knowing the ow rates Q 1 , Q 2 and Q 3 in two steps.
Firstly, the radius R 1 can be calculated by knowing that: and that Q 1 = V πR 2 1 , which leads to the expression: where R 1 is the only unknown and solution must full R 1 < R. With R 1 known, the velocity V is found through V = Q 1 /(πR 2 1 ).
With these parameters known, the radius R 2 is found by using: with only R 2 unknown and nding the solution in interval R 1 < R 2 < R.

Simulations of the diusion equation
Using the experimental values of V and R 1 (mean of R 1,x and R 1,y ), the time-scale analysis was performed (still keeping R 2 /h = 0.32) as described in the main manuscript. This allowed for an estimation of the Na + concentration at dierent radial positions and downstream locations, which is plotted in Fig. 4a-b. From the simulated concentration proles, three values were determined at dierent downstream positions: the centerline concentration (c CL ), the interface concentration at r = R 1 (c IF ) and the mean concentration in the core ( c ).
Compared to the simulation results in Fig. 3 in the main manuscript using the predicted values of core velocity V and radius R 1 , the values are only slightly dierent. The mean Na + concentration distribution in Fig. 6