Precursory flow in the formation of cellulose nanofiber films revealed by multiscale image analysis

Film materials made of cellulose nanofibers (CNFs), i.e., so-called nanopapers, are fabricated from aqueous dispersions of CNFs. The drying in the container causes the phase transition from sol to gel and final state of transparent film. The nonequilibrium and nonuniform nature of the drying calls for the least invasive in-process measurement to understand the process. In this paper, we focus on the transient state of nanopaper formation through the time-series image analysis from optical measurements on the multiple spatiotemporal scales and resolutions. The combination of single-particle tracking and particle image velocimetry reveals the intermittent flow with a low symmetry of space pattern in the middle stage of drying process. The small portion of CNF is sufficient for suppression of coffee-ring phenomena, and the flow is in combination with the emergence of partial structural order. Furthermore, we find that the flow pattern depends on the sidewall material of the sample container. We characterize the three stages of drying process through the flow patterns by the correlation length of velocity autocorrelation function as well as the mean and standard deviation of the flow speed in the containers.

Figure 1

Schematics and digital camera images of the sample containers with sidewalls of 1-mm height consisting of (a) polytetrafluoroethylene (PTFE) and (b) silicone, respectively. It should also be noted that the sidewall with a height of 0.1 mm from the bottom consists of a silicone sheet in both cases of (a) and (b) so that the sealing of bottom gap is satisfied.

Figure 2

Sample set up for SPT obtained by inverted optical microscope. The sidewall of the cylindrical container with a diameter of 8 mm consists of PTFE sheets. $l=4$ mm corresponds to the horizontal center in the container, whereas $l<4$ mm indicates the distance closer to the sidewall whereas keeping the same container diameter 8 mm.

Figure 3

Illumination and camera configurations employed to obtain the time-series images for PIV analysis with (a) indirect and (b) direct illumination. The reflected light from the sample surface is mainly captured by the camera in the indirect illumination, whereas the white light-emitting diode (LED) light directly transmits through the sample to reach the camera in the direct illumination.

Figure 4

The difference between indirect and direct lighting setups in terms of light intensity characteristics as a function of (a) sample volume and (b) drying time series. The light intensity is evaluated by the mean value among pixels in the sample domain. The absolute value of light intensity depends on the camera setups, which are different for indirect and direct lightings (cf. Sec. 2b2). The difference of sample volume approximately corresponds to the sample thickness due to the same container bottom area with the silicone side wall. The sidewall height (i.e., the thickness of a silicone sheet) for (a) was 5 mm to accommodate the increased sample volume.

Figure 5

Time evolution of generalized diffusion coefficient $D_{\mathrm{FB}\alpha }$ [(a)–(c)] and its scaling exponent ${\alpha }_{\mathrm{FB}}$ [(d)–(f)] at horizontal center of the container with different observation heights $h$. Dimensionless time $t^{*}$ is defined so that $t^{*}=1$ corresponds to the macroscopic drying up time.

Figure 6

Time evolution of generalized diffusion coefficient $D_{\mathrm{FB}\alpha }$ [(a)–(c)] and its scaling exponent ${\alpha }_{\mathrm{FB}}$ [(d)–(f)] for different distances $l$ from the sidewall at heights $h$ of (a) and (d) $27\mu \mathrm{m}$, (b) and (e) $533\mu \mathrm{m}$, and (c) and (f) $933\mu \mathrm{m}$, respectively. Dimensionless time $t^{*}$ is defined so that $t^{*}=1$ corresponds to the macroscopic drying up time.

Figure 7

Trajectories in single movie data of 10 s at the horizontal center ($l=4$ mm) and $h=267\mu \mathrm{m}$ corresponding to the data in Figs. 5 and 5(e). Each subfigure corresponds to a square with $166.4\mu \mathrm{m}$ on a side.

Figure 8

Velocity field maps obtained from the PIV analysis in the time series for different sidewall and lighting conditions. The sidewall conditions are schematically shown in Fig. 1. Indirect lighting and direct lighting conditions correspond to Figs. 3 and 3, respectively. Dimensionless time $t^{*}$ is defined so that $t^{*}=1$ corresponds to the macroscopic drying up time.

Figure 9

Time evolution of the mean [(a) and (b)] and standard deviation [(c) and (d)] of the velocity fields and characteristic correlation length ${\lambda }_{\mathrm{VACF}\approx 0.1}$ [(e) and (f)] for the cases with PTFE [(a), (c), and (e)] and silicone [(b), (d), and (f)] sidewalls, respectively. Indirect lighting and direct lighting conditions correspond to Figs. 3 and 3(b), respectively. Dimensionless time $t^{*}$ is defined so that $t^{*}=1$ corresponds to the macroscopic drying up time.

Figure 10

Trajectories in single movie data of 10 s at the horizontal center ($l=4$ mm) and $h=400\mu \mathrm{m}$ when (a) $t^{*}=0.55$ and (b) $t^{*}=0.51$ corresponding to the data in Figs. 5 and 5.

Figure 11

Time evolution of the air-liquid interface at $l=1$ mm in the cases of the PTFE and silicone sidewalls. The positive speed of displacement is defined as the direction corresponding to the decreasing sample height. The interface was determined at 2.5-min intervals by the focal point of observation with the inverted optical microscope. The values of speed has the limitation of time resolution by this interval. The trials of these drying experiments in this figure are independent from the rest of the measurements of other figures whereas the sample conditions including the containers are consistent with them.

Figure 12

Digital camera images of the peeling off of the nanopaper sample from the bottom wall and the corresponding velocity map at the final stage of drying ($t^{*}=0.94$). Indirect lighting and direct lighting conditions correspond to Figs. 3 and 3, respectively. Dimensionless time $t^{*}$ is defined so that $t^{*}=1$ corresponds to the macroscopic drying up time.