Cooperativity and segregation in confined flows of soft binary glasses

When a suspension containing particles of different sizes flows through a confined geometry a size gradient can be established, with large particles accumulating in the channel center. Such size separation driven by hydrodynamic interactions is expected to facilitate membrane filtration and may lead to the design of novel and innovative separation techniques. For this, a wide range of particle concentrations has to be investigated, in order to clarify whether shear-induced migration can be utilized at concentrations close to or above the colloidal glass transition, where particle motion is severely hindered and hydrodynamic interactions are screened. We explore this scenario by studying the flow of binary mixtures of soft colloidal microgels, well above their liquid-solid transition, through narrow microchannels. We find that, even though the flow becomes strongly heterogeneous, in both space and time, characterized by a large cooperativity length, size segregation still occurs. This suggests that even above the glass transition shear-induced diffusion could still be used as a fractionation mechanism, which is of great relevance for process intensification purposes.

Figure 1

Illustration of the experimental system indicating the dimensions of the core-shell microgel particles and microfluidic channels.

Figure 2

(a) Storage (filled symbols) and loss moduli (open symbols) as a function of the angular frequency for a typical sample above ${\varphi }_c$ ($\varphi -{\varphi }_c=0.336$). (b) Storage modulus, at fixed $\omega =10$ rad/s, versus $\varphi -{\varphi }_c$. The solid line is a power-law fit with characteristic exponent $a=2.5$. (c) Flow curves for various volume fractions; the legend indicates concentrations of measured suspensions relative to ${\varphi }_c$, (d) Master curve of flow curves collapsing onto two distinct branches, above and below ${\varphi }_c$. Solid lines are fits as described in the text.

Figure 3

Velocity profiles (a) for $\mathrm{\Delta }\varphi =0.317$ at $\mathrm{\Delta }P=$ 0.05, 0.1, and 0.15 bar (circles, triangles, and squares, respectively and (b) for $\mathrm{\Delta }\varphi =0.158$ at 0.1, 0.3, 0.5, and 0.7 bar [circles, squares, triangles, and diamonds, respectively). (c) Slip velocity as a function of $\mathrm{\Delta }P$ for $\mathrm{\Delta }\varphi =0.158$(squares) and $\mathrm{\Delta }\varphi =0.317$ (circles).

Figure 4

Velocity in the center of the channel $V_x$, normalized by the time-average velocity $\langle V_x\rangle$, as a function of time for $\mathrm{\Delta }\varphi =0.158$ at $\mathrm{\Delta }P=$ 0.1 bar (a) and for $\mathrm{\Delta }\varphi =0.317$ at $\mathrm{\Delta }P=$ 0.05 bar (b) and at $\mathrm{\Delta }=0.1$ bar (c).

Figure 5

Spatially resolved flow field for $\mathrm{\Delta }\varphi =0.317$ at $\mathrm{\Delta }P=$ 0.05. (a) Full velocity field; (b) corresponding nonaffine velocity, in which the affine flow field, obtained from the time average, is subtracted. Flow is from left to right; the total size of the field of view is $\approx 50\times 50\mu m$, with a voxel size for the PIV analysis of 1.08 $\mu {\mathrm{m}}^2$.

Figure 6

Probability distributions of cooperative cluster sizes (in $\mu {\mathrm{m}}^2$) for (a) $\mathrm{\Delta }\varphi =0.317$ at $\mathrm{\Delta }P=$ 0.05, 0.1, and 0.15 bar and for (b) $\mathrm{\Delta }\varphi =0.158$ at $\mathrm{\Delta }P=$ 0.1, 0.3, 0.5, and 0.7 bar. Solid lines represent fits to a power-law distribution with an exponential cutoff. (c) Mean cluster size and (d) maximum cluster size (in $\mu {\mathrm{m}}^2$) as a function of the pressure for $\varphi =0.317$ (circles) and $\varphi =0.158$ (squares). Dotted lines are a guide for the eye.

Figure 7

Normalized fluorescence intensity profiles for $\mathrm{\Delta }\varphi =0.317$ at $\mathrm{\Delta }P=$ 0.7 for three positions in the channel, at (a) 1 cm, (b) 2 cm, and (c) 3 cm from the channel entrance and for three pressures at 2 cm with (d) $\mathrm{\Delta }P=0.05$ bar, (e) $\mathrm{\Delta }P=0.5$ bar, and (f) $\mathrm{\Delta }P=0.8$ bar as a function of the channel width. Light-gray (green) and dark-gray (red) lines show the measured fluorescence intensity, which is proportional to the local concentration, of the large and small microgel colloids, respectively.