Dynamics of the Solid and Liquid Phases in Dilute Sheared Brownian Suspensions: Irreversibility and Particle Migration

Magnetic resonance measurements of migration and irreversible dynamics in the capillary shear flow of a Brownian suspension are presented. The results demonstrate the presence of phenomena typically associated with concentrated noncolloidal systems and indicate the role of many body hydrodynamics in dilute Brownian suspension transport. The application of concepts from chaos theory and nonequilibrium statistical mechanics is demonstrated.

Figure 1

Composite axial velocity for $\varphi =0.08$ suspension flow in 1 mm capillary, average velocity of $0.88\mathrm{mm}/\mathrm{s}$ (${\mathrm{Re}}_{\mathrm{tube}}=0.88$, ${\mathrm{Re}}_p=5.7$). (a) Image of spatial distribution of velocity in plane perpendicular to flow, $14\times 14\mu \mathrm{m}$ resolution. (b) Velocity as function of radius across various diameters (symbols) and the parabolic velocity profile $V_z(r)=V_{\max }(1-r^2/R^2)$ for Poiseuille flow (black line).

Figure 2

(a) Propagators for water (black line) and $\varphi =0.08$ suspension (blue closed squares suspending water, red open triangles core oil particles) flowing at $V_{\mathrm{ave}}=0.88\mathrm{mm}/\mathrm{s}$ (${\mathrm{Re}}_p=5.7$, ${\mathrm{Pe}}_p=39$) over an observation time $\Delta =30\mathrm{ms}$. The order of magnitude differences in $D_w$ and $D_{\mathrm{SE}}$ gives the particle propagator sharper edges. (b) Corresponding residence time distributions.

Figure 3

Effective diffusion $D_{\mathrm{eff}}{}^{*}$ as a function of average shear rate $⟨\dot{\gamma }⟩=-\frac{4⟨v_z⟩}{3R}\propto \mathrm{Pe}$, during flow of $\varphi =0.08$ suspension for the suspending water $D_{zz,f}^{*}$ (blue closed squares) and particles $D_{zz,s}^{*}$ (red open triangles), as well as pure water flow $D_{zz}^{*}$ (blue open squares) measured using single PGSE (inset) which is sensitive to the distribution of reversible velocities, for displacement time $\Delta =100\mathrm{ms}$.

Figure 4

$D_{\mathrm{eff}}{}^{*}$ $\varphi =0.08$ suspension obtained using flow compensated PGSE sequence (inset in (a)), which measures only irreversible stochastic motions. (a) For an average velocity of $0.88\mathrm{mm}/\mathrm{s}$ (${\mathrm{Re}}_p=5.7$, ${\mathrm{Pe}}_p=39$) $D_{\mathrm{eff}}{}^{*}$ for the particle core oil as a function of observation time $\Delta$ in the flow direction $z$, $D_{zz,s}^{*}$ (black closed circles), in the velocity gradient direction $y$, $D_{yy,s}^{*}$ (green closed triangles), and in the absence of flow in the $z$, $D_{zz,s}^{*}$ (black open circles) and $y$, $D_{yy,s}^{*}$ (green open triangles) directions. (b) $D_{\mathrm{eff}}{}^{*}$ normalized by the average shear rate $⟨\dot{\gamma }⟩$ and the square of the particle diameter $4a^2$ as a function of accumulated strain $\gamma =⟨\dot{\gamma }⟩\Delta$.