Dynamics of particle lane formation in confined viscoelastic fluids under shear

Abstract

Simple shear flow can induce flow-aligned chain formation of particles suspended in viscoelastic fluids. Although this phenomenon has been reported for decades, direct {\it in situ} measurements of the alignment dynamics and particle trajectories during chain formation remain limited. Here, we develop an {\it in situ} observation platform based on parallel rotating disks separated by a gap comparable to the particle diameter, enabling simultaneous observation of particle alignment under radially varying shear rates. The narrow gap strongly confines particle motion, thereby enhancing hydrodynamic interactions and collision events between particles. Using a viscoelastic fluid embedding zircon particles as the sample, we find that alignment occurs once the local particle Weissenberg number exceeds unity (Wi$_\mathrm{p} \geq 1$), defined using an effective shear rate based on the wall velocity and the available gap width. Particle tracking further reveals a back-and-forth shuttling motion that accompanies the alignment process. Using the image brightness in a colored fluid as a proxy for out-of-plane position, we show that the shuttling originates from vertical displacement of the particles. We further construct a minimal agent-based model in which the vertical particle position follows a Ginzburg-Landau-type double-well potential, and demonstrate that collision-driven accumulation emerges in numerical simulations. In the strongly confined geometry, alignment occurs by an effective attraction due to collision, which is reminiscent of motility-induced clustering often observed in active matter.

Figures (8)

• Figure 1: (a) Schematic illustration of the sample: oil-in-water microemulsions bridged by telechelic polymers. (b) Schematic illustration of the experimental setup, showing the parallel-plate configuration with a rotating bottom disk and optical access for in situ observation. (c,d) Definition of the observation geometry and coordinate systems. (c) Top view of the bottom disk, defining the radial ($\rho$) and azimuthal ($\theta$) directions. (d) Cross-sectional view around a particle confined between the plates, defining the height ($z$) direction and the effective gap $h-2R$. (e) Storage and loss moduli, $G'$ and $G"$, obtained from small-amplitude oscillatory shear. (f) Steady shear stress, $\sigma$, and the first normal stress difference, $N_1$, as functions of shear rate $\dot{\gamma}$.
• Figure 2: Snapshots of the particle suspension at three angular velocities, shown at four values of the accumulated rotation angle $\Theta=\Omega t$ ($0,\,2\pi,\,4\pi,$ and $10\pi$). (a) $\Omega=\pi/60$ rads; (b) $\Omega=\pi/15$ rads; (c) $\Omega=2\pi/15$ rads. The red dashed circle indicates the critical radius $\rho_c$ at which the local Weissenberg number near a particle satisfies $\mathrm{Wi_p}=1$, where $\rho_c=(h-2R)/(\lambda\Omega)$. Lane formation is observed in regions where $\mathrm{Wi_p}>1$. Scale bar: 20mm.
• Figure 3: Autocorrelation analysis of particle positions in a reference frame centered on a particle and aligned with its instantaneous velocity. (a--c) Schematic illustration of the coordinate transformation used to fix the direction of motion of a reference particle. Particle positions are expressed in a frame rotated such that the velocity of the reference particle defines the $\Delta_\parallel$ direction. (d,e) Spatial autocorrelation function of particle positions, $P(\Delta_\parallel,\Delta_\perp)$, obtained at $\Omega=\pi/60$ rads (d) and $\Omega=2\pi/15$ rads (e). The horizontal and vertical axes correspond to the directions parallel ($\Delta_\parallel$) and perpendicular ($\Delta_\perp$) to the particle motion, respectively. (f) Cross sections of $P(\Delta_\parallel,\Delta_\perp)$ at $\Delta_\perp=0$, corresponding to panels (d) blue dashed line and (e) orange solid line.
• Figure 4: Coordinate transformation to a shifted reference frame used to extract the imposed simple shear flow.
• Figure 5: Time evolution of individual particle positions in the shifted frame. (a, b) Radial positions $\rho_i(t)$ and (c, d) azimuthal positions $\theta_i^*(t)$ for particles initially located at $\rho_i=40$–$45$ mm. Shuttling motion is observed only for $\mathrm{Wi_p}>1$. (e, f) Probability density function $p(v_i^{\theta^*})$ of the azimuthal particle velocity $v_i^{\theta^*}$, evaluated for the same set of particles as in panels (a–d). Here, $\omega_i^*=\omega_i-\Omega/2$ and $v_i^{\theta^*}=\rho_i\omega_i^*$. The distributions are normalized such that $\int p(v_i^{\theta^*})\,dv_i^{\theta^*}=1$. Data are taken over the interval $\Theta=0$ to $2\pi$. Panels (a, c, e) correspond to $\mathrm{Wi_p}>1$ ($\Omega=2\pi/15$ rads), while panels (b, d, f) correspond to $\mathrm{Wi_p}<1$ ($\Omega=\pi/60$ rads).