(231f) Accumulation of Particles at an Advancing Meniscus: Viscous Miscible Fingering in the Converging Parallel Plate Geometry

            When two parallel circular plates with a known volume of a pure viscous fluid placed in between them approach each other, the radius of the propagating fluid front R increases such that R⁸ is linear in time t in the lubrication limit, neglecting the effects of surface tension.  However, when the experiment is repeated with a suspension of rigid particles instead of the pure viscous fluid, the behavior deviates from the R⁸ v/s t relationship after following it for a short period of time (figure 1).  This deviation from the R⁸ v/s t relationship is followed by appearance of fingers at the propagating suspension interface (figure 2).    In this paper, we characterize the meniscus fingering phenomenon for suspension flow in the converging parallel plate geometry on the basis of the shear induced migration phenomenon.  We will also demonstrate the instability during the course of the oral presentation.

Figure 1.  A plot of the radius of the propagating fluid front R raised to the eighth power with time t for a 40% suspension of 100 micron glass spheres in glycerin.  The radius of the front at the beginning of the experiment (R₀) is 5.4 cm, while the induction radius R_c is 8.3 cm.

Figure 2.  An image of the suspension/air interface rendered unstable by viscous miscible fingering.  A 40% suspension of 100 micron glass spheres in glycerin was used in the experiment.  

It is well known that when a suspension of particles is drawn through simple geometries such as tubes and rectangular slots, the suspended particles accumulate behind the advancing meniscus.  The phenomenon of shear induced migration causes the particles in the high-shear stress regions near the wall to migrate to the low-shear stress regions near the center of the geometry.  Since the fluid streamlines at the center have higher velocities than the fluid streamlines near the walls, there is a net convection of particles towards the meniscus, resulting in the packing of particles at the meniscus.  The accumulation phenomenon thus causes a concentration gradient, and therefore a sharp viscosity gradient to be set up at the meniscus, due to the highly non linear relationship of viscosity with concentration.  A tube, which has a single length scale in its cross section, is stable to viscous miscible fingering caused by such viscosity gradients and simply displays a continuously growing packed layer of particles at the meniscus after the induction length is achieved.  However, geometries like the rectangular slot and converging parallel plates, which have more than one length scale in their cross section, are susceptible to the viscous miscible fingering phenomenon.  The induction radius R_c in the converging parallel plate geometry for onset of the instability can be shown to scale as V₀^3/7 /a^2/7, where V₀ is the volume of the suspension charged into the geometry before the experiment and a is the particle radius.  Experiments were performed to verify the induction length scaling and the wavelength of the instability, and the effect of suspension concentration on the variables was also examined.