Experimental collisions of varying roughness wetted particles in the pendular regime compared to numerical simulations

In this work rectilinear collisions of spheres coated in a thin viscous liquid film are considered, where the surface roughness of the spheres was varied. Experiments were performed using a Newton's cradle apparatus and the collision dynamics was measured using particle tracking velocimetry. The experiments showed that the dry and wet coefficient of restitution decreases as the roughness increases. Experimental collisions are compared with numerical simulations to examine criteria that limit the viscous force. We show that a model in which the liquid undergoes a glass transition is in excellent agreement with experimental measurements for smooth spheres, i.e., when the roughness of the spheres is less than the glass transition length. For rough particles, a constant minimum separation distance is more accurate than the glass transition model, which is consistent with the idea that contact occurs on the roughness elements. Furthermore, smoothed particle hydrodynamics (SPH) simulations were used to examine the viscous flow in detail. The SPH simulations accurately predicted the collision outcome for smooth spheres and showed that the maximum pressure was greater than the glass transition pressure used for the discrete element method simulations, supporting the feasibility of the glass transition model. The SPH simulations of rough particles indicate that during a collision the interstitial liquid flows through microchannels between roughness elements as a mechanism to alleviate pressure buildup, and reduce the viscous force consistent with the experimental observations.

Figure 1

Schematic of a collinear collision between dry striking particle $i$ and wetted stationary particle $j$.

Figure 2

Schematic of the Newton's cradle setup.

Figure 3

The glass transition pressure associated length scale as a function of St for chrome steel spheres ($\_\_\_\_$) and alumina spheres ($\_\_\_\_$). The chrome steel case uses $\mu =3$ Pa s while the alumina case uses $\mu =1$ Pa s, as these viscosities correspond to the viscosity used in the collision experiments. The maximum velocities correspond to a value of $\text{St}=20$, as that is the maximum achievable experimentally. The glass transition pressure corresponds to $P_{\text{gt}}=4\times {10}^8$ Pa.

Figure 4

Volume percent of the microspheres and powders applied to the spheres. The median diameters for the microspheres are $28.6\mu \mathrm{m}$ ($\_\_\_\_$) and $65.6\mu \mathrm{m}$ ($\_\_\_\_$), while the median diameters for the powders are $87\mu \mathrm{m}$ ($\_\_\_\_$) and $114\mu \mathrm{m}$ ($\_\_\_\_$).

Figure 5

SEM images via backscatter electron detection for stainless steel (left) and alumina particles (right). (a), (b) The smooth spheres ($R_a<1$ µm) for this study, while (c)–(f) are the rough sphere surfaces. The roughness for the rough cases are (c) 14 µm, (d) 32.5 µm, (e) 44 µm, and (f) 57 µm.

Figure 6

Example snapshot of an alumina smooth particle coated in 1 Pa s silicone oil. The dripping process is exclusively gravity driven.

Figure 7

Oil film thickness over time for (a) stainless steel and (b) alumina particles. The markers correspond to different roughness particles: smooth ($♦$), sandblasted ($\blacksquare$), 14 µm ($•$), 32.5 µm ($▴$), 44 µm ($•$), and 57 µm ($▴$).

Figure 8

Snapshot depicting the different domains during an SPH simulation of a smooth dry sphere striking a wetted sphere.

Figure 9

Snapshot depicting the roughness elements and liquid for a rough SPH simulation: (a) side view with the roughness spheres colored red for an increased contrast, without the fluid displayed, (b) frontal view onto one of the spheres, and (c) view onto the fluid phase, cut in the collision plane, colored blue.

Figure 10

A comparison of $e_{\text{dry}}$ for a range of velocities for (a) stainless steel spheres, (b) chrome steel spheres, and (c) alumina spheres. The mean $e_{\text{dry}}$ of all the data points for a given roughness and material is given in (d) with the error bars corresponding to the standard deviation for the data set. For a given material in (d), the roughness increases from left to right. The roughnesses considered correspond to $<1$ µm ($♦$), 10 µm ($\blacksquare$) 14 µm ($•$), 32.5 µm ($▴$), 44 µm ($•$), and 57 µm($▴$).

Figure 11

Stokes number St versus the wet coefficient of restitution $e$ for a two-body collision of (a) stainless steel, (b) chrome steel, (c) alumina, and (d) sandblasted stainless steel spheres. The markers correspond to roughnesses of $<1$ µm ($♦$), 10 µm ($•$), 14 µm ($\blacksquare$), 32.5 µm ($▴$), 45 µm ($•$), and 57 µm ($▴$). The SS and CS collisions are conducted using 3 Pa s silicone oil with $h_{ij,0}=168$ µm for the smooth collisions, $h_{ij,0}=200$ µm for the 14-µm roughness collisions, and $h_{ij,0}=220$ µm for the 32.5-µm roughness collisions. The alumina collisions are conducted using 1 Pa s silicone oil with $h_{ij,0}=100$ µm. Chosen experiments at high St have error bars shown to provide an indication of the error in the measurements; the error bars have been removed from the other points for clarity.

Figure 12

Comparison of DEM viscous force model to experiments for collisions of two wetted stainless steel spheres (a), (b) chrome steel spheres (c), (d), and alumina spheres (e), (f). Experiments are given by markers and simulations by lines. The data for the metal spheres correspond to smooth spheres ($♦$)($\_\_\_\_$), 14-µm roughness spheres ($•$)($\_\_\_\_$), and 32.5-µm roughness spheres ($▴$)($\_\_\_\_$). The data for the alumina spheres correspond to smooth spheres ($♦$)($\_\_\_\_$), 44-µm roughness spheres ($•$)($\_\_\_\_$), and 57-µm roughness spheres ($▴$)($\_\_\_\_$). The left figures (a), (c), (e) use a minimum separation distance which is derived from the glass transition pressure [Eq. (7)], while the right figures (b), (d), (f) use a minimum separation distance which is constant.

Figure 13

The effect of SPH particle size and $C_0$ on the coefficient of restitution $e$ for a smooth sphere wet particle collision.

Figure 14

Pressure distribution for a collision of smooth wetted spheres at $v_{ij,0}=0.205\mathrm{m}{\mathrm{s}}^{-1}$, artificial speed of sound $C_0=600v_{ij,0}$, and SPH particle sizes of $\mathrm{\Delta }=30$ µm (top) and $\mathrm{\Delta }=15$ µm (bottom). Collision progresses from left to right, and the same time points are presented for both simulations. The SPH boundary particles are colored gray, while the DEM spheres are not shown for clarity.

Figure 15

The effect of SPH particle size on the coefficient of restitution $e$ for a 32.5-µm roughness sphere wet particle collision. The initial conditions are $v_{ij,0}=0.288 \mathrm{m}{\mathrm{s}}^{-1}, h_{ij,0}=220$ µm, and $e_{\text{dry}}=0.66$.

Figure 16

Pressure distribution for a collision of 32.5-µm roughness wetted spheres at $v_{ij,0}=0.288\mathrm{m}{\mathrm{s}}^{-1}$, artificial speed of sound $C_0=600v_{ij,0}$, and SPH particle sizes of $\mathrm{\Delta }=15$ µm. Collision progresses from left to right. The SPH boundary particles are colored gray, while the DEM spheres are not shown for clarity. Left: the pressure evolution at the start of the contact on the initial contact of dry sphere onto the wetted sphere is shown. Middle: the pressure gradient between the two spheres, and from the contact zone to the outer region at a later time point before the solid contact occurs, can be seen. Right: the pressure gradient during the solid contact point of the surface roughness, which are visualized here for clarity in contrast to the other images.