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Register a new userEffect of Wall Friction on 2D Hopper Flow
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We report here on experiments and simulations examining the effect of changing wall friction on the gravity-driven flow of spherical particles in a vertical hopper. In 2D experiments and simulations, we observe that the exponent of the expected power-law scaling of mass flow rate with opening size (known as Beverloos law) decreases as the coefficient of friction between particles and wall increases, whereas Beverloo scaling works as expected in 3D. In our 2D experiments, we find that wall friction plays the biggest role in a region near the outlet comparable in height to the largest opening size. However, wall friction is not the only factor determining a constant rate of flow, as we observe a near-constant mass outflow rate in the 2D simulations even when wall friction is set to zero. We show in our simulations that an increase in wall friction leaves packing fractions relatively unchanged, while average particle velocities become independent of opening size as the coefficient of friction increases. We track the spatial pattern of time-averaged particle velocities and accelerations inside the hopper. We observe that the hemisphere-like region above the opening where particles begin to accelerate is largely independent of opening size at finite wall friction. However, the magnitude of particle accelerations decreases significantly as wall friction increases, which in turn results in mean sphere velocities that no longer scale with opening size, consistent with our observations of mass flow rate scaling. The case of zero wall friction is anomalous, in that most of the acceleration takes place near the outlet.
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Large-scale three dimensional molecular dynamics simulations of hopper flow are presented. The flow rate of the system is controlled by the width of the aperture at the bottom. As the steady-state flow rate is reduced, the force distribution $P(f)$ changes only slightly, while there is a large change in the impulse distribution $P(i)$. In both cases, the distributions show an increase in small forces or impulses as the systems approach jamming, the opposite of that seen in previous Lennard-Jones simulations. This occurs dynamically as well for a hopper that transitions from a flowing to a jammed state over time. The final jammed $P(f)$ is quite distinct from a poured packing $P(f)$ in the same geometry. The change in $P(i)$ is a much stronger indicator of the approach to jamming. The formation of a peak or plateau in $P(f)$ at the average force is not a general feature of the approach to jamming.
We experimentally investigate the response to perturbations of circular symmetry for dense granular flow inside a three-dimensional right-conical hopper. These experiments consist of particle tracking velocimetry for the flow at the outer boundary of the hopper. We are able to test commonly used constitutive relations and observe granular flow phenomena that we can model numerically. Unperturbed conical hopper flow has been described as a radial velocity field with no azimuthal component. Guided by numerical models based upon continuum descriptions, we find experimental evidence for secondary, azimuthal circulation in response to perturbation of the symmetry with respect to gravity by tilting. For small perturbations we can discriminate between constitutive relations, based upon the agreement between the numerical predictions they produce and our experimental results. We find that the secondary circulation can be suppressed as wall friction is varied, also in agreement with numerical predictions. For large tilt angles we observe the abrupt onset of circulation for parameters where circulation was previously suppressed. Finally, we observe that for large tilt angles the fluctuations in velocity grow, independent of the onset of circulation.
We present particulate simulation results for translational and rotational friction components of a shish-kebab model of a colloidal rod with aspect ratio (length over diameter) $L/D = 10$ in the presence of a planar hard wall. Hydrodynamic interactions between rod and wall cause an overall enhancement of the friction tensor components. We find that the friction enhancements to reasonable approximation scale inversely linear with the closest distance $d$ between the rod surface and the wall, for $d$ in the range between $D/8$ and $L$. The dependence of the wall-induced friction on the angle $theta$ between the long axis of the rod and the normal to the wall is studied and fitted with simple polynomials in $cos theta$.
We study the response to shear deformations of packings of long spherocylindrical particles that interact via frictional forces with friction coefficient $mu$. The packings are produced and deformed with the help of molecular dynamics simulations combined with minimization techniques performed on a GPU. We calculate the linear shear modulus $g_infty$, which is orders of magnitude larger than the modulus $g_0$ in the corresponding frictionless system. The motion of the particles responsible for these large frictional forces is governed by and increases with the length $ell$ of the spherocylinders. One consequence of this motion is that the shear modulus $g_infty$ approaches a finite value in the limit $elltoinfty$, even though the density of the packings vanishes, $rhoproptoell^{-2}$. By way of contrast, the frictionless modulus decreases to zero, $g_0simell^{-2}$, in accordance with the behavior of density. Increasing the strain beyond a value $gamma_csim mu$, the packing undergoes a shear-thinning transition from the large frictional to the smaller frictionless modulus when contacts saturate at the Coulomb inequality and start to slide. In this regime, sliding friction contributes a yield stress $sigma_y=g_inftygamma_c$ and the stress behaves as $sigma=sigma_y+g_0gamma$. The interplay between static and sliding friction gives rise to hysteresis in oscillatory shear simulations.
A comprehensive study of the effect of wall heating or cooling on the linear, transient and secondary growth of instability in channel flow is conducted. The effect of viscosity stratification, heat diffusivity and of buoyancy are estimated separately, with some unexpected results. From linear stability results, it has been accepted that heat diffusivity does not affect stability. However, we show that realistic Prandtl numbers cause a transient growth of disturbances that is an order of magnitude higher than at zero Prandtl number. Buoyancy, even at fairly low levels, gives rise to high levels of subcritical energy growth. Unusually for transient growth, both of these are spanwise-independent and not in the form of streamwise vortices. At moderate Grashof numbers, exponential growth dominates, with distinct Rayleigh-Benard and Poiseuille modes for Grashof numbers upto $sim 25000$, which merge thereafter. Wall heating has a converse effect on the secondary instability compared to the primary, destabilising significantly when viscosity decreases towards the wall. It is hoped that the work will motivate experimental and numerical efforts to understand the role of wall heating in the control of channel and pipe flows.
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