Geometric control of powder jet dynamics and energy dissipation

Abstract: Applying an impulsive force to a powder layer shaped with a concave surface generates a sharp powder jet. This phenomenon has been proposed as a method for evaluating the flowability of powders from small amount of samples. In this study, we systematically varied the radius of the initial concave shape as a controllable parameter and quantitatively examined the resulting jet dynamics, focusing on ejection velocity and maximum height. Our high-speed observations revealed that increasing the concave radius led to broader jets with significantly reduced velocity and maximum height. These dynamic quantities followed a scaling relation with drop height, while the scaling coefficient decreased with the concave radius, indicating that the surface geometry directly governs the extent of energy dissipation. Furthermore, a minimal mechanical model incorporating the sliding distance and velocity squared type dissipation of the powder flow reproduces the observed linear dependence of the jet height on the concave radius. These findings establish powder jets as a sensitive probe of dissipation in dynamic powder flow and provide a quantitative framework for comparing powder specific interactions such as humidity, particle size and particle shape.

• The paper demonstrates that increasing the concave radius systematically produces broader, slower jets with a near-linear jet height scaling (R² > 0.994).
• Utilizing high-speed imaging, the study quantifies jet velocity, maximum height, and energy dissipation, revealing that V₍jet₎² scales linearly with drop height H.
• The research establishes a predictive velocity-squared dissipation model, proposing a novel, small-scale diagnostic approach for assessing granular flowability.

Geometric Modulation of Powder Jet Dynamics and Dissipation

Introduction

The study "Geometric control of powder jet dynamics and energy dissipation" (2604.10709) systematically investigates the impact of surface geometry on impulsively-driven powder jets, with a particular focus on energy dissipation mechanisms during pre-jet flow. Conventional powder flowability measurement techniques often suffer from boundary effects and require substantial sample volumes. This paper proposes and explores powder jetting, induced by impulsive impact on a concave-shaped powder layer, as a sensitive, small-scale probe for granular flowability and interparticle interactions.

Experimental Framework

Experiments utilize borosilicate glass tubes filled with monodisperse glass beads (45 μm diameter, 2.5 g/cm³ density, $\phi$ ≈ 0.55) to ensure minimized shape dispersion effects. Concave surfaces of varying radii ($r$ = 5–12 mm, with depth $h = r$) are molded onto the powder layer, enabling geometric control over the sliding distance and thus the dissipation prior to jet ejection. The system is humidity- and temperature-equilibrated to suppress environmental variability. Upon vertical drop (10–110 mm), impact events are captured via high-speed imaging to quantify jet velocity, maximum height, and diameter.

Observed Jet Dynamics and Scaling Behavior

High-speed observations reveal a decisive geometric effect; increasing the concave radius monotonically produces broader, but slower, jets with reduced maximum height. Specifically, the maximum jet reach $L_{\text{max}}$ displays a strong, near-linear dependence on $r$, following $L_{\text{max}} = 0.107 - 3.23 r$ (with coefficient of determination $R^2 > 0.994$), indicating that larger radii intrinsically promote energy dissipation during the particle sliding phase preceding jet formation.

Kinematic analyses show that the squared jet velocity $V_{\text{jet}}^2$ is proportional to the drop height $H$ for all radii—$V_{\text{jet}}^2 \propto H$—implying that the kinetic energy transferred to the jet tip scales linearly with the initial gravitational potential energy. The scaling coefficient $r$0 in $r$1 decreases linearly with increasing $r$2 ($r$3), establishing that surface geometry directly moderates momentum transfer efficiency and dissipation characteristics.

Dissipation Modeling and Mechanistic Insights

A minimal mechanical model interprets the pre-jet flow as a sliding layer subject to velocity-squared, inertial-type dissipation:

$r$4

The derived energy balance connects jet velocity, dissipation, and geometry:

$r$5

Experimental results strongly support $r$6 for dissipation scaling, placing this system's dynamics within the context of Bagnold-type, $r$7, and Voellmy formulations, and reinforcing the dominance of inertial and collisional interactions in dense granular flow regimes.

Notably, the validity of the linear dependence on $r$8 is constrained to regimes where avalanche-like sliding and inertia-dominated flow are present. For excessively large $r$9 or low impact energies, deviations from velocity-squared dissipation behavior are expected, possibly breaking the scaling and geometric control.

Implications and Prospects

This investigation establishes that powder jets, shaped by concave geometry, are highly sensitive probes of dissipation in dynamic granular flows. The geometric-control principle offers a quantitative route to evaluate powder flowability, humidity effects, particle size, and shape interactions. The findings propose a paradigm shift from bulk-oriented powder rheometry methods towards portable, small-volume flowability diagnostics based on jet dynamics.

On a theoretical level, the framework rebuts the adequacy of simple Coulomb friction models in these regimes and gives credence to energy-based dissipation constructs for inertial particulate flows. The generalized model is likely extensible to avalanche-prone particulate and soft-matter systems, given appropriate consideration to material-dependent dissipation exponents.

Future work could elaborate the universality of the velocity-squared dissipation scaling across other particulate systems, investigate nonlinear deviations for extreme geometries, and explore deeper mechanistic coupling between geometric features, interparticle cohesion, and environmental factors (e.g., humidity-driven capillary effects). The methodology paves the way for advanced, high-throughput screening of powder properties in industrial and geophysical contexts.

Conclusion

Geometric modulation of concave powder surfaces provides direct, tunable control over jet dynamics and energy dissipation during impulsive loading. Larger radii systematically increase dissipation, resulting in wider, shorter, and slower jets, with jet velocity and maximum height following robust scaling relations. The proposed velocity-squared dissipation framework quantitatively captures these effects and enables predictive modeling of granular flow phenomena. The research advances both practical diagnostic approaches for powder flowability and theoretical understanding of dissipation in inertia-dominated granular flows.