Patterns of convective flow in a vertically vibrated granular bed

• Several kinds of convection roll in a vibrated granular bed are introduced by Γ–fΓ–f phase diagram.
• The phase diagram of convection rolls can be divided into four regions.
• The vibration frequency plays a significant role on the number and direction of the rolls.
• The grains at different positions collide with the vessel bottom un-synchronously.

When submitted to vertical vibrations for frequencies from 15 to 150 Hz, granular materials show several convective patterns, as symmetric, asymmetric, one single, one pair and multi-pairs of convection rolls. The vibration frequency (f) plays a significant role in the number of rolls and their flow directions, while the vibration acceleration (Γ  ) mainly affects the size of roll and strength of flow. The Γ–fΓ–f phase diagram is presented and divided into the global, local, unstable and non-convection regions. Slope of the granular surface decreases with increase of Γ, and the grains at different positions collide with the bottom un-synchronously.