Angle of Repose

    “Angle of repose” is one of the commonly used physical properties to indicate the flowability of powders. The angle of repose refers to the angle formed between the natural slope of a pile of powder that has settled quietly on a horizontal surface and the horizontal plane.
    When the powder is fine and flows easily, the formed pile has a gentle slope, resulting in a lower angle of repose. Conversely, if the powder is sticky and does not flow easily, the formed pile will have a steeper slope, leading to a higher angle of repose.
    In this way, the angle of repose can be used as an indicator of the ease of flow of powders.

    Measurement Methods for the Angle of Repose

    Angle of repose is often measured using methods involving a funnel and a receiver dish, such as the funnel method. Other measurement methods include internal funnel method and revolving cylinder method. As the angle of repose can vary based on the measurement environment, it’s important to manage the measurement conditions alongside the measured values. For example, in high humidity conditions, powders tend to adhere to each other, resulting in a higher angle of repose.
    • Funnel Method
    In this method, a receiver dish is placed a certain distance below a funnel. The sample is poured into the funnel and allowed to settle onto the receiver dish at a steady rate. The angle of repose is measured when the deposited powder forms a stable pile with a certain height.
    • Internal Funnel Method
    In this method, a small hole is made in the bottom of a container filled with the sample, allowing the sample to be discharged from the container. After the sample has been fully discharged, the angle of repose is measured from the slope formed by the remaining powder in the container.
    • Revolving Cylinder Method
    In this method, the sample is filled into a cylindrical container, and the container is gradually tilted. The angle of repose is measured based on the slope formed by the powder within the container as it revolves.
    While the angle of repose is a commonly used indicator due to its relatively simple measurement, it’s important to note that real-life settled powders often do not form neat slopes. To define the angle of repose even when the slope is not well-defined, the angle is determined indirectly from the coordinates of the powder at specific positions. For example, in the funnel method, the angle of repose is calculated from the endpoints and the peak on the bottom surface.