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. 2023 Aug 11;13:13051. doi: 10.1038/s41598-023-39854-4

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© The Author(s) 2023

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Left panel: Numerically calculated phases as a function of vertical detector angle (along $Q_{y}$ ) for a solid block using Eq. (13) and a speed of rotation of 37.5 rpm (triangles) and for a liquid sample using Eq. (19) at a cone rotation speed of 75 rpm, with a linear velocity profile, leading to the same average speed (circles). The solid line is for a liquid sample at 75 rpm using the same parameters but with a speed deviation of 20% at the shearing surfaces, simulating massive symmetric slip. Right panel: Numerically calculated amplitudes as a function of horizontal scattering angle, along $Q_{x}$ , for the same velocity distributions.