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Better understanding the properties of organic aerosols (OA) is attracting increasing attention because of the important role they play in climate change. The viscosity of OA has been shown to range from liquid to solid/semi-solid across the range of atmospheric relative humidity. A method known as the "bead-mobility technique" has been developed to quantify the viscosity of an atmospheric particle over a range of atmospherically relevant humidities. The method is based on the assumption that the strength of the flow recirculation inside a droplet placed in a shear flow is related to the droplet viscosity. This article presents a simple analytical model which predicts the internal flow in the droplet and provides a correlation relating the strength of the flow in the droplet to its viscosity. The validity of this analytical model is assessed by comparing the analytical results with a corresponding two-phase flow simulation with a moving mesh which captures the motion of the interface. The ability of the analytical model to reproduce experimental data reported in the literature is also quantified. The reasonable agreement between the analytical model and the experimental data confirms that the droplet velocity provides a useful proxy to estimate the droplet viscosity for small liquid samples for which standard viscometry techniques do not apply. Copyright (c) 2019 American Association for Aerosol Research