NOTE A Model for Detachment of a Partially Wetting Drop from a Solid Surface by Shear Flow drop detachment is the ability of a liquid drop to deform while it remains attached to a solid substrate under the influence of an external force. In the Liquid drop detachment from a solid surface by simple shear present investigation, the external force originates due to the presence of a flow is modeled based on the experimental observations available simple shear flow. The deformation of a liquid drop on an inclined plate in the literature. A liquid drop adhered to a solid surface deforms under the influence of gravity was studied by Dussan and Chow (9). On in the presence of a simple shear flow to form an advancing and the other hand, the deformation and movement of a liquid drop on a horia receding dynamic contact angle. The drop slides on the solid zontal solid surface in the presence of a centrifugal force was investigated surface when the drag due to the shearing fluid overcomes the by Extrand and Gent (10). A simple model for the detachment of a partially retentive force due to the contact angle hysteresis. A drop having wetting drop from a solid surface in an external shear flow is presented in an equilibrium contact angle, u e , approaching 180ะ detaches from this study. The model prediction for the liquid drop detachment is compared the solid surface at the onset of its sliding motion. However, a with the experimental results of Mahe ยดet al. (6-8). drop with u e much lower than 180ะ slides on the solid surface and will not detach. With further increase in the shear rate, the sliding MODEL drop detaches from the solid surface when the lift force equals the adhesive, gravitational, and buoyancy forces of the drop. Based
According to Hubbe (1), a solid particle attached to a solid surface has on this premise, an approximate mathematical model for the dethree modes of incipient motion in a steady shear field. These motions are tachment of a partially wetting drop is constructed. The experisliding, rolling, and lifting. Hubbe (1) showed through a theoretical analysis mental results available in the literature for Pristane and Squalane that the critical shear rate for detachment is proportional to a n p , where a p drop detachment are compared for slide and lift as the mode of is the radius of the solid spherical particle and the value of n is 01, 03/2, and 04/3 for sliding, rolling, and lifting, respectively. The value of
detachment. The critical shear rate for the detachment of Pristane
n is determined experimentally to identify the mode of the detachment drops, having u e of 175ะ, is predicted well by the model where process. sliding as the mode of detachment is assumed, whereas the Similarly, a liquid drop attached to a solid surface can have sliding, experimental data for Squalane drops, having u e of 126ะ, is well rolling, and lifting motion in the presence of a simple shear flow. A nonwetpredicted by the model where lift is considered the mode of detachting drop on a solid surface would rotate and translate in a shear field ment. แญง 1997 Academic Press whereas a partially wetting drop would slide on the solid surface under the Key Words: partially wetting drop; steady shear flow; advancing same conditions. The rolling and sliding motion of a nonwetting and par- and receding dynamic contact angles; contact angle hysteresis; tially wetting drop is illustrated in Fig. 1. The wettability of a drop on the sliding drop; lift force; adhesive force; drop detachment. solid surface is determined by the equilibrium contact angle, u e . Mahe ยดet al. (6-8) observed that a Pristane drop (a ramified alkane, C 19 H 40 ) having an equilibrium contact angle (measured from inside the drop) of 175ะ on a glass surface detached from the initial contact point when a critical shear rate was achieved. The Pristane drop was found to detach from the glass