  A model has been developed to describe the collision and possible coalescence
of two driven deformable drops in the Hele-Shaw cell. The interdependence
between hydrodynamic effects and interfacial deformations is characterised by a
film capillary number: Ca_f = (\mu v/\sigma)(R_o/h_o)^(3/2) as revealed by an
analytic perturbation solution of the governing equations for a system with
continuous phase viscosity \mu, interfacial tension \sigma, drop radius R_o,
characteristic relative velocity v and separation h_o between the drops.
Numerical solutions of the model demonstrate the importance of the full dynamic
history of the interacting drops in determining stability or coalescence. The
geometry of the Hele-Shaw cell allows for the possibility of using the model to
infer the time dependent force between colliding drops by measuring their
separation.
