We report experimental results on the deformation of a single drop sus
pended in a medium under uniaxial elongational flow along the central
axis of a converging conical channel made of Plexiglas. Both the drop
and the continuous phases consist of constant viscosity elastic fluids
, so-called Boger fluids. This study reveals several interesting featu
res about the role played by both the drop and matrix elasticities on
the drop deformability. In a given matrix fluid, the drop deformation
decreases as its elasticity increases. For a given drop fluid, the mat
rix elasticity has the opposite effect: the drop deformation increases
with increasing matrix elasticity. An empirical relation between the
drop and matrix deformations is established as a function of the drop
and matrix characteristic elastic times. (C) 1997 The Society of Rheol
ogy.