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We investigate the dispersion of a passive scalar such as the concentrationof a chemical species, or temperature, in homogeneous bubbly suspensions, bydetermining an effective diffusivity tensor. Defining the longitudinal andtransverse components of this tensor with respect to the direction of averagedbubble rise velocity in a zero mixture velocity frame of reference, we focus onthe convective contribution thereof, this being expected to be dominant incommonly encountered bubbly flows. We first extend the theory of Koch et al.(1989) (which is for dispersion in fixed beds of solid particles under Stokesflow) to account for weak inertial effects in the case of ordered suspensions.In the limits of low and of high P\'eclet number, including inertial effect ofthe flow does not affect the scaling of the effective diffusivity with respectto the P\'eclet number. These results are confirmed by direct numericalsimulations performed in different flow regimes, for spherical or very deformedbubbles and from vanishingly small to moderate values of the Reynolds number.Scalar transport in arrays of freely rising bubbles is considered by ussubsequently, using numerical simulations. In this case, the dispersion isfound to be convectively enhanced at low P\'eclet number, like in orderedarrays. At high P\'eclet number, the Taylor dispersion scaling obtained forordered configurations is replaced by the one characterizing a purelymechanical dispersion, like in random media, even if the level of disorder isvery low.

The effective diffusivity of ordered and freely evolving bubbly suspensions