  Diffusion flame streets, observed in non-premixed micro-combustion devices,
align parallel to a shear flow. They are observed to occur in mixtures with
high Lewis number ($Le$) fuels, provided that the flow Reynolds number, or the
Peclet number $Pe$, exceeds a critical value. The underlying mechanisms behind
these observations have not yet been fully understood. In the present paper, we
identify the coupling between diffusive-thermal instabilities and Taylor
dispersion as a mechanism which is able to explain the experimental
observations above. The explanation is largely based on the fact that Taylor
dispersion enhances all diffusion processes in the flow direction, leading
effectively to anisotropic diffusion with an effective (flow-dependent) Lewis
number in the flow direction which is proportional to $1/Le$ for $Pe\gg 1$.
Validation of the identified mechanism is demonstrated within a simple model by
investigating the stability of a planar diffusion flame established parallel to
a plane Poiseuille flow in a narrow channel. A linear stability analysis,
leading to an eigenvalue problem solved numerically, shows that cellular (or
finite wavelength) instabilities emerge for high Lewis number fuels when the
Peclet number exceeds a critical value. Furthermore, for Peclet numbers below
this critical value, longwave instabilities with or without time oscillations
are obtained. Stability regime diagrams are presented for illustrative cases in
a $Le$-$Pe$ plane where various instability domains are identified. Finally,
the linear analysis is supported and complemented by time dependent numerical
simulations, describing the evolution of unstable diffusion flames. The
simulations demonstrate the existence of stable cellular structures and show
that the longwave instabilities are conducive to flame extinction.
