equation for the pressure is Laplace' \;s equation\; thus\, mathematical models for

H ele-Shaw flows are amenable to complex analysis. W e consider here one such problem\, where a

bubb le is moving steadily in a Hele-Shaw cell.

This is like the classical Taylor-Saffman bubble\, exc ept we suppose the

domain extends out infinitel y far in all directions. By applying a conformal m apping\, we produce

numerical evidence to sugge st that solutions to this problem behave in an

analogous way to well-studied finger and bubble pr oblems in a Hele-Shaw

channel. However\, the se lection of the

ratio of bubble speeds to backgr ound velocity for our problem appears to follow

a very different surface tension scaling to the c hannel cases. We apply techniques in exponential

numerical results\, in cluding the predicted surface tension scaling laws .

Further\, our analysis sheds light on the mul tiple tips in the shape of the

bubbles along so lution branches\, which appear to be caused by swi tching on and

off exponentially small wavelike contributions across Stokes lines in a

conforma lly mapped plane. These results

are likely to p rovide insight into other well-known selection pro blems in

Hele-Shaw flows. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR