A rotary device comprising a first rotor rotatable about a first axis and having at its periphery a recess bounded by a curved surface, and a second rotor counter-rotatable to said first rotor about a second axis, parallel to said first axis, and having a radial lobe bounded by a curved surface, the lobe having a front surface and a trailing surface, the first and second rotors being coupled for intermeshing rotation, wherein the first and second rotors intermesh on rotation thereof, wherein the recess and lobe surfaces are contoured such that during passage of the lobe through the recess, the recess surface is continuously swept, by both a tip of the lobe and a movable location on the front surface of the lobe, defining therebetween a transient chamber of variable volume, the transient chamber having a progressively increasing or decreasing volume between the recess and lobe surfaces, wherein, in use, the transient chamber functions as the expansion or compression chamber of the rotary device for compression or expansion of a working fluid and for at least part of the rotary cycle the transient chamber being defined entirely by the surfaces of the lobe and the recess; the ratio of the maximum radius of the lobe rotor and the maximum radius of the recess rotor being greater than 1 characterised in that the geometry of the or each lobe is determined by the inner radius of the lobe ρ Li, the outer rotor radius at the tip of the lobe ρ Lo, the outer radius of the recess rotor ρ Po, and a circular arc segment A l of radius R l defining a bulk of the lobe; in which the swept area is maximised in accordance with the condition: ρ Po + ρ Li ≤ 1 q 1 + q 2 ρ M l 2 + 1 27 1 + 2 q 3 R l 2 in which q is the ratio of angular velocities of the recess and lobe rotors and ρ Ml is the separation between the centre of the lobe rotor and the centre of the circle from which the arc that at least in part defines the shape of the lobe is taken; ρ Po, is the outer radius of the recess rotor; ρ Li is the inner radius of the lobe; and R l is the radius of circular arc segment A l defining a bulk of the lobe the first and second rotors intermesh on rotation thereof, wherein the recess and lobe surfaces are contoured such that during passage of the lobe through the recess, the recess surface is continuously swept, by both a tip of the lobe and a movable location on the front surface of the lobe, defining therebetween a transient chamber of variable volume, the transient chamber having a progressively increasing or decreasing volume between the recess and lobe surfaces, wherein, in use, the transient chamber functions as the expansion or compression chamber of the rotary device for compression or expansion of a working fluid and for at least part of the rotary cycle the transient chamber being defined entirely by the surfaces of the lobe and the recess; the ratio of the maximum radius of the lobe rotor and the maximum radius of the recess rotor being greater than 1 characterised in that the geometry of the or each lobe is determined by the inner radius of the lobe ρ Li, the outer rotor radius at the tip of the lobe ρ Lo, the outer radius of the recess rotor ρ Po, and a circular arc segment A l of radius R l defining a bulk of the lobe; in which the swept area is maximised in accordance with the condition: ρ Po + ρ Li ≤ 1 q 1 + q 2 ρ M l 2 + 1 27 1 + 2 q 3 R l 2 in which q is the ratio of angular velocities of the recess and lobe rotors and ρ Ml is the separation between the centre of the lobe rotor and the centre of the circle from which the arc that at least in part defines the shape of the lobe is taken; ρ Po, is the outer radius of the recess rotor; ρ Li is the inner radius of the lobe; and R l is the radius of circular arc segment A l defining a bulk of the lobe q is the ratio of angular velocities of the recess and lobe rotors and ρ Ml is the separation between the centre of the lobe rotor and the centre of the circle from which the arc that at least in part defines the shape of the lobe is taken; ρ Po, is the outer radius of the recess rotor; ρ Li is the inner radius of the lobe; and R l is the radius of circular arc segment A l defining a bulk of the lobe