When a surfactant-stabilised oil droplet with an ultralow interfacial tension is trapped in the focus of two laser beams and pulled apart (by moving the laser beams) a configuration of two droplets connected by a thin tether of oil results. The tether radius depends on the ratio of the bending modulus to the renormalized interfacial tension, which takes into account the spontaneous curvature of the interface. The force exerted by the tether on the droplets is shown to be asymmetric with respect to the phase inversion temperature of the emulsion, in agreement with experiment. Fluid can be pumped from one droplet to the other via the tether by increasing the optical pressure on one droplet. The flow is a combination of Poiseuille flow within the thread of oil and the external flow around a rigid cylinder, with the surface velocity determined by tangential stress balance. For typical viscosities of oils and the continuous aqueous medium, flow is predominantly in the external medium. The normal stress balance leads to a variation in the radius of the thread with distance. The radius is shown to decrease approximately linearly with a slope proportional to the volumetric flow rate through the tether. For a tether of a given length, there is therefore an upper limit to the flow rate that can be generated by pumping with optical traps.
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