Electrospinning is based on so-called bending instability which results in an erratic spiralling motion of the liquid jet as it proceeds towards a collecting electrode, where it is eventually deposited as a mat of micro/nanosized fibres. Most electrospinning models formulated within the slender approximation rely, however, on an inconsistent description of electrostatic interactions which renders them grossly inappropriate whenever the discretization is either too coarse or too fine. The present work aims at proposing a discrete slender model which is numerically consistent (allowing use of arbitrary fine meshes) and remains accurate even for coarse meshes. At the same time, efficient numerical techniques based on hierarchical charge clustering are introduced that drastically decrease computational times. Finally, a versatile boundary value method is implemented to enforce fixed-potential boundary conditions, allowing realistic electrode configurations to be investigated.Copyright line will be provided by the publisher Electrospinning is a simple and relatively inexpensive mean of producing continuous fibres with diameters ranging from micrometers down to a few nanometres. Nonwovens of electrospun fibres are obtained from a jet of polymer solution stretched by an electric field. Although most polymeric solutions or melts may be used for electrospinning, the achievement of stable operation is usually the result of a tedious trial-and-error parametrical optimization procedure. On the other hand the physical and mathematical description of the electrospinning process remain in a premature state. The existing discrete models are based on point charges connected by dumbbell elements [1][2][3][4][5]. One serious concern relates to the evaluation of short-range interactions, which in the case of standard discrete integration methods require very dense grids due to the large contribution of short-range electrostatic interactions within distances of the order of the fibre radius [1,6]. As the fibre radius is about 10 3 − 10 5 times smaller than the macroscopic scales of interest, it appears most desirable to devise a discrete model that exploits the slenderness of the fibre to evaluate short-range interactions in an efficient manner. Likewise, the computation of long-range electrostatic interactions can easily become intractable due to the O n 2 operation count for a pairwise evaluation of interactions between n elements. In addition current numerical models are based on the assumption of a static external electric field, whereas in reality the external field is modulated by the net space charge of the fibre so as to keep constant the potential over the electrodes. An efficient handling of long-range interactions can theoretically achieve O (n log n) operation count, or even O (n) for the fast multipole method (FMM). The proposed here treecode algorithm [7] considers particle-cluster interactions and achieves O (n log n) complexity. Generally it is a time-dependent three-dimensional generalization of known slender models...