טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentOren Shay
SubjectDipolophresis of Ideally - Polarizable Cylindrical Particle
Pairs
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Itzchak Frankel


Abstract

This work is an analytic investigation of the dipolophoretic motion of a pair of identical ideally polarizable, initially uncharted circular - cylindrical particles freely suspended in an unbounded electrolyte solution under a uniform external electric field. The main motivation is to examine whether and under what conditions particles eventually stick together or move away from each other.

The analysis is carried out within the framework of the common thin electric double layer (EDL) limit and sufficiently weak fields. A quasi - steady solution is derived for a given instantaneous particle - pair configuration, based on the fact that the motion occurs on a time scale much longer than the typical time of the EDL - charge - distribution relaxation and the external - field rates of change.

Results show that particle - pair trajectories have a point symmetry relative to the mid - point of their line of centers (LOC) which is a fixed point. The effect of each component of the field (parallel or perpendicular) to the LOC acting separately is a symmetric motion along the LOC. Owing to the nonlinearity inherent in both the DEP and ICEP mechanisms, the interaction between field components generates a ‘lateral’ motion manifested in LOC rotation. We consider the motion under a constant DC field and the effect of frequency on the time - average particles motion under harmonic fields: an AC field in a constant direction or a rotating field of a constant magnitude. 

In general, with increasing frequency (within the frequency range studied), particle motion in an extending part of the plane is toward ‘pairing’. Trends of the results are rationalized in terms of the frequency effect on the relative magnitude of the DEP and ICEP mechanisms which have conflicting effects on LOC rotation - a monotonic decrease of ICEP because of a diminishing EDL charging as opposed to the initial strengthening of the DEP mechanism associated with increasing local electric field perpendicular to the particle surface.

The results show substantial qualitative differences between the modes of motion under an AC field in constant direction and a rotating field, respectively. To gain insight into these differences, an asymptotic solution for (moderately) large particle separations has been obtained. This solution shows that under an AC field in a fixed direction, leading - order terms are mutually canceling and lateral motion is therefore governed by higher - order terms, the largest of which is associated with the ICEP mechanism. In contrast, under a rotating field, no such mutual cancelation of leading - order terms occurs and lateral motion is governed by the (nondecreasing with particles separation) DEP torque which gives rise to large lateral velocities for remote particle pairs.