Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow

Abstract

Two unequal rigid spheres are immersed in unbounded fluid and are acted on by externally applied forces and couples. The Reynolds number of the flow around them is assumed to be small, with the consequence that the hydrodynamic interactions between the spheres can be described by a set of linear relations between, on the one hand, the forces and couples exerted by the spheres on the fluid and, on the other, the translational and rotational velocities of the spheres. These relations may be represented completely by either a set of 10 resistance functions or a set of 10 mobility functions. When non-dimensionalized, each function depends on two variables, the non-dimensionalized centre-to-centre separation s and the ratio of the spheres’ radii λ. Two expressions are given for each function, one a power series in s−1 and the other an asymptotic expression valid when the spheres are close to touching.

Correlation Force Spectroscopy for Single Molecule Measurements

“…Onishi [106] give the following asymptotic expressions: As shown in Figure 5-6, these expressions agree with our data for *…”

“…I compared our experimentally calculated interparticle hydrodynamic interaction with available theories that were developed for the hydrodynamic interaction between two spheres at low Reynolds and frequency numbers [105,106]. Our experimental data are in good agreement with these theories at near touching separations to about 2 s  , which supports our choice of characteristic length described above.…”

“…At small separations between the spheres ( 2 s D   ) the measured value of the interparticle friction is well predicted by low frequency number theory (Jeffry's expression from Ref. [106]). This suggests that I use a frequency number for the interparticle hydrodynamic interaction that includes an explicit dependence on the separation of the spheres, for example, .…”

“…The fluid flow near, and in the far field of a single colloidal particle has been studied by Stokes (1851) and Boussinesq (1903) [101][102][103][104]. The hydrodynamic interaction between two particles at near touching to large interparticle separations has also received considerable attention [105][106][107][108].…”

Hydrodynamic orienting of asymmetric microobjects under gravity

“…Once it happens, the spheres remain at contact owing to lubrication forces [26]. Such configurations will be called 'chains'.…”