Thermophoretically induced large-scale deformations around microscopic heat centers

Abstract

Selectively heating a microscopic colloidal particle embedded in a soft elastic matrix is a situation of high practical relevance. For instance, during hyperthermic cancer treatment, cell tissue surrounding heated magnetic colloidal particles is destroyed. Experiments on soft elastic polymeric matrices suggest a very long-ranged, non-decaying radial component of the thermophoretically induced displacement fields around the microscopic heat centers. We theoretically confirm this conjecture using a macroscopic hydrodynamic two-fluid description. Both, thermophoretic and elastic effects are included in this theory. Indeed, we find that the elasticity of the environment can cause the experimentally observed large-scale radial displacements in the embedding matrix. Additional experiments confirm the central role of elasticity. Finally, a linearly decaying radial component of the displacement field in the experiments is attributed to the finite size of the experimental sample. Similar results are obtained from our theoretical analysis under modified boundary conditions.

Hydrodynamic description of elastic or viscoelastic composite materials: Relative strains as macroscopic variables

“…5, A co and A in in general cannot be obtained from coarse-grained macroscopic velocity fields v co and v in . Establishing corresponding two-or three-fluid hydrodynamic descriptions [51,[60][61][62] for (visco)elastic composite materials will be an interesting subject for the future.…”

“…In this expression, the coefficients κ ij are related to heat conduction [9], D ij and D (T ) ij describe diffusion and thermodiffusion [9,[56][57][58][59][60], respectively, while ν ijkl comprise the viscosities [9]. Next, the coefficients ζ x ijkl include irreversible relaxation processes of strains [51,61], e.g.…”

Collision and separation of nickel particles embedded in a polydimethylsiloxan matrix under a rotating magnetic field: A strong magneto active function

“…In the final step, another layer of PDMS (of the same composition) was poured over the first, which was cured for another 24 h at 60 • C. Thus, the particles are fully encapsulated by the matrix material (Fig. 1 b) and figure 3 in [26]. As dimensions of the final PDMS gels exceed the particle diameters (and their typical displacements) by a factor of ≈ 10, the influence of the boundaries on the particle motion can be neglected.…”

“…In samples similar to the ones studied here, it has been shown that non-local matrix-mediated interactions can be described in an iterative procedure inspired by the Oseentensor formalism in hydrodynamics [26]. Here, the system is described as an interplay between mutual magnetic forces and the opposing elastic matrix deformations caused by particle displacement.…”

“…Even though the Ni particles are themselves 3D objects with well-defined dimensions, the assumption to treat the magnetizable Ni particles as point-like dipoles is valid for substantial particle separation [20, [53][54][55][56]. This is also validated in [26] by comparing experimental results with a theoretical approach, where well-separated particles experience distance oscillation during rotation of the external field. Assuming identical magnetic moments m and a magnetization parallel to the applied field, the dipole interaction force between two particles i and j is given [34,57]:…”