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We discuss the motion of colloidal particles relative to a two component fluid consisting of solvent and solute. Particle motion can result from (i) net body forces on the particle due to external fields such as gravity; (ii) slip velocities on the particle surface due to surface dissipative phenomena. The perturbations of the hydrodynamic flow field exhibits characteristic differences in cases (i) and (ii) which reflect different patterns of momentum flux corresponding to the existence of net forces, force dipoles or force quadrupoles. In the absence of external fields, gradients of concentration or pressure do not generate net forces on a colloidal particle. Such gradients can nevertheless induce relative motion between particle and fluid. We present a generic description of surface dissipative phenomena based on the linear response of surface fluxes driven by conjugate surface forces. In this framework we discuss different transport scenarios including self-propulsion via surface slip that is induced by active processes on the particle surface. We clarify the nature of force balances in such situations.
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Detailed control over the motion of colloidal particles is relevant in many applications in colloidal science such as lab-on-a-chip devices. Here, we use an external magnetic field to assemble paramagnetic colloidal spheres into colloidal rods of several lengths. The rods reside above a square magnetic pattern and are transported via modulation of the direction of the external magnetic field. The rods behave like bipeds walking above the pattern. Depending on their length, the bipeds perform topologically distinct classes of protected walks above the pattern. We demonstrate that it is possible to design parallel polydirectional modulation loops of the external field that command up to six classes of bipeds to walk on distinct predesigned paths. We use such parallel polydirectional loops to induce the collision of reactant bipeds, their polymerization addition reaction to larger bipeds, the separation of product bipeds from the educts, the sorting of different product bipeds, and also the parallel writing of a word consisting of several different letters.
Ferrofluids belong to an important class of highly functional soft matter, benefiting from their magnetically controllable physical properties. Therefore, it is of central importance to quantitatively predict the dynamic magnetic response of ferrofluids. Traditional dynamic theories, however, are often restricted to the near-equilibrium regime and/or only apply to nearly ideal ferrofluids that are monodisperse, dilute enough, and weakly interacting. In this paper I develop a self-consistent and nonperturbative dynamical mean field theory for typical ferrofluids which are often polydisperse, concentrated, and strongly interacting, possibly driven far from equilibrium. I obtain a general nonperturbative expression for the dynamic magnetic susceptibility, quantitatively agreeing with the spectra obtained from Brownian Dynamics simulations on both mono- and bidisperse samples. Furthermore, I derive a generic magnetization relaxation equation (MRE) for both mono- and polydisperse ferrofluids by employing the projection operator technique in nonequlibrium statistical mechanics. This MRE is in simple closed form and independent of which model is employed to approximate the equilibrium magnetization curve. Existing models can be recovered as low-order approximations of my generic and nonperturbative MRE. My theory can play a key role in studying the dynamics of ferrofluids and other polar fluids. It may also have substantial and immediate consequences to various ferrofluid applications.
In soft matter structure couples to flow and vice versa. Complementary to structural investigations, we here are interested in the determination of particle velocities of charged colloidal suspensions of different structure under flow. In a combined effort of theory and experiment we determine the Fourier transform of the super-heterodyne field auto-correlation function (power spectrum) which in frequency space is found to be well separated from homodyne contributions and low frequency noise. Under certain conditions the power spectrum is dominated by incoherently scattered light, originating from the unavoidable size polydispersity of colloidal particles. A simple approximate form for the low-wavenumber self-intermediate scattering function is proposed, reminiscent to the case of non-interacting particles. We experimentally scrutinize the range of applicability of these simplified calculations on employing a parabolic electro-osmotic flow profile. Both for non-interacting and strongly interacting fluid particle systems, the spectra are well described as diffusion-broadened velocity distributions comprising an osmotic flow-averaged superposition of Lorentzians at distinct locations. We discuss the performance and scope of this approach with particular focus on moderately strong interactions and on multiphase flow. In addition, we point to some remaining theoretical challenges in connection to the observed linear increase of the effective diffusion constant and the integrated spectral power with increasing electric field strength.
In the short letter, we explain an improved transform theory for colloidal-probe atomic force microscopy (CP-AFM). CP-AFM can measure a force curve between the colloidal probe and a wall surface in a colloidal dispersion. The transform theory can estimate the normalized number density distribution of the colloidal particles on the wall from the force curve measured by CP-AFM. The transform theory is important for study of the stratification of the colloidal particles on the wall, which is related to fundamental studies of colloidal crystal and glass.
Single and double paramagnetic colloidal particles are placed above a magnetic square pattern and are driven with an external magnetic field precessing around a high symmetry direction of the pattern. The external magnetic field and that of the pattern confine the colloids into lanes parallel to a lattice vector of the pattern. The precession of the external field causes traveling minima of the magnetic potential along the direction of the lanes. At sufficiently high frequencies of modulation only the doublets respond to the external field and move in direction of the traveling minima along the lanes, while the single colloids cannot follow and remain static. We show how the doublets can induce a coordinated motion of the single colloids building colloidal trains made of a chain of several single colloids transported by doublets.
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