# Difference between revisions of "Magneto-mechanical mixing and manipulation of picoliter volumes in vesicles"

Birgit Hausmann

## Overview

Magnetic manipulation, positioning, agitation and mixing of ultrasmall liquid volumes has been realized utilizing superparamagnetic beads in giant unilamellar vesicles. In the presence of a magnetic field the beads align to form extended chains while a rotating magnetic field provokes the chains to break up into smaller fragments caused by the interplay of viscous friction and magnetic attraction.

## Results and Discussion

While a magnetic field gradient generates a force on the magnetic dipole chains a rotational field introduces spinning. An electroformation method was used to fabricate the vesicles. The lipid in chloroform was deposited onto two indium tin oxide (ITO) coated glass slides and the organic solvent was evaporated in vacuum. An aqueous solution containing the superparamagnetic beads was added to the dried lipid. The two ITO plates were mounted in parallel and an electric field was applied. Finally, the voltage was increased to facilitate the separation of vesicles. A theoretical minimum magnetic field of $59 \mu T$ is needed to align the superparamagnetic beads (of $1 \mu m$ size) within the vesicles in chains. Since the force to move the vesicle containing beads is proportional to the magnetic field gradient and it also has to be equal to the hydrodynamic drag force, the necessary field can be estimated. The direction of the magnetic field gradient also determines the direction of movement of the vesicles. A rotating magnetic field causes the superparamagnetic chain to rotate inside the vesicle, eventually causing a rotation of the vesicle itself. A fluorescein was added continuous phase fluid to prove that the vesicle is not leaking any content. At high cons the fluorescence. When a vesicle is moved across the microchamber, repeated rotations of the chains were initiated without detection of any fluorescent signal, which shows that the vesicle is leakproof. But, adding the membrane-porating surfactant Triton-X causes water to permeate through the membrane and a strong increase in fluorescent signal can e observed (Fig. 3). When the content of the vesicle is released, the intravesicular fluid volume mixes diffusively with the surrounding bulk solution. The magnetic beads within a vesicle can be used to enhance mixing by active agitation. A rotating external magnetic field is applied to magnetic chains. When a critical frequency of chain rotation is reached the bead chains split into smaller fragments. A model is provided to estimate the number of beads at critical frequency: it can be calculated balancing the tangential drag force with the attractive magnetic force acting between the beads that make up the chain. The experimental results for chain breakup at different viscosities are compared with the theoretical model in Fig. 5. Small tracer particles were placed in close proximity to the microstirrer to account for the fluid flow. The trajectories of these tracers reveal circles around the center of the microstirrer superimposed on small oscillations of the same frequency of the magnetic stirrer (Fig. 6). The inset of Fig. 6 shows the effects that the angular velocity of the overall circular motion of individual tracer beads decreases - thus decreasing the spatial period length of the oscillating trajectories - with distance from the center of the stirrer.

The mixing efficiency is depending on the diffusion coefficient of the particles that are to be mixed. For small particles, mixing is dominated by diffusion, while for large particles, advection is more important. The ratio of these two effects is characterized by the Péclet number. The diffusion coefficient was estimated to be $9.4\cdot 10^{-12} m^2s^{-1}$ , which corresponds to a radius r=23 nm of a particle in water. The proposed mixing mechanism is therefore most effective for nanoparticles with a radius >20 nm.