Optimization of Pathway Pattern Size for Programmable Biomolecule Actuation

Magnetophoretic Micro‐Distributor for Controlled Clustering of Cells

“…To understand the dynamics of the magnetic bead under various conditions, it is necessary to analyze the magnetic force exerted on the magnetic bead. The magnetic force can be expressed with three components in the tangential ( φ ) direction, radial ( ρ ) direction, toward the center of the micromagnet from the bead, and vertical ( z ) direction with respect to the micromagnet surface, [ 30,31 ] $$\begin{equation} \vec{F}=\frac{{\chi}_{v}V}{2{\mu}_{0}}\ \nabla \ \left(\vec{B}\cdot \vec{B}\right)={F}_{\textit{mag}}^{\varphi}\ {\widehat{e}}_{\varphi}+{F}_{\textit{mag}}^{\rho}{\widehat{e}}_{\rho}+{F}_{\textit{mag}}^{z}{\widehat{e}}_{z} \end{equation}$$ $$\begin{equation} \left\{ \def\eqcellsep{&}\begin{array}{l}{F}_{\textit{mag}}^{\varphi}=\displaystyle\frac{{\chi}_{v}V}{{\mu}_{0}}\frac{1}{\rho}\left({B}_{\rho}\frac{\partial {B}_{\rho}}{\partial \varphi}-{B}_{\varphi}\frac{\partial {B}_{\varphi}}{\partial \varphi}\right)\\ [10pt] {F}_{\textit{mag}}^{\rho}=\displaystyle\frac{{\chi}_{v}V}{{\mu}_{0}}\l...$$…”

“…To understand the dynamics of the magnetic bead under various conditions, it is necessary to analyze the magnetic force exerted on the magnetic bead. The magnetic force can be expressed with three components in the tangential (𝜑) direction, radial (𝜌) direction, toward the center of the micromagnet from the bead, and vertical (z) direction with respect to the micromagnet surface, [30,31] where 𝜒 v is the magnetic susceptibility of the moving bead, V is the volume of the magnetic bead (m 3 ), and 𝜇 0 is the permeability of vacuum (4𝜋 × 10 −7 N A −2 ). When the magnetic bead moves along the micromagnet with a constant curvature (disk shape), it is under phase-locked con-ditions with a constant balanced force without changing the magnetic forces.…”

Concentric manipulation and monitoring of protein-loaded superparamagnetic cargo using magnetophoretic spider web

“…The calculated mean magnetic moment per particle is 6.4 × 10 − 14 A m 2 , where the density of the particles is 1.4 × 10 3 kg m − 3 . 39 It is noted that magnitude of the effective field on the sensor surface is always smaller than that of the applied field because the effective field is the vector sum of the applied and the stray fields. Figure 5c shows the calculated field distribution Equation (2) with z equal to sum of particle radius (1.4 μm) and passivation layer of sensor (700 nm), where the minimum field is revealed (−691.4 μT) near the particle center, and the maximum field (139.6 μT) is revealed for outside of particle (x = ± 2.5 μm).…”

Magnetically Characterized Molecular Lubrication between Biofunctionalized Surfaces

“…This proposed method is much easier and faster to determine the frictional force than the previous method of measuring the varied phase-locked angles . DNA coating on the Au surface increases the maximum velocity about 30%, compared with the SiO 2 interface, and in turn, a higher operation velocity is afforded by optimization of the micromagnet size . The friction coefficients at the strept/DNA and strept/SiO 2 interfaces were evaluated as 0.07 and 0.11, respectively, regardless of both the vertical force and the velocity.…”