Temperature-Induced Tunable Particle Separation

An effective approach to isolation of submicrometer-sized particles is desired to separate cancer cells and healthy cells or in therapy for Parkinson’s disease and Alzheimer’s disease. However, since bioparticles span a large size range covering several orders of magnitude, the development of an adequate separation method is a challenging task. We consider a collection of noninteracting Brownian particles of various sizes moving in a symmetric periodic potential and subjected to external unbiased harmonic driving as well as a constant bias. We reveal a nonintuitive, yet efficient, separation mechanism based on a thermal-fluctuation-induced negative-mobility phenomenon in which particles of a given size move in a direction opposite to the applied bias. By varying solely the temperature of the system, one can separate particles of various strictly defined sizes. This approach may be an important step toward the development of point-of-care lab-on-a-chip devices.

Figure 1

(a) Average velocity $⟨v⟩$ as a function of the static force $f$ for two different values of the friction $\gamma$. (b) Average velocity $⟨v⟩$ versus thermal-noise intensity $D\propto T$ for different values of $\gamma$. The other parameters are $a=5.75$, $\omega =3.75$, $f=0.1$, and $D=0.0002$.

Figure 2

(a) Average velocity $⟨v⟩$ versus the friction coefficient $\gamma$. ANM is observed only for a narrow interval marked in gray. (b) An enlargement of this region. The parameter values are as follows: $a=5.75$, $\omega =4.0$, $f=0.1$, and $D=0.0006$.

Figure 3

(a)–(c) Friction coefficient (proportional to the particle size) ${\gamma }^{\ast }\propto R$ for which the Brownian-particle velocity attains its global minimum $⟨v{⟩}_{min}\equiv ⟨v⟩({\gamma }^{\ast })$ as a function of temperature $D\propto T$. The gray bars represent the friction-coefficient interval $\delta \gamma$ in which the ANM effect occurs [see Fig. 2]. The cyan region marks the range of the particle size $\gamma \propto R$ corresponding to the vicinity of the minimum; that is, $[⟨v{⟩}_{min}-0.05⟨v{⟩}_{min},⟨v{⟩}_{min}]$. The other parameters are as follows: (a) $a=5.55$, $\omega =1.5$; (b) $a=5.75$, $\omega =1.65$; (c) $a=5.75$, $\omega =5.65$. In (a)–(c) the bias $f=0.1$. (d) The minimal velocity $⟨v{⟩}_{min}$ (left axis) as well as the resolution capacity $\delta \gamma$ (right axis) versus temperature $D$ for the parameter regime corresponding to (c).