Tunable Mass Separation via Negative Mobility

A prerequisite for isolating diseased cells requires a mechanism for effective mass-based separation. This objective, however, is generally rather challenging because typically no valid correlation exists between the size of the particles and their mass value. We consider an inertial Brownian particle moving in a symmetric periodic potential and subjected to an externally applied unbiased harmonic driving in combination with a constant applied bias. In doing so, we identify a most efficient separation scheme which is based on the anomalous transport feature of negative mobility, meaning that the immersed particles move in the direction opposite to the acting bias. This work is the first of its kind in demonstrating a tunable separation mechanism in which the particle mass targeted for isolation is effectively controlled over a regime of nearly 2 orders of mass magnitude upon changing solely the frequency of the external harmonic driving. This approach may provide mass selectivity required in present and future separation of a diversity of nano- and microsized particles of either biological or synthetic origin.

Figure 1

(a) The force-directed velocity curve $⟨v⟩(f)$ is depicted for the two parameter regimes corresponding to normal (blue) and anomalous (green) transport behavior in the form of NM. Note the sensitivity of the latter effect with respect to changes of the dimensionless mass $m$. The chosen parameters are $a=10$, $\omega =5.95$, and $D=0.001$. (b) The directed velocity $⟨v⟩$ versus mass $m$. In the inset we present the blow up (red region) showing the interval of the NM phenomenon as marked by the gray area. Parameters are $a=5.125$, $\omega =3.75$, $f=1$, $D=0.0001$.

Figure 2

Two-dimensional map of the directed velocity $⟨v⟩$ of the Brownian particle as a function of the externally applied periodic driving frequency $\omega$ and mass $m$. The magnitude of velocity $⟨v⟩$ is indicated by the color code with blue indicating regimes with NM. Chosen remaining parameters are set at $a=5.9375$, $f=1$, $D=0.0001$.

Figure 3

The dependence of the mass $m^{*}$ tailored for separation as a function of the external driving frequency $\omega$ for zero temperature $D\propto T=0$ with fixed $a=5.125$ and $f=1$. In the inset we present a different regime with $D=0.001$ allowing for efficient and tunable mass separation via negative mobility.

Figure 4

The mass $m^{*}$ targeted for separation (color coded scale) via the NM effect as a function of the external ac-driving strength $a$ and frequency $\omega$ for different values of the bias $f$. Thermal noise intensity is set to zero $D=0$.