The Zimm model applied to extended single polymers

A mean field theory is developed for the Zimm model and compared to the exact solution, computed numerically, for the case of a single extended polymer. An analytic calculation in the dumbbell approximation extends the preaveraging treatment. We find that the dynamic scaling of the preaveraged Zimm model is preserved for short polymers, but that the relaxation function is inhomogeneous in length for long polymers. These calculations can be applied to recent experimental results

A Microfluidic Rectifier: Anisotropic Flow Resistance at Low Reynolds Numbers

It is one of the basic concepts of Newtonian fluid dynamics that at low Reynolds number (Re) the Navier-Stokes equation is linear and flows are reversible. In microfluidic devices, where Re is essentially always low, this implies that flow resistance in microchannels is isotropic. Here we present a microfluidic rectifier: a microscopic channel of a special shape whose flow resistance is strongly anisotropic, differing by up to a factor of 2 for opposite flow directions. Its nonlinear operation at arbitrary small Re is due to non-Newtonian elastic properties of the working fluid, which is a 0.01% aqueous solution of a high molecular weight polymer. The rectifier works as a dynamic valve and may find applications in microfluidic pumps and other integrated devices

Microfluidics: Fluid physics at the nanoliter scale

Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Péclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world

A Self-Assembled Microlensing Rotational Probe

A technique to measure microscopic rotational motion is presented. When a small fluorescent polystyrene microsphere is attached to a larger polystyrene microsphere, the larger sphere acts as a lens for the smaller microsphere and provides an optical signal that is a strong function of the azimuthal angle. We demonstrate the technique by measuring the rotational diffusion constant of the microsphere in solutions of varying viscosity and discuss the feasibility of using this probe to measure rotational motion of biological systems.Comment: 3 pages with 2 figures (eps format). Paper has been submitted to Applied Physics Letter

Direct Measurement of Hydrodynamic Cross Correlations between Two Particles in an External Potential

We report a direct measurement of the hydrodynamic interaction between two colloidal particles. Two micron-sized latex beads were held at varying distances in optical tweezers while their Brownian displacements were measured. In spite of the fact that fluid systems at low Reynolds number are generally considered to have no “memory,” the cross-correlation function of the bead positions shows a pronounced, time-delayed anticorrelation. We show that the anticorrelations can be understood in terms of the standard Oseen tensor hydrodynamic coupling

Microfabricated rubber microscope using soft solid immersion lenses

We show here a technique of soft lithography to microfabricate efficient solid immersion lenses (SIL) out of rubber elastomers. The light collection efficiency of a lens system is described by its numerical aperture (NA), and is critical for applications as epifluorescence microscopy [B. Herman, Fluorescence Microscopy (BIOS Scientific, Oxford/Springer, United Kingdom, 1998). While most simple lens systems have numerical apertures less than 1, the lenses described here have NA=1.25. Better performance can be engineered though the use of compound designs; we used this principle to make compound solid immersion lenses (NA=1.32). An important application of these lenses will be as integrated optics for microfluidic devices. We incorporated them into a handheld rubber microscope for microfluidic flow cytometry and imaged single E. Coli cells by fluorescence

A microfluidic oligonucleotide synthesizer

De novo gene and genome synthesis enables the design of any sequence without the requirement of a pre-existing template as in traditional genetic engineering methods. The ability to mass produce synthetic genes holds great potential for biological research, but widespread availability of de novo DNA constructs is currently hampered by their high cost. In this work, we describe a microfluidic platform for parallel solid phase synthesis of oligonucleotides that can greatly reduce the cost of gene synthesis by reducing reagent consumption (by 100-fold) while maintaining a 100 pmol synthesis scale so there is no need for amplification before assembly. Sixteen oligonucleotides were synthesized in parallel on this platform and then successfully used in a ligation-mediated assembly method to generate DNA constructs 200 bp in length

Behavior of Complex Knots in Single DNA Molecules

We used optical tweezers to tie individual DNA molecules in knots. Although these knots become highly localized under tension, they remain surprisingly mobile and undergo thermal diffusion with classical random walk statistics. The diffusion constants of knots with different complexities correlate with theoretical calculations of knot sizes. We show that this correlation can be explained by a simple hydrodynamical model of "self-reptation" of the knot along a polymer

An apertureless near-field microscope for fluorescence imaging

We describe an apertureless near field microscope for imaging fluorescent samples. Optical contrast is generated by exploiting fluorescent quenching near a metallized atomic force microscope tip. This microscope has been used to image fluorescent latex beads with subdiffraction limit resolution. The use of fluorescence allows us to prove that the contrast mechanism is indeed spectroscopic in origin