The working principle of immunoassays is based on the specific binding reaction of an analyte-ligand protein pair in physiological environments. However, for a diffusion-limited protein, the diffusion boundary layer of the analyte on the reaction surface of a biosensor would hinder the binding reaction from association and dissociation. The formation of such association and dissociation layers thus limits the response time and the overall performance of a biosensor. In this work we have performed a two-dimensional full time scale finite element simulation on the binding reaction kinetics of two commonly used proteins, C-reactive protein ͑CRP͒ and immunoglobulin G ͑IgG͒. By applying a nonuniform ac electric field to the flow microchannel of the biosensor, the electrothermal force can be generated to induce a pair of vortices to stir the flow field. With the aid of the vortices and a suitable choice of the location of the biosensor, the fluids flowing over the reacting surface can be accelerated fast enough to depress efficiently the growth of the diffusion boundary layer on the reaction surface, and enhance the association or dissociation of analyte-ligand complex. The interference patterns of the flow field due to the existence of the sensor at different locations of the microchannel could cause different degrees of enhancement to the association and the dissociation. By changing the location of the sensor the largest enhancement is found at the position near the negative electrode. For the configuration of the microchannel we studied, the initial slope of the curve of the analyte-ligand complex versus time can be raised up to 5.17 for CRP and 1.93 for IgG in association, and 3.74 for CRP and 1.28 for IgG in dissociation, respectively, under the applied ac field 15 V rms peak-to-peak and operating frequency 100 kHz. At this optimal sensor location, we also studied the effect of various settings of temperature boundary conditions on the top and bottom walls, including the two limiting cases, namely, constant temperature and thermal insulation on both walls. We show that varying the temperature boundary conditions can cause an essential effect on the enhancement of the binding reaction and can be employed to find an optimal binding enhancement. Utilizing these simulation results, an improved design incorporating a pair of electrodes and a neck region near the reaction surface is demonstrated. The sensor is fixed to locate at the middle of the bottom side. With the existence of the stirring flow field, the association rate of the 30 m neck is 2.73 times faster than that of the original channel with no neck.
The transient motion of an anisotropic elastic bimaterial due to a line force or a line dislocation is studied. The bimaterial is assumed to be at rest and stress-free for t < 0. The line source is applied at t = 0 and maintained for t > 0. A formulation which is an extension to Stroh's formalism for anisotropic elastostatics is employed. The general solution is expressed in terms of the eigenvalues and eigenvectors of a related eigenvalue problem. The method is used to obtain the analytic solutions without the need of performing integral transforms. Numerical examples of the GaAs bimaterial due to a line force or dislocation are presented for illustration.
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