Selective trapping of nanoscale bioparticles (size <100 nm) is significant for the separation and high-sensitivity detection of biomarkers. Dielectrophoresis is capable of highly selective trapping of bioparticles based on their characteristic frequency response. However, the trapping forces fall steeply with particle size, especially within physiological media of high-conductivity where the trapping can be dissipated by electrothermal (ET) flow due to localized Joule heating. Herein, we investigate the influence of device scaling within the electrodeless insulator dielectrophoresis geometry through the application of highly constricted channels of successively smaller channel depth, on the net balance of dielectrophoretic trapping force versus ET drag force on bioparticles. While higher degrees of constriction enable dielectrophoretic trapping of successively smaller bioparticles within a short time, the ETflow due to enhanced Joule heating within media of high conductivity can cause a significant dissipation of bioparticle trapping. This dissipative drag force can be reduced through lowering the depth of the highly constricted channels to submicron sizes, which substantially reduces the degree of Joule heating, thereby enhancing the range of voltages and media conductivities that can be applied toward rapid dielectrophoretic concentration enrichment of silica nanoparticles (approximate to 50 nm) and streptavidin protein biomolecules (approximate to 5 nm). We envision the application of these methodologies toward nanofabrication, optofluidics, biomarker discovery, and early disease diagnostics.