a Microfluidic chip as stitched microscopy image (upper half) and as the concentration plot of a finite element method (FEM) simulation of the full geometry (lower half). Arrows indicate inflow of 57 µM methylcellulose in PBS (MC, flow rate Qsa = 48 nl s−1) and 50 mM polyethylene glycol 8000 in PBS (PEG8000, flow rate Qsh = 8 nl s−1) forming a stable virtual fluidic channel between two liquid–liquid interfaces represented in dark gray (upper half) and in white (lower half). Scale bar is 50 µm. Top inset shows a bright-field image of the central constriction and the projected squared intensity gradient (arb. units) across the full channel width. Virtual channel width corresponds to distance w (white dashed lines) between the center of both intensity maxima. Scale bar is 10 µm. Bottom inset shows a cross-sectional view of the calculated (FEM) polymer concentration inside the channel. b Velocity profile (black circles) inside the center of the constriction derived from FEM simulations with the corresponding MC concentration distribution (blue solid line) used to identify the virtual channel width w. The red and the blue dashed lines indicate the parabolic flow profiles of the outer and inner aqueous phases. c Dynamic viscosities of sample and sheath solutions as a function of shear rate. Virtual channel formation is performed using MC as sample buffer (blue) and PEG as sheath buffer (dark red, orange, bright red). Data points are measured and for shear rates greater than 3000 s−1 the shear-rate dependency is modeled as a power-law fluid (solid blue line) and as Newtonian fluid (solid orange and red lines). d Relative virtual channel width \(\tilde w\) as a function of flow rate and viscosity ratios. The plot summarizes n = 146 experiments using different concentrations of MC, PEG8000 (PEG8K), and PEG40000 (PEG40K) for sample and sheath solution. The black curve is a solution to Eq. (1).