multimaterial DIW printer uses two separate ink dispensers joined at a single nozzle junction to simultaneously 3D print two viscoelastic inks through a single nozzle. Some models have been established to help control the printing of viscoelastic inks, but they have not been applicable for use in structures with complex compositional gradients. [18,22,23] As illustrated in Figure 1A, the toolpath of the printer is directly coupled with a desired composition (Φ) in order to determine the dispensing rate of each material. A distinction between the programmed dispensing rate of an ink (Q i ) and the measured flow rate out of the nozzle (Q Ni ) must be made when considering how to obtain an accurate compositional profile. Ideally, the increases and decreases in the measured ink flow rate synchronously follow the programmed dispensing rate. In reality, a number of factors introduce significant differences between the ideal ink dispensing rates and the realized outputs. Achieving accurate compositional 3D printing involving gradient transitions requires that we account for more complex behaviors, such as hydraulic compliance and non-Newtonian ink response, that result in significant differences between the programmed Q i and the realized Q Ni ( Figure 1B). For binary compositional changes within the same component, a combination of ink retraction and over extrusion can be used to account for these nonidealities. [22] For gradient compositional changes, the microfluidic circuit analogy (MCA) can be used to model and inform the ink dispensing profile that is required to achieve accurate compositional control ( Figure 1C).Here, we first describe the MCA model that is used to prescribe the ink-dispensing profile for improved compositional deposition accuracy in 3D-printed geometries with compositional gradients. We outline a calibration procedure to extract the MCA model parameters, which are then used in the MCA model to quantitatively guide the ink-dispensing profile for the desired compositional gradients to be printed. We finally validate the model in a DIW system using viscoelastic polydimethylsiloxane (PDMS) inks with time-dependent compositional changes. The ability to print multiple materials with accurate compositional profiles in a programmable manner enables the fabrication of new functional materials that were previously inaccessible.We use a model based on the microfluidic circuit analogy to determine the correct ink dispensing profiles required for 3D printing of structures with compositional gradients requires accurate dispensing control to achieve desired profiles. Here, empirical data are used with a model based on the microfluidic circuit analogy (MCA) to project dispense rate profiles that yield improved compositional accuracy in the printed part. Since minor variation in the experimental setup for each printing session can result in significant changes, a calibration procedure is developed to measure the system response. This calibration enables the extraction of the empirical MCA model parameters speci...