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Being motivated by the delivery of drugs and vaccines through subcutaneous(SC) injection in human bodies, a theoretical investigation is performed usinga two-dimensional mathematical model in the cartesian coordinate. In general, alarge variety of biological tissues behave as deformable porous material withanisotropic hydraulic conductivity. Consequently, one can adopt the fieldequations of mixture theory to describe the behavior of the interstitial fluidand adipose cell present in the subcutaneous layer of skin. During theprocedure, a medical person takes a big pinch of the skin of the injectionapplication area between the thumb and index finger and holds. This processpulls the fatty tissue away from the muscle and makes the injection processeasier. In this situation, the small aspect ratio (denoted as $\delta$) of thesubcutaneous layer (SCL) i.e., $\delta^2\sim0.01$ would simplify the governingequation for tissue dynamics as it becomes a perturbation parameter. This studyhighlights the issue of the mechanical response of the adipose tissue in termsof the anisotropic hydraulic conductivity variation, the viscosity of theinjected drug, the mean depth of subcutaneous tissue, etc. In particular, thecomputed stress fields can measure the intensity of pain to be experienced by apatient after this procedure. Also, this study discusses the biomechanicalimpact of the creation of one or more eddy structures (s) near the area ofapplying injection, which is due to high pressure developed there, increasedtissue anisotropy, fluid viscosity, etc.

Two-phase Modeling of Fluid Injection Inside Subcutaneous Layer of Skin