"in each particular case" is grammatically correct and is commonly used in written English.
It is typically used to introduce a specific example or instance within a broader context. Example: In each particular case, the judge must carefully consider the evidence presented before making a decision.
This misleads readers and viewers not just in each particular case.
The court ruled that no general rule in international law existed permitting states to grant diplomatic asylum; a legal basis had to be established in each particular case.
The question of whether animals were the immediate objects of a cult is extremely difficult to judge in each particular case.
It will commence with a statement of the general principle of Expression;—that serviceable actions become habitual in association with certain states of the mind, and are performed, whether or not of service, in each particular case.
Given a limited number of proteins that are druggable, it is important to identify as many chemical effectors as possible to define the best regimen of anti-cancer therapy in each particular case.
A rational bankruptcy system would also scrap the separate chapters altogether, along with the complicated paperwork now required to document and justify the chapter choice in each particular case.
The signals corresponding to the cyclophilin mRNA were used to normalize the changes in mRNA levels for each particular case.
Such a division, say the court in that case, must be founded upon the circumstances of each particular case; and in that view the court here entirely concurs.
The role of the Estonian Criminal Police was to handle the formalities in each particular Gypsy case, which was then submitted to the Political Police, who exercised the highest authority over the Gypsies in Estonia.
I'm pretty sure the 350 million active Facebook Messages users (most without the new features), 363 million Hotmail users, 303 million Yahoo Mail users, 175 million Twitter users and 171 million Gmail users all have some overlap, each using whatever service is most efficient in each particular use case.
The ability of language to perform these functions depends on the skill with which its users understand each other in any particular case.
